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AN OPTICAL RO C SāOR r0r 7EJPi"2 iC I, IML013PY
by
Peter Robert Harnett BSc., ARCS, MSc., DIC.
MARCH 1980
A Thesis submitted for the degree of
Doctor of Philosophy of the University of London
Physics Department
Imperial College
London SW7 2BZ
AN OPTICAL PROCESSOR FOR GEOPHYSICAL. IMAGERY
A review of the development of coherent optical
processing, with particular reference to applications in the
earth sciences, is provided. This forms a basis for defining
the extent and direction of the subsequent investigations.
The results of experimentation on a pilot optical
system are described, and utilised in choosing features to be
incorporated in the design of the main system. The construction
of the latter is explained in detail.
Several studies involving the application of the
processor to real problems are presented, These concern images
from satellite_, aerial and surface sensors. The techniques used'.
include band-pass filtering, directional filtering and the?
extraction of directional statistics.
ACIMOWLEDGEMENTS:
Many thanks to all who have helped me, but especially
- to Professor W.T. Welford, Dr. M.E.. Barnett, Dr. T.H.. Williams,
Mr. G. Talbett and many other colleagues of the
Optics Section, Imperial College;
- to Dr. J.W.. Norman and the students of the Photogeology Section,
Imperial College;_
to Dr. J. Townsend and Dr. C. Justice of the Geography
Department, Reading University;
- to suppliers of imagery acknowledged individually in
the body of this thesis:;;
to the Science Research Council and the Department of
Industry for financial support;
- and to my wife for moral support in the face of the most
ill aspects of Saturn.
CONTENTS:
VOLUME I - TEXT VOLUME II - FIGURES
CONTENTS OF VOLUME I
CONVENTION: PART 2'
CHAPTER P. Q
SECTION P.Q.R
1 INTRODUCTIONS
1.1 THEORY AND PRACTICE
1.1.1 Fourier Transform Theory
1.1.2 Some Physical Analogues
1.2 DEVELOPMENT AND APPLICATIONS
1.2.1 Development of Processors
1.2.Z.Apglications to Geophysics
1.3 THE CURRENT PROJECT
1.3.1 Main Objectives
1.3.2 Preliminary Objectives
Page
12
15
21
23
25
33,
40
49
52
56
62
64
66
2 THE PILOT BENCH Page
2.1 PRINCIPLES.
2.1.1 Mathematical Concepts
2.1.2 Physical Concepts
2.1.3 Optical Practicalities
2.2 DISPLAY
2.2.1 Experimentation
2.2.2. Recommendation
2.2.3 Implementation
2.3 VIDEO-PROCESSING
2.3.1 Problems
2.3.2 Techniques
2.'3,-..3 Roles:.
2.4 DIRECTIONAL SAMPLING
2.4.1 Design and Construction 68
2.4.2 Uniformity and Simulated Object Tests 77
2.4.3 Automation and Real Object Tests: 84
2.5 DIRECTIONAL FILTERING
2.4.1 'Inclusion' and 'Exclusion' Filtering 93
2.5.2 Tramples (Zero order passed:); 96
2.5.3 Examples: (Zero order blocked) 98
5
3 THE MAIN BENCH page
3.1 LAYOUT 100
3.2 COMPONENTS:
3.2.1 Illumination System 103
3.2.2 Transform. Lens System 109
3.3.3 Object/Filter/Image Stages 114
3.3.4 Display and Sampling System 118
3.3 SUPPLIERS 124
4 APPLICATIONS
4.1 BACKGROUND;
4.1.1 Fracture Trace Analysia 126
4.1.2 Terrain. Classification 134
4.2 DIRECTIONAL. STATISTICS.
4.2.1 Queensland Aerial Image 137
4.2.2 'FAMOUS:' Sonar Image 143
4.3 FEATURE. ENHANCEMENT
4.3.1 Botswana 'LANDSAT' Image- 145
4.3.2 Dartmoor 'LANDSAT' Image 147
4.4 CONCLUSIONS:
APPENDIX: Convolution
150
154
REFERENCES_ 157
1.1 THEORY AND PRACTICE=.
The roots of Coherent Optical Processing lie in the
mathematical concept of Fourier transform theory and in the
physical phenomenon of diffraction. This chapter serves to
introduce these themes and to demonstrate the connection
between them..
1.1.1 Fourier Transform Theory
Fourier transformation is an operation that links--
distributions in two domains, where the dimensions of one
domain are inversely proportional to the dimensions of the
other. This is shown, by the mathematical statement of the
one-dimensional Fourier transform from the distribution f(x)
in the xi-domain to the distribution F(u)) in the u-domain z
+00
La
-2niux c.x. () e Relation(1.1)1
since the exponent, involving the product ux, must be dimension-
less. The: inverse transform relation, which must be satisfied
simultaneously with Relation(1.1).1 in order for F(u). and f(x)
to constitute a Fourier pair is:.
{co fx = 150'f'2iCtU.K ~~ e CL.
Relation ( 1 .1 ) 2_ _co
A. significant aspect of these relations is that the
value of the dista bution- at any one point in one of the domains
depends on the values:of the distribution at all points in
the other domain, i.e.
-2Tri.ux r — 1 fc.x)e.
at) uvu,
Relation(1.1)3
+00 +2fl LU.x f(xt J Ftt-t)e reu.
x_x2 Relation (1.1)4
Thus: the 'information' represented by the value of F(u)
at a. single point u=u1 results from contributions of information
represented by the continuum of values3of f(x), (and vice-
versa for x=x2). Loosely speaking the information associated
with the value F(u1) can be considered to be in some sense a
'synopsis;' or 'general view' of a particular aspect, (the
"u1 aspect"), of the information associated with the whole=
distribution f(x). Similarly, the information associated with
the value ffx2) can be considered to be a particular 'synthesis',
(the "x2 synthesis")) of the information associated with the whole
distribution F(u):.
More specifically, the sinusoidal nature of the functions
e +Zttcux
and e-2Triax means that the 'synopses;' or 'syntheses*
take the form of spectral distributions; i.e.. for any parameter
x, there exists: another parameter u which is proportional to
and therefore related to the 'frequency' of x;, hence any
'reasonably well-behaved' functiont f(x) can be represented. by
a group of sine waves having a frequency distribution (spectrum)
F(u);, where the functions:f(x) and F(u) are linked by
Relations(i.1)1 and (1.1)2..
This is the essential 'philosophy'" of Fourier theory;: at
more detailed exposition of the concept, which also introduce
the major mathematical. properties of Fourier transform pairs,
is given in Section 2.1.1.
1.1.2 Some Physical Analogues.
The mathematical properties of Fourier transforms have
several important consequences, one of these being that the
transforms of periodic., functions consist of distributions of
discrete frequencies:, (rather than continuous ranges of
frequencies), i.e. periodic functions can be represented by a:
superposition of a series of harmonics of a simple sinusoid.
Fourier transforms have thus found useful application in areas
of science which involve waveforms or repetitive structures.
The one-dimensional theory has usually been applied to
situations where the dimension concerned is time, (the inverse
dimension being temporal frequency)., the most familiar examples
being the analysis of electrical waveforms: and mechanical
vibrations.
o 'reasonably well-behaved' implies that the function must bey certain common mathematical constraints on continuity, etc., •
the precise details of which can be found in the references; quoted.
The multi-dimensional theory, using spatial dimensions
(or spatial frequencies in the inverse domain) has become
prominent in materials science, where it is embodied in the
phenomena of electron and X-ray scattering or diffraction..
In this context, the regular structures are typically crystal
lattices, and 'Fourier space' is related-<to the 'reciprocal
space' of the crystallographer.
Optical diffraction resembles a 'scaled-up version' of
X-ray or electron diffraction since the wavelengths involve&
(and the diffracting structures normally under study): are=
several orders of magnitude larger. The scattering mechanisms
are not identical, but are sufficiently similar to have
prompted the construction of optical diffractometers (using
scaled-up crystal models) for use as diagnostic instruments.
The model could be adjusted to provide an optical diffraction
pattern comparable with the electron or X-ray diffraction pattern
produced:by a real crystalline substance of the (unknown)
structure to be determined, (LIPSON 1972.);
Fourier transforms have been implicitly usedi in optics:,
for a considerable time; following Abbe's explanation of
microscope resolution in terms of the filtering of optical
diffraction orders (from a periodic object), by the l:elms-aperture,
an extensive body of work known as the 'diffraction theory of
image formation' was developed (see BORN and WOLF 1970)'. Thus,
mathematically, the propagation of light through image-forming
systems came to involve Fourier transform relationships of
various degrees of complexity (depending on the degree- of
coherence of the light), being particularly simple for 'fully
coherent' light..
- 10 -
Contemporaneously with this, Fourier transforms were being
increasingly usad.in the field of electrical engineering to
describe the transmission of signals through circuits or networks:.
it was found that one of the most important ways of characterising
a network or network component was by its frequency response,
(which indicates the way in which it 'modifies' or 'filterW
sinusoidal signaissas a function of their frequency); hence
it became convenient to perform Fourier analyses on communications
signals (i.e. to break them down into sinusoidāl components.>
for treatment.-
Communications signals may be non-periodic and of arbitrary
shape (including pulses-and arbitrary modulations of
sinusoidal carrier waves)-, as opposed to pure sinusoidal waves.
Hence electrical engineers gained much experience in handling
continuous (as well. as discrete) frequency spectra.. Moveover,
since the signals; concerned could. represent 'information' of
some sort (e.g. spoken works, television pictures, instrument
readings), the concept of 'frequency filtering' of information
became familiar.
The growing realisation that optical imaging using coherent
light corresponded in form to the transmission of signals
through electrical systems}, led_to an 'en masse' transfer of
More precisely, the correspondence is between linear, isoplanatic optical systems and linear, time-invariant electrical systems.
terminology and technique from the field of electrical
engineering to that of optics. Just as electrical signals
could be conceived of as 'one-dimensional, temporal distributions.:
of information' so optical images could be represented as
'two-dimensional, spatial distributione5 of information . Hence=
spatial frequency spectra and spatial frequency filtering became
recognised as important entities in 'image processing systems)
(the optical counterpart of electrical. signal transmission
networks).
A detailed presentationof the physical process of
coherent optical imaging in terms of the mathematical concept
of Fourier transforms is given in Section 2.1.2:.
-- 12 -
1.2 DEVELOPMENT AND. APPLICATIONS;
1.2.1.Development of Processors
The concept of holography, originated by Gabor in 1948,
concerns the storage and retrieval. of (usually) optical
information via the spatial modulation of a spatial "carrier
wave" (i.e. an optical interference pattern):.. Besides serving
to attract increase&interest in the field of 'optical
information processing', it was later to be used for the construct-
ion of complicated spatial filters, in particular those known
as 'matched filters' (see below).
By .1950h,, the configuration of optical hardware
consitituting a classical coherent optical processor, as
shown in Fig..(2.117, was well established 'on paper*, but its.
appearance 'in the laboratory/ did not become common until the
invention of a reasonably powerful coherent light source
(i.e. the laser). Early papers thus tended to be theoretical,
dealing with such topics. as. deriving the general conditions_
on power spectra necessary for spatial filtering to enhancer
the signal-to-noise ratio of the optical information channel
(O'NEILL.1956) - (the coherent optical version of a.perennial
problem in electrical engineering)-. The major practical use
of optical processors at this time was as analogues: for X•-ray
diffraction or electron diffraction from (e.g..) crystals,
polymers and fibres (TAYLOR and LIPSON 1960,:
- 13 -
With the arrival of the laser, (arounth1964): coherent
optical processors began to operate at levels of intensity
appropriate to normal 'visual' images, (e.g. continuous tone
photographic transparencies):.- Their application to transparencies
of geophysical phenomena soon began to be investigated,
particularly by Pincus and Dobrin, Fontanel and Bauer, (see
Section 1.2.2)..
(VAN DER LUGT 1964) gave a theoretical_ exposition and
reported:practical demonstrations of 'matched optical
spatial filtering'. This is usually acheived by interfero-
metrically (holographiaally) recording the diffraction pattern
from an object transparency, to act as a spatial filter for a,
different object transparency;; the filtered image that results
consists of the convolution and cross-correlation between the
objects and is a measure of their similarity or 'matching'
(see. GOODMAN 1968-b/. Such operations. were seen to be of
potential value to problems in the field of character andIpattern .
recognition, (e.g. fingerprint matching/ or change detection,
(e.g. plotting cloud movement in meteorological satellite
photographs).
In addition to matched. filtering, a considerable amount
of coherent optical processing work at this time was concerned
with 'image restoration', i.e. using spatial filters to correct
images which had been degraded in some way at the time of
recording, (e.g.. by motion-blurring or misfocussing). The
progress made in this field, (particularly by contributors
such as Marechal, Preston, Cutrona, Leith and Upatnieks:), is
summarised in (TIPPETT et. al. 1960., (DE: VELIS and REYNOLDS: 1967);,
(GRASSELLI 19691 and (SHULMAN 1970):..
-14-
Another important application was found to be in the
generation of images from 'synthetic aperture radar' recordings,
(=RONA et.al. 1966).. This resulted from the similarity
between the mathematical descriptions of the propagation and
interference of the radar signals (which, in this type of radar,
form an essentially coherent recording system), and of the
light waves in a coherent optical processor employing lenses
of a special shape, (usually cylindrical and conical),,
(see GOODMAN 1968). S=ynthetic radar images have themselves
become very relevant to geophysical studies; (see? Chaper 4.1).
By 1970, coherent optical processing had become sufficiently
well-established.<to stimulate attention to technical details
and the formulation of specific designs;; e.g.. for lenses,
(BLANDFORD.1970), (VON BIEREN 1971), and liquid. gates, (to
suppressspurioussphase variations of the object transparency)`,
(HARBURN and RANNIKO. 1971);.. Large, 'purpose-built' processors
were developed: for use with geophysical image transparencies
(LENDARIS; and STANLEY 1970) , (PRESTON and DAVIS 1972):; the.
former being intended: specifically for satellite photographs (see: Section 1.2.2)..
The early 70's saw comprehensive reviews; of spatial
filtering techniques; (BIRCH 1972));; of the 'hardware' of coherent
optical processors (PRESTON JR.. 1972-a, etc.); and the emergence
of a debate on the relative merits of optical processors versus✓
digital computers with regard to the handling of textural
information, (DAVIS: and PRESTON 1972)x, (PRESTON JR. 1972)'.
It was recognised that although optical 'computers' excelled
in the ability to carry out certain parallel (associative)
operations on images at relatively high speed and low cost,
- 15 -
many pattern recognition and classification tasks also required
the adaptive programming qualities inherent in digital computing..
The conclusion was that coherent optical processors, would
prove to be of most value in such tasks if combined or 'hybridised:'
with digital systems, either as routine 'pre-processors' of
optical images (e.g. by providing diffraction-plane data as input
information to a digital programme), or as 'learning devices3'
to facilitate the selection of an optimal filtering operation
(for a specific task); which would subsequently be translated into
a digital form. Further work has tended to confirm this conclusion..
(Practical aspects of coherent optical processing equipment
are discussed in Section 2.1..5).
1.2.2_Applications to Geophysics
The main feature of coherent optical processing that ham
been found to be of importance to geophysical images is its
ability to quantify and classify texture.. A.detailed exposition
of this is given in Chapter (2.1), from which the following
synopsis is drawn.
Consider a two-dimensional image, together with its Fourier
transform (diffraction pattern) as shown in Fig«(1.2):1, where
x;y are the co-ordinates of space in the image and u,v are- the
corresponding co-ordinates of spatial frequency in the transform,
The points P in the transform plane, distant r from the origin
in direction 0/ 8+180° correspond to a sinusoidal 'grating'
pattern in the image plane, having a period*, and aligned along
e t qo° f Al-2:7e ; the amplitude of the grating being
proportional to the amplitude or 'strength of signal' at the
points P. This 'grating' can be considered to be a fundamental
16 -
component of texture, since diffraction theory showsethat
shape, texture, pattern or distribution of light in the
image can be built up by superposition of ;a: 041.1e ta'on 6f.
'gratings' such as these, with the appropriate periods, directions
and amplitudes. Thus, just as the diffraction pattern consists
of the superposition of allī.the points P, P', P" etc, so the
image consists:of the superposition of their corresponding
'gratings'.
If the image texture has strong directionality, this
will`be readily apparent in the angular distribution of the
transform, as shown by Fig.(1.2):2. Similarly, if the image
texture has a predominant granularity or scale, then this will,.
be manifested.in the radial distribution of the transform, Fig..(1.2).3.
Thus the relative directional strength of structures.: in the image
can be numerically assessed by measuring the light energy in
corresponding (90°-shifted) sectors of the diffraction pattern;
whilst the 'coarseness,' or 'fineness,' of the structures can be
similarly estimated_from measuring light energy in annular bands
of.spatial frequencies.
Methods such as these can form the basis. of a texture
classification technique: the measurements of light energy in
particular sectors, annuli or any other defined region of the
diffraction pattern (or possibly ratios and higher-order functions
of the measurements): can represent the values of a matrix or
multi-dimensional vector (i.e. a single entity, but made uip of
several components)•, that characterises the texture of the image.
Texture cLasses:can then be defined in terms of the properties;
of this matrix or vector (i.e., of the interrelationships between
its components). An example of this technique (GRAEMENOPOULOa
1975). is discussed later in this section.
-17—
Using the above terminology, spatial frequency filtering
of the Fourier plane can be consideredito be an operation that
separates or enhances textures or particular components of
textures,. For instance, Fig..(.1.2)-4 shows that directional
blocking of the diffraction pattern can be used to separate. out
features characterised. by a particular direction. (Similarly,
annular filters can be usedito enhance discrimination of image
regions having different degree•, of 'granularity' or 'scale'
of texture)).
Apt ācat .Qix „ of coherent optical processing to transparencies
of geophysical imagery was first demonstrated in the paper of
(BARBER:1949), in which the periodicities of sea-surface waves
were inferred from the diffraction patterns of verticalaEerial
photography.. The light source used was a. mercury lamp, so
photographic recording of the diffraction patterns took many
minutes; however, the advantages of this method over direct
visual. inspection of the photograph were made evident, particularly
for scenes-displaying a spread or range of periodicities.
Interest in these techniques was,revived by the advent of
the laser, with a particular emphasim on their application to
essentially 'binary' images, (e.g.. transparenciea; of maps-,
charts, etc..):, as exemplified: by (DOBBIN et.al. 1965) and
(P.INCUS.and DOBBIN 1966). The former paper demonstrated the
ability of directional spatial filtering to select particular
features or anomalies in seismographic: data traces (cf. Eig.(1.2):4).
The latter showedithat directional filtering could be used to
enhance the orientation of grain boundaries in photomicrographs
of rock samples and to isolate particular (directional) sets of
lineaments in fracture trace overlays, the value of inspecting
-18-
the diffraction patterns, of contour maps (etig. magnetic contours):,
in order to give a numerical assessment of the strength of
directional trends_:, was noted, and later work on the spatial
filtering of such maps has produce& significant results
(ARSENA.ULT et . al . 1974).
The techniques, were also applied to the analysis3of
lamination in rocks (PINCUS and ALI 1968);; and the use of
high-pass filtering on continuous tone images to enhance boundaries
or fine detail was shown in (DOBBIN 1968). (.PINCUZ 1969) described:
the plotting of contours of the diffraction pattern intensity
(;or of the density of a photographic recording of the pattern).,
as a -means=of measuring the distribution of grain sizes in rocks.
This application has been the subject of extensive study using
the fairly sophisticate&. optical bench of the Kansas. Geological
Survey, as reported in (PRESTON and DAVIS 1972).
In addition to these studiesainvolving 'micro' geophysical
features, coherent optical processing was re-applied to the
'macro' features displayed in aerial photographs. ('ONTANEL.et.al.
1967) used directional filtering to exclude dominant lineament
directions and therefore reveal sub-dominant trends, as a
pre-processing operation for photo-interpretation « CBAUER et.al..
1967) used the same operation to reveal a system of glacial
crevasses which (in the unprocessed photograph) had been obscurest
by surface relief caused by differential melting.
Analysis of sea-surface images was continued, (sTILWELL.1969Y,
being particularly stimulated by the growing availability of
satellite imagery (NOBLE,1970),.. The wide synoptic coverage
provided by these images has become of value in understanding
large-scale phenomena such as the behaviour of long-wavelength
swells; the interpretation of the diffraction pattern data haw
been treated in considerable detail by (YAS:XJRIRO SUGIMORL 1975).
f
- 19 -
The advent of the ERTS: (now LANDSAT).satellite programme
encouraged the building of processors with larger input formats
(i.e. greater than 35mm width), e.g.. the bench developed for the
General Motors Company, described by (LENDARIS:and STANLEY 1970). ;
this employed a scanning slit and photomultiplier arrangement to
measure the light energy in portions of the Fourier plane, and:
a similar system was used.by (NYBERG et.al. 1971). The latter
showed examples of its application in providing a numerical
description of the directionality in aevera iphotographs of
geological structures, including moraines, block-fields, fractures
and glacial striations.
An alternative method of measuring the light energy in
the diffraction pattern was provide&by photodetector arrays:.
(JENSEN 1973) mentioned a detector using wedge and ring shaped
array elements (now marketed: commercially),, in which the signals .
from the elements were read-in to a digital. computer in rapid
sequence. This method has been favoured for terrain-type.
(land-use): classification tasks, in which the computer uses..
diffraction-plane measurements to form a vector, whose values can make up 'spatial frequency signatures~' associated: with
particular types of terrain.. Classification can proceed via
the mathematical techniques:familiar to 'multi-spectral analysis',
simply substituting the spatial frequencies of the terrain
structure in place of the temporal frequencies of its reflected
radiation spectrum.
It has proved possible to develop promising terrain
classification algorithms-for tANDSAT imagery based on a mixture
of spectral (tonal) and spatial (textural) parameters; see.
(CORBETT 1973, GRAEMEN0P0ULO& 1975).
- 20 -
The above provides only a brief summary of the applications
of coherent optical processing to geophysics;; more comprehensive
and illustrative surveys are included in (McCŪLLAGH 1971) and
(McSEITH 1974).
- 21 -
1.3 THE CURRENT PROJECT
1.3.1 Main Objectives
The project on which this thesis is based was commenced in
1972 and its aim was the development of a coherent optical
system intended primarily for application to ERTS (LANDSAT)
imagery.. This requirement set the specifications for the
dimensions of the system, whilst great attention was paid to
the quality of the optics involved, in order to maintain the
high resolution and accurate density characteristic of the images..
Under finance from the Department of Industry, the Coherent
Optics Group at the Blackett Laboratory of Imperial College:
were able to make use of the talents and experience of
Professors W.T. Welford. and C.G.. Wynne as lens and system
designers, the manufacturing skills of Imperial Cbilege Optical
Systems for glassware and the high-precision engineering
abilities of the Applied Optics lens-mounting group for lens.
barrel design, assembly and testing. Project co-ordination was
in the charge of Dr. M.E.. Barnett.
At an early stage in the project, contact was made with
potential users of the images and information that the bench
was intended to supply.. Thus, guidance could be obtained in
developing the equipment and processing operations to produce
results in a form that would be of most practical use, (i.e.
there was a strong user-orientated factor in the development
and operation of the bench).
- 22:-
In particular, liaison was maintained with the photo-
geologists at Imperial College, under Dr. J.;./.. Norman, from
which it became clear that an azimuthal diffraction pattern
scanner of the type described by Nyberg'° should be considered
an essential part of the system.. This would provide a tool. for
the compilation of directional fracture-trace statistics in the
form of 'rose diagrams' which have been recognised as important
indicators of geological structure, e.g.. with regard to the
prediction of areas of mineralisation, (HUNTINGDON 1969),
(NORMAN and HUNTINGDON 1974)
,It was recognised that in addition to ERTS.transparencies,
the bench should be able to handle images at a variety of scales,
so that the results of carrying out diffraction pattern analysis
or filtering on a particular area of terrain, as recorded: by
different types of sensor (e.g. satellite versus aerial photography),
could be easily compared.. This requirement demanded a certain
amount of flexibility in the display system, particularly for
the Fourier plane, where it was seen to be important that the
apparatus should be capable of displaying the diffraction
pattern at a variety of scales, so that different ranges of
spatial frequency could be examined in detail. (It transpired:
that a closed circuit television system with video-processing
options played;. the major part in meeting these objectives..).
It was also decided that a holographic cross-correlation
matched filtering arrangement should be incorporated in the
bench so that change-detection studies. on time sequence images
could be pursued. It has been suggested that the distribution
-23—
of wind vectors --manifested by the change of cloud positions
in sequential scenes of meteorological satellite imagery, can
be rapidly determined by such a method..
Another objective that was envisaged in the long-term plan
was that the bench should be capable of adaptation to some
degree of automation.. This would be desirable for applications
requiring a routine operation to be repeated on a large number
of scenes (e.g. successive frames on a roll. film), or on a large
number of sub-scenes within a single frame. Thus, the design
of the equipment should make some provision for conversion to
automatic or semi-automatic operation, as options.. (The latter
was successfully demonstrated, at a fairly early stage, for the
generation of rose diagrams from azimuthal scanning of the
diffraction pattern, see Section 2.4.3).
1.3.2 Preliminary Objectives
Whilst the design of the transform lenses. was well established.
at the start of the project, (see: Section 3.2.2)., it was seen
that a considerable amount of experimentation was necessary in
order to specify details of the other components of the processing
bench.- Moreover, it was known that the high-precision manufacture
of the glassware and supporting barrels for the lenses would;
be a rather lengthy process..
Therefore it was decided to construct a temporary 'pilot'
bench, using standard laboratory components and optics of
moderate quality, for the purpose of developing and testing
components and techniques proposed for the 'main' bench. In this
context, particular priorities were the object plane/Fourier plane/
- 24 -
image plane display system and the Fourier plane (diffraction
pattern); scanner.
The pilot bench operated on a much smaller object format
than the main bench (a 35mm. diameter object plane, to accomodate
standard 35mm. x.24mm. film frames instead of the 70mm. x:70mm.
ERTS transparencies), but had a comparable Fourier plane size
and fairly good aberration correction.. The range of work
performed. on this bench is described in Part 2 of this thesis.
Construction of components for the main bench proceeded
in parallel with the pilot bench work, thus allowing a fairly
swift transition from pilot bench to main bench to be made on
completion of the main transform lenses:, (Part 3 of this thesis).
-- 25 —
2.1 PRINCIPLES.
The intention of this chapter is to demonstrate the principles
that are embodied: in the operation of an orthodox.coherent optical
processing bench. This is a subject that has been covered in great
detail by several publications (notably BRACEWELL (1965) and
GOODMAN (1968)). However it is felt necessary to include at this:
point a summary of those concepts and practical details that are
essential to the understanding of later chapters of this thesis...
The provision of a self-contained account of this nature is thus
principally intended to familiarise the subject of coherent optical
processing to its potential users from other'disciplines.
Section 2.1.1 introduces 'spatial frequency spacer and
'frequency filtering' as purely theoretical concepts, and deals
with the fundamental Fourier theorems in their one-dimensional
form, later extending the ideas into two dimensions,.. Section 2.1.2
explains how optical images and operations can be expressed in
two-dimensional 'oūrier-transform terms. Section 2..1.3 shows some
optical analogues of the theorems, and derives; practical results
for use in subsequent chapters..
Where statements are made or results presented without proof,
it is to be understood that an adequate treatment exists::either
in one of the above references, or in one of the other general
references.
2.1.1 Mathematical Concepts:
A_one-dimensional function f(x) and its Fourier transform
F(u) are related by the expressions: tco •
23-rcux FCu) = f 5<x) e. ~x
foo =+ao
IL) e 276-cix _oo
Fourier transformation
P.elation(2..1)1
Inverse Fourier transformation
Relation(2.,1)2
-26-
The symbolic shorthand for this relationship is:.f(x)ribF(u).
Alternatively, we can use the symbols T, Ti to represent
Fourier transform and inverse Fourier transform operators,
respectively, whence:.:
E(u):. = T { f (41
f(x) = T tF(.n).}
from which it is obvious that
T ACT f(41 = f(x).
also, it can be easily shown that:_
T ET f f(x)}J f(-x).
Relation(2.1)3
Relation(2.1)4
In rigorous Fourier transform theory, the functions.f(x), F(u);
must satisfy certain mathematical conditions, but these are
automatically fulfilled if the functions are physically
realisable.
Let us now suppose that the variable x:has the dimension of
length, i.e. that it represents the co-ordinate of one-dimensional
space.. Since the exponent 217C iux: used in Relations(2.1)1 and
(2.1)2 must be dimensionless, it follows that the variable u
must have the dimension of length' i.e.. that it must represent
the co-ordinate axis of one dimensional reciprocal space. It im
here worthwhile to consider the corresponding relationship that
applies to time-varying (rather than space-varying) phenomena.
-27-
For the temporal case, we can simply replace x.by t (time) and
u by f (frequency) . This allows us to analyses temporal signals
in terms of their frequency spectrum, a technique that playe&a
fundamental part in communications theory. By analogy with this,
the Fourier transform of a spatially-varying signal is known as
the spatial frequency spectrum which extends over spatial frequency
space+ or "Fourier space". Examples of some Fourier transform
pairs are shown in Fig.(2.1):1; note that the pure cosinusoidal
waveform, being composed:of only a single frequency, is represented
at only a single value of the abscissa=in spatial frequency space.
Fourier transforms exhibit a number of useful properties_•
which can be presented mathematically as follows, given that
f(x) &-u)
g(X) G(u)
Addition fl(x) g(x 7 (n) +- G(ug Relation(2.1)5
Similarity f aF(au) Relation(2.1)6
i.e. 'spreading out' a function in x (or multiplying its period)
by a factor a, 'closes up' its transform in u (or divides its
frequency). by a factor a.
-28-
Shift f(x-a)raF(u) • e -27ti u a Relation(2.1)7
i.e. shifting a function along the x axis by an amount a
multiplies its transform by a phase factor proportional to a,
but does not change the amplitude of the transform.
Qonvolutiont 4:Rx) 411 g(xx# (u) . G(ug Relation(2.1)8
i.e. the transform of a convolution of two functions is the
product of their individual transforms. (Convolution is a _
difficult operation to grasp, but it plays an important part in
Fourier theory; for those unfamiliar with the concept, I have
provided_ an explanation in the Appendix:to this thesis, thus.
avoiding a break in the natural sequence of this section). Note
that these theorems are all reversible.
A_particularly interesting result occurs when a function
f(x) is convolved with a 47—function g(x-a). The examples of
Fig.(2.1)1 show that::
O(x)~
applying the shift theorem, we sew that s
S (x-a) T e-27tiva
• The symbol @ indicates the convolution operation.
- 29 -
hence, by the convolution theorem:
i(x). @ S(m-a) F(u). e -27tiva
but the shift theorem states that t
f(x-a) P(u) e 2 g iva
hence:: f(x) @ g(x-a) - f(x..a). Relation(2.1)9
A-consequence of this is that a. string of delta functions, when
convolved with a function f(x) yields a string of 'replicas _'
of that function; i.e.
- 30 -
This 'replication' property has important consequences in the
analysis of repetitive structures of patterns. Fig.(2.1)2
demonstrates the derivation of the spatial frequency spectrum
of a square wave by representing the wave as a convolution of
a rect function with a 'Dirac comb' function. This type of
analysis can be applied to both ordered and disordered distributions;
in either case, the shape of the individual element in real space:
(i.e. the function that is replicated to form the distribution):
controls the shape of the overall envelope in spatial frequency
space; (or vice versa).
It is possible to apply Fourier transform theory to
functions in any number of dimensions;; however, for optical
diffraction theory, two-dimensional transforms are the
appropriate theoretical concept. The two-dimensional forms of
relations (2.1)1 and (2.1)2, are
—2T(i (ux + vy): f(x,y) e dx dy Relation(2.1)10
f (x,y) *27r'i (ux: * vy)
F(u,v) e du dv Relation(2.:1)11
31 -
All_the properties demonstrated for the one-dimensional theory
are valid, correspondingly, for the two-dimensional forms. Some
examples of two-dimensional Fourier transform pairs are shown in
Figs.(2.1)3,k.
The technique known as 'spatial frequency filtering' is a
method of changing a function f(x:,y), into a different function
g(x,y), by performing some operation S upon the Fourier transform
F(u,v)_ (where f(x,y) Jr& F(u,v) )
i.e.. if T=_ 2-dimensional Fourier transform: operator
I T= 2-dimensional inverse Fourier transform operator
S:ei2-dimensional frequency filtering operator
let F(u,v) = T f f(x,y)} , G(u,v). T f g(x,y)}
. also G(u,v)- = S>{ F(u,v)}
then G(u,v). =. ST f f(x,y)}
T(g(x,y)) = ST{ f(x,y)}
••• TI T{
g(x,y)} = Ti ST [f(x,y)}
-32—
But T T tg(x,y) = g(x,y);`gwo-dimensional version of
Relation(2.1)427
g(x,y) = TST ff(x,y)} Relation(2..1)-12
The mathematical formulation of 'spatial frequency filtering'
thus consists of three operations:-
a).' Fourier transformation of the function f(x,yl.
b) Operating upon the spatial frequency spectrum F(u,v) to
convert this to a modified spectrum G(u,v).
c) Inverse Fourier transformation of G(u,v) to form the new
function g(x,y).
The operator S- is commonly known as the spatial frequency filter..
The mathematical significance of spatial filtering can
by appreciated by examination of the structure of Relations..(2..1)10
and (2.1)11. The integral definitions imply that the value
of F(u,v) at any single point (ui, vi) of 'Fourier space'. depends
upon the values of f(x,y) over the whole continuous set of points
(x,y) of 'real space'. Hence a 'Fourier space' operation performed
ata single point (u1, vi)- of F(u,v) corresponds to a continuous:
set of 'real space' operations on all. points (x,y) of f(x,yY..
i.e.• Serial or 'point-sequential' operations in Fourier space
correspond to parallel or 'point-associative' operations, in
reāl space.
i oi°āeiit beami, a°-'the omTēx z~ir"+eiitz~~ on'.;o
x~c-iciēnt;oH,;d1l ~i`ats _.iaf:tYrē:' sctcēW :ēfl t3ē•ivēYi
- 33$ -
2.1.2 Physical Concepts
. The relationship between the mathematical entity of Fourier
transformation and the physical phenomenon of optical diffraction
is demonstrated in the following conceptual experiment, which
utilises a 'one-dimensional' optical model.
Consider a 'one-dimensional screen' of infinite extent
lying along the x axis, Fig..(2.1)5, (in this treatment it can be
visualised as a thin section of a two-dimensional screen lying
in the x-y plane). The screen has a complex amplitude transmittance
q(x) for light of wavelength X and is illuminated by a
collimated coherent beam of light of this wavelength, travelling
in the z direction. There is no spatial variation across the
A = Āe> IAA) t where W
c = velocity of light,
t = time
The light is diffracted by the screen, which can be considered
to give rise to a continuum of infinitesimal 'secondary sources
of 'light (as in Huyggnst rriric•i ~ e)~. Defin .ntr %the, complex-14
transmit;tpd .?4?htr~sk.gi al~ Z °a .d•irect4.o~~; ;n-Q] ~n,'P 3 a,t` i•.%•:
angle + to the z axis as A:D (4))', Fig. (2.1)5 shows that the
contribution dA D (40. from an infinitesimal element dx_
- q(1147 t) by definition
I cidet Arnr).itude
-34-
at distance =from the origin is given by:.
1,(x) e = sin
Relation(2.1)13
Integrating over the whole screen,
41)
♦0 lab
( e 2rri. )x
= A. e: dxti . —co q
where c,(x and Q(.51 ) constitute a Fourier pair.
Thus if we consider only the spatial:_ variations of the complex:
amplitude, and normalise the incident strength to unity, we find.
- Qt A' G 4) maps the Fourier transform of $(x);. i.e.. that the
diffracted complex amplitude as a function of angle, maoa the
Fourier transform of the complex amplitude transmission of the
screen. If the diffracted light is collected by a lens of focal
-35-
length f, as shown in Fig..(2.1)•6, then we can consider a parallel
beam of light, travel Ting at an angle 4 to the z axis, to be
focussed down to a single point in the back aocal.. plane of the
lens, distant x' from the z axis, where x( = f tan(+). is If +.~l:small, .then_.siin+ tan + , so that q(s
h~ ), becomee q(7 u-) f ) hence :.
q(x) # Q(- f )
Relation (2..1)14
The variable P defines a spatial frequency;: Relation(2.1)14 implies (in one-dimensional terms) that the complex_ amplitude
distribution A(x')` in the back focal plane of the lens maps_ the
Fourier transform or spatial frequency spectrum of the complex
amplitude distribution 'q(x). generated by the screen, (with a
scaling factor Xf).
The method demonstrated in deriving this result is the
basis- for a more realistic treatment using a two-dimensional
object plane and back focal plane, such as is provided by
(SHULMAN 1970-a): which parallels the diffraction theory of light
propagation as expounded in (BORN and WOLF 1970). The more
rigorous mathematics employed shows that for an aberration-free
lens of infinite aperture, there is a two-dimensional Fourier
transform relationship between the complex amplitude distributions
in its front and back focal planes, i.e.. that:
-36--
F
Q (• ' hf)~
+00
J q(x,y) e-z ic i -3►'f a e2-271i Y dx dy _ao
Relation(2.1)15
where q(x,y) represents the complex amplitude in the front focal
(x-y) plane,
ft . n: If IV n' back focal!.
(x/-51.1 ) plane,
with scaling factor Xf, as before.
Note that for an exact Fourier transform of a diffracting. object
transparency to be obtained in the back focal plane of the lens,
the position of the transparency must be restricted: to the front
focal plane; this condition dictates the 'classical' arrangement
of a Fourier analysis bench, shown in Fig..(2.117.• The first
lens forms a map of the Fourier transform of the object
(in complex amplitude) in its back focal plane, which is loosely
termed-the 'diffraction plane', 'the transform plane', 'spatial
frequency plane' or 'Fourier plane', (the latter being the most
commonly used description) of the complete system. A similar
-37-
transformation occurs through the second half of the system,
so that the complex-:amplitude distribution in the back focal
plane of the second lens consists of the transform of the transform
of the object distribution; the two-dimensional version of
Relatiōn(2.1)4, viz:-
T T { f (g'y): f(-x; -y)
shows that thissdistribution is simply the original object
distribution inverted along both axes, i.e. an inverted image
of the object.. By using a second lens of the same focal length
as the first, the scale of the image plane is the same as that
of the object plane;: (if lenses of different focal lengths are
used, there is magnification or demagnification of the image
relative to the object)'.. To conform with the mathematical
notation of Section 2.1.1, it is common practice to denote the
spatial frequency co-ordinates as (u,v), where these are related
to the actual spatial, co-ordinates(x', y), in the Fourier plane-
b7 k'' ==-Aft'
— 38 —
thus,
too
Q(u,v) = SS q(z,y) e -27r i(ux +- vy -voJ
dx dy Relation(2.1)16
X f v :.
The physical significance of 'spatial frequencies' as
descriptors of an object or image structure can be comprehended.
by reference to Figs.(2.1)8,9.. Fig.(2.1)8 demonstrates
visually how the square wave that was synthesised by a convolution
in. Fig..(2.1)2 can be analysed as a sum of a series of cosine
waves:.. Each pair of S -functions in its frequency spectrum
transform to a cosine harmonic, the amplitude of which is
governed by the sine function envelope;; the t1 (fundamental)
harmonic has the same periodicity as the square wave, whilst
the addition of the higher harmonics to it contributes to the
'squaring-up' of the edges. In this case, the function is
composed of discrete harmonics, but in general, an arbitrary
function would be composed of a continuous spectrum of these
simple cosine waves; the Fourier transform thus indicates. the
'strength' or amplitude of each of the cosinusoide.l frequency
components present in the analysis.
The nature of optical propagation makes it desirable to
represent any two=d :merisioh l." im ē ās' IDeiri ''compōsc z spectrum
of . cosinusoidal -complex amplitude 'grātin s' . From
-39--
i' 7 tu1.t :rn:; . each one of these 'gratings' produces a pair of
complex amplitude 6-functions in the Fourier plane (see
Fig.(2.1)9). The S -functions-lie along a direction in space
perpendicular to the 'grating-line' direction; their distance
of separation along this direction is proportional to the
spatial frequency of the 'grating', and their complex amplitude
strength (i.e. 'height') is proportional to the depth of modulation
or amplitude of the 'grating'. By applying the addition
theorem (Relation(2.1)5), we see that just as the image consists
of a continuous spectrum (in spatial frequency and direction)
of 'grating', so the Fourier transform of the image consiata
of a continuous distribution of the corresponding 1-function
pairs. (Note that this pairing implies 180°-rotational symmetry
in the Fourier - plane), ! This das:rr~:;but'~Gn ;z .~.thu rF .a:t,Od to:: the ''
statistical distribution Of orientations spatial frequencies
present in the image. For instance, if the Fourier plane exhibits
strong complex amplitude along a particular radial direction,
then this is an indication of a prevalence (in contrast, length
or numerousness) of features running in the perpendicular
direction in the image. Conversely, a strong annular zone of
complex:amplitude in the Fourier plane corresponds to a predominance
of a particular 'coarseness' or 'fineness'' of structure in the.
image. Hence, by making suitable measurements on the light
distribution in the Fourier plane of the system, we can gain in-
formation about the directional and textural properties of the
object/image.
40
By physically masking the Fourier plane in some way
(e.g. by opaque or partially-transmitting screens, phase-
changing plates, etc.) the techniques of optical spatial frequency
filtering can be realised.. As an example of this, if the object
transparency contains structures having a particular orientation,
then these can be eliminated from the 1:1 image by placing opaque
wedges aligned radially along the perpendicular direction in
the Fourier plane. Similarly, the textural content of an image
can be modified by placing discs, holes or annuli in the Fourier
plane, (concentric to the optical axis of the system).
A•significant fact, shown in Fig.(2.•1)7 is that diffracted:
light arising from structures of a given orientation and spatial_
frequency is collected from all. points of the object and focussuedi
to .h 14..anle irr t . FbVvi-or
Cola-Una t on of the. tyro ;factors :
a) The nature of coherent optical diffraction;
b) The focussing property of lenses;.
which makes it possible to apply controlled parallel-processing
operations to optical images.
2.1.3 Optical Practicalities.
The previous section demonstrates that image formation in
a coherent optical diffraction bench is a physical analogue of
Fourier-transform processes; the most significant asaumptionss
made are that:
-41 -
i) The object/image are of infinite extent;
ii) The lenses are of infinite extent (aperture).
and are aberration-free-.
This section will-outline the effects and limitations introducedi
by the use of a practically realisable system.
As a useful_ starting point, it must be appreciated that
the optical Fourier transform relationships of 2.1.2 apply to
distributions of complex amplitude and not intensity. Although
it is possible to 'record complex amplitude' by the use of
holographic techniques, one is most frequently concerned with
observing, recording or measuring the intensity distributions in
the various planes of the system.. Using the notation of
Fig..(2.1)7 we find. that :-
intensity distribution in object plane = i(x,y) = q(x,y), q*(x,y)
" Fourier . '!; = I(u,v) = Q(u,v) 41* (11,v)
" image nY Ei(-x,-y). = q(-x,-y). q*(-w,+y)
where * indicates complex conjugation.
The inversion relationship between object and image still holds,
but since q(x,y):* Q(u,v), it is apparent that there is no simple
direct relationship between i(x,y), and I(u,v). However, since
the overall 'shape' or 'form' of i(x,y) and I(u,v) corresponds
with that of the real parts of q(x,y) andQ(u,v) respectively
(i.e.. i(x,y) =- 1q(x,y), 2 , I(u,v) = 1 Q(u,v) 2 f ), then one finds .
-42-
that for many Fourier-analysis-based tasks, the confinement of
measurements to intensities: is not a serious- restriction; indeed,
the phase information lost is often irrelevant, making it positively
advantageous to obtain intensity measurements directly.
The distribution I(u,v) =:IQ(u,v)1 2 is often termedithe
power spectrum or Wiener spectrum.. It is also the far-field:
(Fraunhofer) diffraction pattern of the object, (although this
latter term is sometimes used ambiguously with respect to complex:
amplitude or intensity)..
We now consider the effects of substituting real conditions^
in place of the ideal ones assumed in (i) and (ii). above..
Fig.(2.1)10 shows✓ a situation in which the object is now of
finite size, although the lenses remain infinite and unaberrated
as before. A-single parallel diffracted beam of light from
the object (corresponding to a single spatial frequency in its
structure).: is focussed to a 'single point' in the Fourier plane,
and then reconverted to a parallel beam which forms a component
of the image.. Since the lenses: are: of infinite aperture, they
willi accept diffracted beams even when the angle of diffraction
approaches 90° (if we neglect such phenomena as reflection of
light from the lens surfaces, and the breakdown of the simple
'wall angle' diffraction formula); hence the diffraction pattern
is of infinite extent although the object is finite.
The Fourier transform relationship expressed in Relation(2.1)16
requires that the integration (of diffracted light contributions)
be taken over infinite limits in object space. In order to do
this, we can consider the object plane distribution to be
- 43 -
truncated by multiplication with a rect function (in one
dimension) or a pill. function (in two dimensions), having a
width or diameter equivalent to the actual width or diameter a
of the object. By reference to the convolution theorem
(Relation(2.1)8): and to Fig.(2.1)3, it is seen that the Fourier
transform of the object plane distribution is convolved with 4
sine function (in one dimension) or Airy function (in two dimen-
sions). Thus the replacement of an infinite object by a finite
object of diameter a (i.e.. limited by the 'truncation' function,
pill- (ā , ā)) I, results in the replacement of infinitesimal
points in the Fourier plane by finite:spots of light (i.e4 definedi
by the 'point-spread function', Airy (au,av))..
To obtain the image plane distribution by transformation
from the Fourier plane, it is demanded mathematically that wee
should integrate over infinite limits in the latter;,. since we have
shown that the diffraction pattern is of infinite extent (i.e.
not truncated) then the image must be a 'perfect' (i.e..
infinitely weil]_-resolved) replica of the object.. Thus 'infinite-
simal' points in the object would be rendered as 'infinitesimal'
points in the image if the lens apertures (and hence the
Fourier plane) were: infinite.
Now consider the situation of Figs.(2.1)11,12,13, where
both the object and the lenses are of finite size (but the
latter are still. required to be aberration frees)`. For angles
of diffraction up to 44 , (i.e.. spatial frequencies up to s1),
the situation in the Fourier plane is identical to the previous
'infinite lens' case, i.e. the Fourier transform relationship
is valid.. However, for angles such as c2 (where 4).0).(41* i3 ) 9
-44-
partial vignetting effects can occur, whereby contributions from
certain regions of the object may be lost from the system, leading
to a breakdown in the transform relations between object and
'Fourier' plane (and hence between 'Fourier' and image plane).
For angles of diffraction greater than + , total vignetting
takes place.
In order to obviate these vignetting effects, it is
necessary to provide a stop in the Fourier plane, as shown in
Fig..(2.1)14, which gives a sharp upper limit snot (angle of
diffraction 4 maxl to spatial frequencies passed-by the lenses
from/to all.parts of the object/image.. Thus there is effectively
a truncation function in the Fourier plane which validates the
transform relationships between object/Fourier/image planes:: in
a 'finite lens' system.. There is now finite resolution in the
image plane, since the truncation function pill.(2su ) 2sv )
max: max transforms to a point-spread function Airy (2s
max. x-, 2s mmay):..
Alternatively, (and more appropriately), we can express. the image
resolution limit by stating that Et defines the highest spatial MOt
frequency consinusoidāl complex amplitude 'grating' that can be
passed by the system (i.e. treating the image as an additive
assembly of gratings:rather than as a convolutive assembly of
point-spread functions). If::
a = Physical diameter of the object field..
b= ft I t " Fourier t r
= - Maximum spatial frequency passed by the system max
4 mare = Maximum angle of diffraction
max = Maximum semi-angle of ray cones forming points in the
Fourier plane
these parameters by:.
b 2Xfs max
a *-b
b 2f
e max 74 2f
Relation(2.1)17
Relation(2..1)18
Relation (2..1).19
Relation(2.1)20
--45 -
p = Aperture of the transform lens;
f = Focal length of the transform lens
A = Wavelength of the light usedi
Then in the situation exemplified by Fig.(2.1)14, we can relate
Relations (2.1)17-20 and Fig..(2.1)14 effectively define
the fields, ray angles and conjugates over which the lenses
must be 'aberration corrected' in order that the Fourier
transform relations be valid.. The fact that the two sets of
conjugates are symmetrical flee- Fig..(2.1)157 encourages a
symmetrical design for each transform lens, particularly in
the special case of equal diameter object and Fourier fieldst
(i.e. when a=b, D=2a =2b). This point is covered more fully in
discussion of the main bench design:, Section 3.2.2
Two other factors (also covered in greater detail later)
which are relevant to the transition from 'theoretical' to
'practical.' systems are:-
This case has been used in Figs.' 2.1)14,15
-46-
(fir_); reflection properties of the lens:surfaces
(iv) scattering tt it tt tt tt
Real glass lenses reflect some proportion of an incident
beam of light, which may thus be lost from the system; additionally,
there may be multiple reflections (particularly in multi-element
lens designs) which, given the coherent nature of the light,
can lead to optical interference effects in the system.. In
order to prevent this, it is desirable to put an anti-reflection
coating on the lens surfaces (i.e. to 'bloom' the lenses).. The
fact that Fourier transform lenses are normally designed for
use at only one wavelength makes it possible, to attain very good
reflection suppression from only moderately sophisticated
coatings.
The use of coherent light also leads to problems if there
is scattering from the lens surfaces or from bubbles, etc..
in the glass itself Ideally one should check the glass blanks
for bubbles before generating the lens surfaces, and careful
inspection of the polished surfaces should be made before
anti-reflection coatings are applied.. Features such as striae
or scratches can cause spurious linear features in the diffraction
pattern of an object, whilst 'pitting' may lead: to a more
random scattering ('speckle'), adding to the background noise
level in both the diffraction and image planes of the system.
Once coated, it is very important to protect the lenses from
dust, etc. (as far as possible) in order to keep the noise level
low.-
-47-
The beam that is used to illuminate the object should also
be reasonably 'clean'. The illumination system commonly usedi
gee Fig..(2.1)1g acheives this by focussing the 'raw' laser
beam onto a small pinhole; this acts as a 'low-pass' spatial
filter, removing high spatial frequency noise from the beam.
It is evident that the collimator should have a standard of
aberration correction (for the single conjugate set: front
focal plane-.Ó), surface finish, etc., similar to that of the
transform lenses.
Fig..(2.i)17 shows the arrangement of the principal elements
in a 'classical' coherent spatial filtering bench, having an
overall"_ magnification (image-object) of -1, The lenses are
shown as simple singlets;, but in reality would be multi-element
units (in order to attain the necessary degree of aberration
correction). Many variations on this basic layout are possible,
using different magnifications, or enabling particular types of
observation, measurement and recording of the Fourier and image
plane light distributions to be made.
To conclude this section, some practical results from
a transform bench are presentedI in Fig.(2.1).18, for comparison.
with the theoretical examples of Figs(2.1)3,4.. Note that the
'theoretical'kunctions are represented by the 'practical' point-
spread.functione3 of a finite-aperture system.
Figa.(2.1)19,20 show examples of directional and annular
filtering respectively.. In Fig..(2.1)19t, the vertical grating
t In this case convolution between the individual grating spectra has made it necessary to block all_ parts of the Fourier plane except that corresponding to the inclined grating alone..
-48..
has been eliminated by blocking the horizontal direction in the
Fourier plane (along which its spatial frequency spectrum
extends). In Fig..(2.1)•20, a low-pass-filter has been applied:
to block out all_spatial frequencies equal to or greater than
the 'fundamental' (.1st. harmonic) of the fine grating, which
is thus eliminated completely. The lower harmonics of the
coarse grating are passed by the filter, so its basic
structure is retained; however, there is obvious degradation
of the grating since the higher harmonics have been blocked
out..
-49-
2.2 DISPLAY
2.2.1 Experimentation
a), The requirement of a manageably large Fourier plane
with reasonable aberration correction but only 35mm input
format led to a choice (for the pilot bench) of a long focal:
length doublet telescope objective as the first Fourier
transform lens.. If used in the conventional arrangement, (object
in front focal plane), this would have led to a very long
overall:. system;. hence, the object was placed well_ inside: the
focal length of the transform lens. This change of conjugate
has two additional effects:-
i) There: is a departure from the strict obedience to the
exact Fourier transform of Relation(2.1)16; it can be shown
(SHULMAN 1970-a) that a quadratically varying phase error
is introduced, in the expression for the Fourier plane complex:
amplitude distribution, but does_not affect the intensity
distribution (power spectrum); since the pilot bench was not
intended for use in a holographic filtering mode (unlike the
main bench)., this factor was of no practical concern here..
ii.) One must expect some change in the image aberration
correction of the lens (this is not invariant of conjugate).;;
however since the light distribution in the major plane of
interest .(the Fourier plane) can be considered to result from
-50-
the focussing of parallel. diffracted beams from the object,
one should expect good correction in this plane from a lens
of this (telescopic) type.
The actual specification was:- focal length f = 850mm.
bens aperture D:= 55mm.., object distance u - 100mm. By
calculation using a modification of the results of Section
2.1.3 one finds that this gives a Fourier plane diameter of 42mm.
at a spatial frequency of 50c/mm. over an object plane diameter
of 50mm.. The object illumination optics consisted of a
standard microscope objective beam exp4.uder (focal length 8mm.)
and pinhole filter, with a doublet collimating lens (focal
length 250mm.)• giving a beam diameter of 35mm..
b),, In addition to the above conditions, it was decidedlto
plan for an overall: system magnification (final image planer
object plane) of about *2_, in order to obtain a final image
of a size permitting rapid visual inspection. Bearing in mind
the long focal length of the first transform lens, this require-
ment produced a very long overall system, and it was found
necessary to fold the optical path at some point; this fact
was turned to advantage as explained in paragraph (c). The
magnified final image was obtained in two stages>: a large
aperture triplet lens (focal length 200mm.) was used as the
second transform lens, the real image produced by this being
enlarged and re-imaged by a doublet relay lens (focal length
100mm.).
- 51
c): Preliminary experimentation ha& suggested the desirability
of providing some form of simultaneous display for at least
one Fourier-pair of planes in the system; it was hence decided
to make a double fold in the system, allowing simultaneous
side-by-side viewing of the Fourier plane (obtained via a
beam-splitter) and the final image plane, on a ground-glass_
observation screen, (an arrangement which also helped to
compact the system). A. scale diagram of this configuration
is shown in Fig(2.2)1. As shown in the figure, the addition
of a second beam splitter and a microscope objective allowed
projection of a magnified image. of the central region of the
Fourier plane onto the same viewing screen.. The three display
functions of the overall_system are illustrated in Figs(.2.2). 2-4.
d). As several of the lens surfaces in this system were of
only moderate quality, and possessed no antireflection
coatings, the resultant images suffered significant degradation
by speckle and double-reflection interference rings; however,
some simple filtering experiments were performed, such as:-
low-pass filtering (using an iris diaphragm),
high-pass. filtering (using a circular spot of opaque
silver paint on a glass slide),
directional filtering (using a narrow slit).
- 52 -
The test objects includeditransparencies.of simple
binary geometrical figures (regular and random arrays of
circles, lines etc. of various sizes and spacings), and
copies of actual ERTS scenes, reduced to a 25mm x 25mm format.
2.2.2 Recommendation
The quality of the filtered images obtained was considered
too: poor for serious investigation at this stage, but these
experimemis did. confirm that simultaneous display of the
Fourier transform and final image planes, at fixed magnification
should be regarded: as an essential requirement of the final
system, It was further reckoned that this should constitute
a minimal display facility, it being deemed-highly desirable
to include, in addition, some provision for viewing the
original object plane simultaneously with the Fourier and final
image planes, and also some means of displaying subsections of
all these planes at a variable magnification, the magnification
control for the Fourier plane to be independent of that for the
object/image planes. Justification for this development
rests on the following considerations:
a) Discussions with geologists had already stressedithe
importance of the ability to examine subsections of a
geophysical scene, in order to compare and relate. - analyses
of these' subsections to an analysis of the whole scene.- This
is particularly important for ERTS. pictures, where a singles
frame covers an area of a size likely to encompass several
- 53 -
major variations in terrain type and structure. Magnification
of such a subsection in real time allows easier recognition
of the features under investigation, and hence permits a
more rapid matching of a particular geological feature to
its corresponding power spectrum, as viewed in the Fourier-.
transform plane.. This facility is central to the use of the
optical bench in a 'training' mode for a terrain classification
scheme based (at least partly) on Fourier plane information,
(envisaged as a possible task for the,main bench)..
b) Tba pilot bench studies showed that the 35mm format
copies.. of 70mm original ERTS:transparencies contained very little
information 'strength' (interpreted as relative intensity
in the power spectrum) at spatial frequencies higher than about
20c/mm, and appeared., to display significant azimuthal
variations in the power spectrum only at spatial frequencies
of 5c/mm or less; similar figures were found to be typical of
other sorts of remote sensing imagery at this format;
(seeūFig.(2.3)6).. At this range of spatial frequencies, it
is reasonable to expect only a minor reduction in depth of
modulation during a 70mm to 35mm format photographic reduction,
thus suggesting (for ERTS: imagery, at least) that for a 70mm
format input, one should not expect to find major contributions
in intensity to the diffraction pattern at spatial frequencies
in excess'of 10c/mm, and that significant directional
information might be confined to spatial frequencies of
2.5c/mm or less. In studies using 70mm format ERTS imagery
- 54—
therefore, one should find it necessary to investigate in
detail this central region of the diffraction pattern,
(corresponding to a patch of approximately 6mm diameter in
the physical Fourier plane of the main bench);; hence the
need: for a magnification system for the Fourier plane display..
The emphasis on this region of the power spectrum for
70mm ERTS.imagery was however complemented by the need to
ensure an adequate Fourier plane display for non-ERTS1 object
inputs, possibly outside the field of remote sensing, (e.g..thin
rock section microstructures), in which the information
content was liable to extend to higher spatial frequencies_.
Thus it was found that in order to retain resolution of
detail in the Fourier plane, while coping with power spectra
from a variety of inputs, it would be highly desirable to
build-in a variable Fourier plane magnification system, in
addition to the object/image plane magnification system
mentioned previously.
c) The crude filtering exercises perfomed on the pilot system,
Some examples of which appear in Figs.(2.5)2,3,4,7, were
sufficient to give a suggestion of the types of operation
that might be applied to geophysical images on the main bench.
It became apparent from these exercises that the usefulness of
filtered imagery in enhancing or suppressing pictorial features
should be ascertained by comparison with the unfiltered scene.
Simultaneous display of the unfiltered and filtered: images allows
one to make a swifter general assessment of the degree of success:
-55-
of a filtering operation in extracting a given category of
feature information.. This holds good whether the filtering
operation is such as to cause only subtle modifications to the
image (in which case one can estimate its effects by reference
to the appearance of selected 'test' features belonging to the
category under investigation), or whether more drastic changes
are; implemented; compare the sets of Fig..(.2.5)2 and Fig..(2.5)4.
(1)' If simultaneous display of the Fourier plane in addition
to the unfiltered'. and filtered images is realised, then one can
monitor the changes imposed on the image by the filter, with
'real-time' reference to the size, shape, location and orientation
of the filter itself. Hence one has the basis of a rapid feed-
back system for control and optimisation of Fourier plane:
operations, with a human operator acting as an evaluative link
between the filtering operation and its result.. Lee block
diagram representation Fig.(2.47.
The significance of such a system as shown in Fig.(2.2)5
is its emphasis on the importance of the processor as an
interactive learning tool4 however it should be noted that
this does not reduce its capabilities as an automatic batch-
processing facility. In Fig.(2.2)5, the substitution of
an electronic control unit (incorporating a pre-programmed,
sequence of instructions for control over optical processing
operations and input/output data), for the human 'evaluation
unit', would allow conversion from one aspect to the other..
- 56 -
Indeed it was envisaged at this stage in the project, that many
image processing problems might best be tackled by initally
using the optical bench in its interactive learning capacity,
in order to determine a suitable sequence or group of operations
which would then be utilised in an automatic batch-processing
routine.
2.2..3 Implementation
Experience with the pilot bench had shown that although
the aforementioned displays might be obtained by the use of lenses,
beamsglitters, etc. alone, this was a somewhat clumsy and
inflexible procedure. It was decided. to carry out some trials
using a closed.circuit television system as a~ display channel,
with a view to building this into the main bench design, if
found suitable for the task. For these display tests, copies
of 70mm x:70mm ERTS. imagery was used (i.e. 55mm x 55mm picture
size), and the folded, pilot bench system was modified to give
1:1 magnification between object and final image planes.
The CCTV system chosen comprised a high resolution
separate-mesh vidicon fitted to a solid-state monochrome
television camera, and 17" (43cm) monitor of industrial quality.
The vidicon spectrall.response characteristic:under tungsten
illumination was designed to match the human visual response
curve, peaking at about 550nm; as a result its true characteristic
(independent of source), peaked at 4?5nm, conveniently close
to the 488nm wavelength of the laser.- Resolution of the complete
system was quoted at about 300 x 300 picture points over the
- 57 -
displayed field.. By racking the vidicon tube, (a control
provided on this type of camera)., a very wide range of
magnifications and field sizes could be catered:for. The
camera was used without the ground-glass:observation screen,
when displaying the Fourier plane, and protection against
damage to the vidicon tube by the intense 'zero-order' light
was afforded by either:
i) Blocking half the Fourier plane with a knife edge.
iii). Using a thin wire to block the zero-order «
iii) Projecting the Fourier plane onto a thin glass slide
bearing a small drop of silver paint to act as the 'zero-
order stop'.
It was usually found necessary to place a field lens in the
plane under observation, in order to direct all ray bundles into
the physically small aperture of the camera lens.. For
examination of very low spatial frequencies in•the-Eburier
plane, 'primary' magnification was provided by a 100mm f/4
enlarger lens and 'secondary' magnification by the:CC:TV system..
The spatial. performance of the system is summarised. in
Fig.(2.2)6,7 with particular reference to use with 55mm x.55mm
ERT. images.
Although the linear dynamic range of the system was
quoted at about 60-100 intensity units, it was realised that
use of the laser output power control would allow placement of
this anywhere within a total range of 104 intensity units,
a figure commonly reckoned to include all useful information
- 58 -
in the power spectra_ of geophysical images. In fact
(PRESTON JR. 1972-a) suggests that one can estimate the
maximum „possible signal to noise ratio in the optical Fourier
transform plane by taking as 'signal' the intensity of the
central. Airy disc lobe, for a 'uniform-field' object input;.
the same reference quotes a value for this quantity of 40dB
(104:•1) as being typical of a diffraction-limited lens system
possessing high quality surface finish and antireflection
coatings. This optical noise. is of course stationary in time;. when using the CCTV system, one has to contend also with
temporal fluctuations (as a result of the vidicon dark current
and video-signal-associated noise), which can lead to 'final'
signal-to-noise ratios of between 10041 and 1 :1 (20dB - l:dB);,
as measured: by displaying the video-signal on an oscilloscope.
Despite this, the television proved to be a very convenient display
device for both the Fourier transform plane and object/image
planes. Moreover, later studies_ on the pilot bench and main
bench, (e.g. Section 4.2.1) have suggested that in many
instances, the image information expressive of a particular
geological process (e.g. foliation, fracture-zoning etc.) can
be characterised: by a spatial frequency band of sufficient
'narrowness' that the corresponding intensity variations in the
transform plane are contained within the effective dynamic range
of the television channel, i.e. that the spatial-frequency-bandwidth
limits of the CCTV system measurements are broad enough to allow
extraction of useful_ geological information without shifting
the mean position of the band, in the Fourier domain.
-59-
A further factor that favoured the adoption of CCTV
display was its provision of contrast control, which made
possible simple intensity enhancement operations, a
particularly useful feature when examining the inherently
diffuse-Fourier transforms of quasi-random objects, as demonstrated
by the following example.
Fig..(2.2)8 is an image formed by sonar scanning of an
area of the seabed off Hartland Point, S.W. England.. The
area. shown is about 3km x 2km in size, at a depth of about
1003n and includes an exposure of faulted Palaeozoic rock
beds.
For the 35mm;format image used:in the bench, the scan-line
frequency was about 30c/mm.. Figs.(2.2)%9,10 are records of the
diffraction pattern taken directly on 35mm.'Pan F' film in
the Fourier plane at two different exposure levels=. These
are to be compared with Figs.(2.2)11,12 which show the CCTV
picture of the diffraction pattern at two.diffrent monitor
contrast settings. It can be seen that the contrast control
allows one to readily distinguish the envelope of the low-
spatial-frequency 'core' of the pattern from that of the higher
spatial frequencies; to perform the equivalent operation by
direct photographic recording generally requires-a change of
exposure and development times.
An assessment of the contrast range on the television
monitor was made by photographing the television image of a
standard neutral density step-wedge, and comparing this with
a direct photograph of the step-wedge, made using the same
illuminating source, recording emulsion, and film processing
-60-
conditions.. Defining:a s, ADĒ, A Dp , as the photographic
step-sizes of respectively: the standard step-wedge, its
direct photographic recording, and the photographic recording .
of its television image;. also, defining P as the photographic contrast co-efficient and YT as the 'effective monitor contrast',
one can putt
A D p
A D: = p
p (-ŌT Aps) D p vt~ s..
So that Zri. = A P
providing that the photographic exposure is such as to place:
the density steps on the linear part of the (H-D) characteristic
in both cases.. (This simple analysis ignores non-linearities
in the equivalent CCTV characteristic). ADI D _ (for thre
AD different monitor contrast settings) and A P
were measured by
taking densitometer traces across the photographic negatives,
and yielded the following results:
WT (typical minimum) - 1.4 (absolute minimum) = 0 (of course)
IT- (typical maximum) 2.0 (absolute maximum). = 2.7
61 —
These results were taken from the traces shdtm in Figs.(2.2):
13-16, and represent the television channel Ō value.. at the
mid;.point of the input intensity range;; comparison of the-
curved envelope of Figs.(2.2)14-16 with the linear envelope of
Fig. (2.2)13. illustrates the non-linear nature of fhe input/output
intensity characteristic of the television (i.e.. the dependence+
of f on input intensityk. It should be noted that the
departures from 'level' (uniform density)_ of the 'treads'
in the density staircase result from the systematically
non-uniform intensity distribution of the illnminaeting source
(an enlarger light-box). A consequence of this is that
measurements of åD (density range between steps) were made
at the step-edges or 'risers' in order to avoid: error due to
this effect.
In all, the CCTV system was considered to be a sufficiently
important asset to warrant its inclusion in the main bench.
In order to meet the display requirements mentioned in Section
2.2.2., it was decided to 'use two complete CCTV channels:. one
to handle the object and image plane information, the other
to deal exclusively with the Fourier plane. Details of the
main-bench display are given in Section
- 62
Z. 3 VIDEO-PROCESSING
2.3.1 Problems.
It should be mentioned at this stage that the transforms✓
shown in Figs.(2.2.)9-12 were obtained from an object
transparency that had been mounted in refractive-index-matching liquid., in order to reduce photographic grain noise
(PRESTON JR.. 1972-b)t. This noise arises from the random
variations of optical path-length through the emulsion and
film base, caused mainly by the granularity of the emulsion..
By enclosing the transparency in a 'gatis4 of transparent
fluid,of a similar refractive index, between optical flat.,
one can . compensate for thickness. (although not refractive index)`
variations. In the case of Fig.(2.2)8, aacrude gate was formed
by placing the transparency in microscope immersion oil],between
cover glass slides. Some idea of the improvement gained by using
even this simple construction can be gleaned from Figs..(2.3)1,2,
which are identically exposed. and proceesed_recordings of the
diffraction patterns from 'gated' and 'ungatedt' identical copies
of the sonar image mentioned previously. A-significant feature
of the 'ungated.image' transform is the increasedazimuthal
spread of light about the major direction of diffraction,
when compared to the 'gated image' transform.
-63-
This mounting technique was used extensively during
the pilot bench experiments, but was superseded. by an
improved liquid gate in the main bench design, details of
which are to be found in Section ;*•3.:
In addition to grain noise in the diffraction pattern,
one also expects a certain amount of scattering from the
optical elements of the transform lens, due to multiple
reflections and imperfections in the surface finish
(PRESTON JR. 1972-a).. It was recognised that this could not
be avoided on the pilot bench (which employed: 'stock' lenses)
and was considered:to be a major factor governing any difference
in quality between pilot bench and main bench results.
Underlying these factors, both of which have a bearing.
upon the task of providing a meaningful quantification of
diffraction-plane information, one must consider also the
statistical nature of the Fourier-transform itself. Since-
the individual features that comprise: any one feature-classy
or category present in remotely-sensed geophysical imagery
can be described-as 'quasi-random' in nature (i.e. possessing
w certain amount of variation in size, shape and photographic
density), it follows that the development of feature
categories based on Fourier-plane information depends not
so much on accurate 'point-by-point' intensity measurementa--
of the diffuse diffraction pattern, but rather on the
identification of intensity 'structures' or 'regions' in
the plane, which can be associated with specific feature
classes, (see GRAEMENOPOULOS; 1975),. (In this work the term
camera and monitor,- (BARIvETT AND :TILLTA!I3 1979).
- 64 -
'spatial signature' is used to describe Fourier plane
structure in a broad land-use classification context).
As mentioned before, the CCTV channel is a valuable asset
in this task; it was discovered, however, that its powers
could be greatly extended by the inclusion of an electronic
video-signal processor (developed by a colleague, Dr. T.H.. W'i.11:iams
at the Applied Optics section, Imperial College), between the
2.3.2 TechniQuew
The basic action of the video-processing unit, is
illustrated in Fig.(2.3).3; the continuous variations in
intensity of the incoming video-signal are converted to
'step-functions' by slicing the signal as shown « The mean
value about which slicing is performed is set by the
'level' control of the processor, which then assigns a
single intensity to all. points on the input signal lying
within each 'slice:' or range of intensity.. In this example,
there are four equal ranges spaced symmetrically about
'level', the size of the combined range (termed the 'window')
also being controllable. Points on the input video-signal
which lie above or below the limits set by the 'level' and.
'window' controls are assigned to the further slices:--
'peak white' and 'base black' respectively.
The data reduction operation implicit in this technique
appears to be of considerable value when applied to diffraction
-65-
plane information, as shown by the following example.
A.35mm format black and white transparency, copied from
a colour composite LANDSAT-A. frame, was used as input to
the optical bench. The area analysed, shown in Figs..(2.3)4,5,
includes the western section of the Grand Canyon, leading
into Lake Mead, Arizona. Fig.(2.3)6 shows the diffraction
pattern as displayed on the TV monitor, without the video).-
processor. As described in section 2.2.3, the intense
central portion of the plane has been stopped out to protect
the TV vidicon. The numbers on the photographically superimposed'
scale indicate spatial frequency in cycles-/mm of the transparency
(of approximate.scale 1.10 million); the region of the
Fourier plane shown thus covers spatial frequencies of about
0.1 - 1.2 cycles/km on the ground', corresponding to
spatial periods of 10 - 0.8 kms. This display suggests that
topographic structures characterised by this range of widths
are relatively strongly represented along alignments 0000 --090°
(bearing in mind the discussion of Section 2.1.21, and
weakly represented along alignments 090° - 180°.. However,
the diffuse nature of the diffraction pattern makes it
difficult to discern finer details of its structure. Fig..(2.3)7
shows a video-processed. version of the pattern, in which
the controls have been adjusted to position all four of the
'equal intensity range' slices over most of the displayed'
section of the Fourier plane. In this mode, it becomes possible
to pick out individual lobes of the diffraction pattern
(e.g. at 010°, 090°x, 130°, corresponding respectively to 100°,
180°, 040°, in object space), which may specify directions of
-66-
particular significance. An alternative form of display is
shown in Fig.(2.3)8, where the application of a further
controllable electronic operation, aptly termed. 'relief',
allows enhancement of the boundaries between the slices,
and gives a graphic representation of the 'hill of intensity'..
Figs.(2.3)7,8, show the display at one particular setting
of the 'level' and 'window' controls; manipulation of these
gives scope for the examination of more specific-regions
or parameters of the diffraction pattern.. For instance, by
making the 'window' very narrow, (effectively merging the
four equal-range slices into one), and redisplaying the
'peak-white' area as 'base-black', one can acheive the
'contouring' effect shown by Fig..(2.319, where the only part
of the pattern displayed.. is that of intensity equal to the value
of 'level'.
2.3.3 Roles
The above example demonstrates the capacity of the
video-processor to produce a very rapid, moderately accurate,
quantitative representation of Fourier plane data. Intensity
accuracy, in terms of linearity and noise, and spatial
accuracy in terms of geometrical distortion and resolution,
depend.essentially on the quality of vidiaon tube and monitor;.
signal degradation in the processor itself can be made negligible
by refinement of the electronics beyond those of the prototype
version employed in these studies. Whilst the performance
of the system, as defined by these parametersi is somewhat
- 6? -
inferior to that of the scanning sector described in the
following Chapter 2.4, it should be remembered that the latter
device was developed for the fairly specific (though important)
task of quantifying directional information from the Fourier-
plane in a routine, usually non-interactive, way. The television
display and video-processing equipment was intended to be
used ēither in a complementary role, (as a fast interactive
device to select data for more detailed measurement by the
scanner), or in its own right, to aid more diverse studies of
Fourier-plane and image plane information, (see:e.g. Section
4.3.2)..
-68-
2.4 DIRECTIONAL SAMPLING
2.4.1 Design and Construction
In pursuing the basic idea described in Sections 1.2.2
and 1.3.1, an azimuthal scanning and measurement system for
the diffraction plane was devised as follower.. (See Figs.(2.4)1,2,3.)
Discussions with photogeologists had suggested. that the
sampling sector angle should be variable within limits of
about 1° and 15° of arc, allowing the angular resolution
to be set with regard to the particular material under
investigation.. 'Eyeballed' rose diagrams are frequently
compiled in 5o or 10° steps, the choice of step-size
depending mainly on the geologist's estimate of:-
.(a) The limits of statistical variation of direction
appropriate to a given geological structure.
(b)i The amount of labour and time involved relative
to the value of the information extracted.
Regarding (a);; in many instances, a geologist's
background knowledge and experience may define the point
at which no increase of physically significant information
can be obtained by an increase in angular resolution. The
-69-
relevance of this to machine-derived roses is that 'over-
sampling' can occur, possibly necessitating subsequent
averaging of the output data, unless: the geologist's
recommended angular resolution can be implemented at the
scanning stage; (when 'eyeballing', sheer effort is an
efficient deterrent to oversampling).
In contrast there are also circumstances under which
a geologist might desire to construct rose diagrams- with
an angular resolution somewhat higher than usual, (e.g. in
order to distinguish between 'linear' and 'shallow arcuate'
macroscopic trends in a fracture trace group, by plotting
roses for a series of subsamples within the group). In
such cases., consideration (b): becomes prominent for eyeballed
material, but may be greatly relaxed by the use of machine
derived measurements of sufficient angular resolution.
In addition to the sector angle specifications, ,
one must consider also the radial limits (high and low
spatial-frequency cut-offs), of the sector aperture.. At this
stage in the project, there was little experience in relating
the spatial frequency spectrum of an image to its inherent
geophysical information content;; however, the pilot studies
discussed in Section 2.2.2, suggested coverage from the
projected design maximum of the main bench lenses
(N 80-90 c/mm) down to about 2.5 c/mm. The lower limit is
subject to both theoretical and practical constraints-as
f ollows
-
-70-
(a). In general theoretical terms, we can relate a spatial
frequency of (for example) 2.5 c/mm to structures in the
object plane transparency having a characteristic 'size'
or periodicity of 15 c/mm =0.4 c/mm. On 55mm xti55mm
ERTSima imagery, (where Imm represents about 3«36km or 2 miles):
this represents structures on the ground of characteristic
'size' 1.3 km. From the standpoint of lineament analysis
a low frequency limit of this order of magnitude would:
generally allow the sampling sector to include all features
for which statistical compilation is an appropriate technique;;
within a single ERTS.frame, linear features of this width
or wider are morem rite 1.e to analysis as specifics
individual elements—of-the terrain, since they are not
likely to forma. sample large enough for statistical parameter&
to have much meaning (we are here treading the boundary between
serial. 'Object plane' and parallel 'Fourier plane' techniques✓
of classification)). Experience has shown however (see:e.g.,
Section 4.2.1), that for lower-level imagery (e.g., aerial photos),
it may be valid to include 'on bench' spatial frequencies lower
than 2.5 c/mm in rose diagram generation.
(WI The exclusion of very low frequencies is necessary in
order to prevent their contribution to the integrated light
energy 'swamping' that of higher frequencies within the sector
of integration: it must be remembered that the power spectrum
of geological images- typically peaks sharply towards zero
spatial frequency, i.e. the energy per unit spatial
frequency range rises very rapidly at 'very low' spatial
frequencies where 'very low' is here taken to imply 'comparable
to that of the image aperture itself'; as a quantitive example,
- 71 -
one might reasonably choose to exclude all. spatial frequencies
corresponding to periods greater :hah 10 of the aperture
diameter; for a diameter of 55=1 - this would mean a low-frequency
cut-off of .v 0.2 c/mm - well within the limit suggested in
(a).; even with a 10mm diameter 'subsample' aperture, (for which
the corresponding cut-off would be A+ 1 c/mm), the geological/
statistical considerations of the previous3 paragraph still.
predominate.. Nevertheless, the radial variation of the power
spectrum must obviously be borne in mind when dealing with
measurements derived from integrations over a finite radial range,
(a point which will. be resumed later).
CO, Additionally, one is faced-with the practical difficulties
of manufacturing a scanning aperture to fit a spatial frequency
plane whose scale is pre-determined by the focal length of
the transform lens. Adapting Relation(2.1)17 we find that for
the main bench design ( A 0
r = 0.341 s
where r(mm). is the radial distance in the Fourier plane
associated with a spatial frequency s(c/mm)'. A=low-frequency
cut-off of 2.5c/mm is equivalent to an inner radius of
0.85mm for the sampling sector. This is; sufficiently small
to suggest that the sector disc-should be rotated via. a
circumferential rather than axial drive. However, if
we set a tolerance of 1%- on radial deviation, then the
inner and outer radii of the sector must be concentric to
.488 zu.103mm. f 7 x:102mm) .s-
-72--
8.5/4"; it was decided to relax this tolerance to 3%
(i.e. centring to 25pm or 0.001"), pending actual trials
of the device..
A summary of the sector specifications is given in
Fig..(2.4)a,.
Some thought was given to the possibility of.
synthesising the sector by photographic means using 'Kodak
Photoplast' material, which consists; of a very high contrast
emulsion ('Kodalith'). on a rigid, transparent plastic
substrate. This idea was rejected since it might lead to
undesirable light scatter in the transparent sector aperture:,.
and would involve a series of fixed.-sector angles rather
than a single adjustable unit..
The eventual design, Fig..(2.4)3, utilised two overlapping
thin steel discaB, which were clamped:at their circumference
into a. recess in the body of the device (for detail see
Fig.(2.4),6);; the sector angle was governed by the angular
overlap of the discs, which could be manually adjusted on
releasing the clamping ring. A. small' diameter central hole in
the discs supported. the shaft of a watchmakers' screw;, the
head of this screw, suitably smoothed and blackened, acted
as a block to the lowest frequencies in the Fourier plane «
The disc surfaces were also coated with a strongly absorbing
matt black paint.. The cylindrical body was mounted in the
inner race of a large diameter needle-race-bearing, the
latter being chosen to comply with , the narrow tolerance on
'radial wobble'.. The housing of the outer race was mounted _
- 73 -
on x..y-z translation stages (to allow precise postioning
of the sector centre), and also supported the rotational_
gear drive. Fig(2.4)4 is a schematic illustration of the
drive mechanism; use of a worm gear and circumferential gear—
ring gave a system with small angular backlash, whilst
leaving the region behind the sector disc clear for the
passage of light to the photomultiplier. The meshing waa
set to allow -0.2° angular freeplay in the sector (a wider
tolerance, since it was envisaged that the sector would,
normally be driven in only one direction).. However, the
ball-races supporting the worm shaft were seated on spacers,
adjustment of which could reduce the freeplay, (at the expense
of increased gear wear). For the initial trials of the sector,
the worm shaft was driven manually via a contrate wheel; a
stepping motor was introduc.ed_later, when the scanning system
was automated, as described-in section 2.4.3.
The transfer of light from the sector disc plane to
the photomultiplier can be accomplished in several. ways..
An obvious arrangement is to use a lens to re-image the
Fourier plane, with change of magnification if desired.,
onto the photomultiplier face; however, this sets undesirably
high tolerance limits on the photocathode uniformity, since
different sector positions image onto correspondingly different
portions of the photomultiplier face. Instead of this, one
can place the leas immediately behind the sector disc, with
the photomultiplier face in its back focal plane; it then
acts as a 'field lens' to the Fourier plane (as shown in Fig.(2.4)5),.
light from each point in the sector aperture being spread.
- 74 -
over the same region of the photomultiplier facet. The lens
aperture:A is determined by the Fourier plane diameter b
whilst its focal length F relative to a given photomultiplier
face?is set by the maximum semi-angle 6 of the ray-cones max.
forming points in the Fourier plane. An input object of radius
40mm (diagonal of ERTS transparencies) and spatial frequency
90c/mm, used with a transform lens of 700mm focal length
leads to:- (see? Relations (2.1117 and (2.1)20):
= 2 xt 0.341 x 90mm 60mm
maw _ ,an 70 radians. q0 0.06 radians
and thus
A. = 70mm minimum (allowing space for mounting)
F = 0112 mm 04175mm maximum (for 10mm photomultiplier
face radius);
in practice a stock lens of L = 75mm, F = 150mm was used,
only moderate aberration correction and surface finish
being required for this task.
t It is important to bear in mind however that the distribution of light over this region is spatially non-uniform and will. vary in a non-uniform way as the sector rotates;.see-Section 2.4.2.
-75-
In choosing a photomultiplier it was borne in mind
that the apparatus required only moderate performance in
terms of dynamic range, sensitivity, response time and
cathode area.. Preliminary measurements on the power spectra..
of ERTSsimages (F.F. GRAY - private communication) suggested
that the light level at a spatial frequency of 2.5 cycles/mm
might typically be about 103 times its value at 90 cycles/mm..
(The latter being essentially the noise level due to scattering
this can be considered a convenient maximum figure for the
required dynamic.. range, the actual angular variation in the
power spectra being, in general, considerably less« Calculations
on the absolute light levels in the main bench, (later confirmeds
experimentally), estimated a power in the collimated-object
beam of about 25mW, yielding about .25mW.in the Fourier plane
if all frequencies.below 2.5c/mm are excluded, thus giving
about 1.5e, or 1500nWin a 2° sector. For a standard 11-stager
photomultiplier, rated sensitivity is about 200 Amps/lumen or
1.6 x 105 /444#J, with a maximum allowable anode current of
102/AR , and hence a maximum allowable light level. of 0.6nW.
The 'excess gain ' would: thus be Ō 6 = 2500. if the whole
sector down to the 2.5c/mm low frequency limit were used, but
might only be about 2.5 for measurements taken in a high-frequency
annulus;, compensation could be easily effected by control of
the photomultiplier power supply, adjustment of the laser source
power, or the use of filters.
-76-
The photomultiplier tube chosen was a 30mm diameter general
purpose type with a low dark current 'S' cathode. This was
coupled to a digital panel meter which displayed the reading
in four digits and produced an output suitable for connection
to a tape punch.. Subject to the availability of extensive s
digital computing services,-this choice of output was
preferred to the alternative of an analogue voltmeter with
polar chart recorder, since it offered:
a), more flexibility in display, since the punch
tape information could be transferred_to a wide,
range of output peripherals, providing e.g.. continuous
or histogrammed polar plots on paper or microfilm;
or line-printed linear histograms and reading listings.
b); the possibility of manipulating the information
e.g., by averaging, normalising etc., and of
incorporating additional information from the tape
e.g. correction factors from monitored fluctuations
of the laser output power.
c)- easier incorporation into an automatic or
semi-automatic system.
Although this technique would not provide the 'instantaneous'
hard-copy of a chart-recorder, some form of display could
be obtained from a computer terminal within a few minutes
of tape generation, so this was not considered to be a
serious shortcoming.
-77-
Direct photomultiplier-meter coupling via a load resistor
was found= to be unsatisfactory, since the requisite resistor
value was non-negligible compared to the input impedance of
the panel meter, leading to static (D.C.). inaccuracies in the
reading; moreover, the finite capacitance of the measurement
circuits gave rise to an unduly long RG; time, (many seconds).
causing dynamic inaccuracies, i.e. inability of the meter
to follow photomultiplier signal changes at a reasonable rate..
These problems were overcome by replacing the load. resistor by
an PET 'current to voltage converter', presenting a large
input impedance to the photomultiplier and a small. output
impedance to the meter. With this modification, the
restabilisation time of the meter, following x:103 to 1 change
in photomultiplier signal level, was typically only • - 1
second, thus allowing dynamic testing of the full. sector
disc/photomultiplier/panel meter combination..
2.4.2 Uniformity and Simulated. Object Tests..
The purpose of this stage in development was to
ascertain whether the scanning unit was functioning correctly
with respect to simple object inputs, before proceeding
to more complicated. 'real.' objects; in particular, to check
that the system was free from angular bias.. The first test
transparency consisted: of a slit (clear on opaque background).
of width 0.1mm=and length 15mm, mounted in immersion oil..
Readings were taken at 5° intervals, using a sector of 5°
width, over the full spatial frequency range allowed by the
-78 -
pilot system (2.5 - 50 cycles/mm); the general form of the
photomultiplier output readings was such as displayed. in the
graphs of Fig.(2.4)7. After several scans, the following
general observationssemerged:-
1). For a fixed object location, the peak output signal
(i.e. at the two diffraction lobes of the slit), showedi
significant variations with respect to object ori:e:ntat:i.on
2)- For a fixed slit orientation, the peak output signal
showed&significant variations with respect to object
location within the object, , 1nne
31 For fixed.. slit location and orientation, the peak output signal showed significant variation between the two
opposite diffraction lobes (of theoretically equal
intensity)..
Result (3), was attributed to mechanical eccentricity of
rotation of the central stop of the sector discs, a problem
which is considered in Section 2.4.3y(until the modifications.
described therein were made, the effect was eliminated by
iteratively lining-up the centre of the Fourier plane with
the centre of eccentricity)..
- 79 -
Results 1) and 2) were thought to be due to a non-uniform
distribution of sensitivity over the photomultiplier cathode
face. Discussion of this is based on the example of Fig..(2.4)7,
which also demonstrates the order of magnitude of the variations
involved. In this figure, the four plots correspond.
to the respective radial slit positions A,B,C,D as indicated,
and the 90° shift in plots B & 11 relative to plots A-& C
has been compensated for, so that the peaks line up to
facilitate comparison. Referring now to Fig..(2.4)8, it will
be realised that the light distribution impinging on the.
diffuser in front of the photomultiplier, when used in the mode
suggested in Section 2.4.1, is effectively a demagnified image
of the object, spatially filtered by the. sector aperture in .
the Fourier plane. Although the diffuser spreads this light
out over a large region of the photomultiplier face, it is
evident that different object positions will tend to be
associated with correspondingly different regions of the
photomultiplier face; hence spatial non-uniformities of
sensitivity in the latter will_ lead to the undesirable variations.
mentioned above.
In order to put the problem on a more quantitive basis,
it was decided to construct a_map of the photocathode
sensitivity. This was done by removing the photomultiplier
from the sector disc assembly and projecting the collimated
beam (normally used for object illumination) directly onto the
diffuser;. the beam was stopped down to 2mm diameter by an iris
diaphragm, and the photomultiplier, with its diffuser, was
- 8o
traversed-on an x-y grid across the stationary light spot,
readings being taken at 2mm intervals. (This method ensured
that the intensity of the light spot remained constant over -
the scan, and was thus chosen in preference to the alternative
of scanning the light spot across the stationary photomultiplier,
which would have demanded a much higher spatial uniformity of
intensity in the initial collimated beam>. The resultant
matrix- of readings was converted to a contour plot of
sensitivity (in arbitrary units) over the photomultiplier face,
which constitutes Fig.(2.4)9..
The steep falx-off at about 25mm.diameter indicates the
approximate limit of the photocathode sensitive area.. However,.
the most interesting feature is the distinct asymmetry about
an axis trending approximately 100/190°, causing 'above
average' readings around_the 90° radius and 'below average'
around_ 270°; remembering that the filtered image isinvertedi
with respect to the original object, we can see-that this
plot tends to confirm the results of Fig.(.2.4)7.. Further
to this, by calculating the integral of the sensitivity
function along radii 0°, 90°, 180°, 270°, out to a distance
of about 3mm (corresponding to the size of the demagnified
slit image), a crude estimate of the angular bias for the
test object was obtained, and was found to agree.in order
of magnitude with the observed variations of Fig..(2.4)7.
These findings cast serious doubt on the suitability
of the photomultiplier as the detector in this application:.
in the above example, deviations of up to 10% from the mean
- 81
were observed; these were far i elow_:the •projected -:
levels of precision in other components of the main bench
optical system, and are perhaps unacceptably :low even to geologists_..
Moreover, there was no chance of applying systematic
correction factors, since the errors involved were strongly
object-dependent.
L possible escape from this quandary was provided by
noticing that if the matrix:of readings forming the basis:
of Fig,(2.4)9 was 180°-averaged about the centre.(i.e the
average of each diametrically-opposite pair of readings was
substituted in place of both members of the pair), then the
resultant contour plot, shown in Fig.(2.4)'10, became highly
symmetrical (i.e. with a much-reduced angular bias) and fairly
flat out to a diameter of 15mm. By calculating integrals of
this averaged function along several radii, out to a distance:
of 7.5mm, the maximum angular bias inherent in this plot was
estimated to be about - ; %, a quite tolerable figure.
The implication of this: is that if a light distribution
possessing 180° rotational symmetry impinges concentrically
on the photomultiplier diffuser, (within the 15mm diameter
circle), the resultant photomultiplier output will be effectively
free:from angular bias effects.. The two-dimensional power
spectrum of an object, as generated on the bench, is just such
a distribution. Moreover, use of this distribution would also
overcome the 'positional bias effects' mentioned earlier,
although in their place would be some 'spatial frequency bias'
due to the rise in averagA sensitivity towards the centre of
the photocathode. A•true demagnified re-imaging of the
diffraction pattern onto the photomultiplier diffuser would
-82-
require the addition of an extra lens in the light path through
the scanning assembly; however, it was noted that the short
depth of focus of the collecting lens allowed a good approx-
imation to the desired symmetry to be obtained, simply by strong
defocussing of the photomultiplier and diffuser relative to the
collecting lens. Subsequent test measurements were made using
this new arrangement.
In the next test, the object transparency used. was a
negative of the previous one (i.e. an opaque bar on a clear
background); this was done in order to gain some measure of
the difference in 'scattered, light level:.' between 'positive'
and. 'negative'" versions3 of the same object, 'scattered light'
here being taken to be principally light entering the Fourier
plane as a result of scattering from dust or defects on the
transform lens surfaces, (oil. immersion being used to minimise
emulsion-grain scattering at the object). The results are
shown in Fig.(2.4),11, where plots (a) and (b)• correspond to
the appropriate indicated bar positions; note the large
discrepancy in signal level between the two lobes of plot (`a):,
(approximately perpendicular to the axis of antisymmetry in
the photocathode)•. Plots (c)- and (d), are 180°-averaged versions_
prepared. from (a) and (b) respectively, and demonstrate the
effectiveness of this procedure;. their peak heights differ by
only ' 1 % from the mean, a figure almost as good as that
theoretically predicted above from Fig.(2.4)10.. The peak signal
level compared to the scattered light level for this plot is
about 3, which compares with a value of about 15 for the
-83-
'positive' object (taken as a mean from the plots of
Fig..(2.4)7).. These figures are rather low, indicating the
considerable amount of spurious scattering that was present
in the pilot system, and emphasising the desirability of a_
very high standard of surface finish and cleanliness in the
main bench.. Also, there is a marked increase in scattering
in changing from a 'positive' to a 'negative' object, which
has especial importance with regard to the prospect of applying
diffraction pattern analysis to fracture trace overlays; it
confirms that there is a significant advantage to be gainedl
in using clear 'targets' against an opaque 'background'
rather than vice-versa..
The final test in this series used: the opaque bar object
but omitted the oil immersion procedure. The result appears,
(180°--averaged), in plot (e) of Fig.(2.4).11, and shows not
only ax further large increase. in the scattered. light 'level:',
but also much broadening of the diffraction lobe due to
emulsion-grain scattering, thus confirming the necessity of
index-matching of the object transparency for making diffraction
pattern measurements. For comparison, the other results
mentioned in this section are also summarised on this graph,
normalised_ to the same peak value.
It should be emhasised that the success of the 180°-averaging
technique employed in these tests depended: on the essentially
fortuitousrantisymmetry in the spatial distribution of sensitivity
over the photomultiplier face, (although this might be a syste-
matic result of the method of manufacture of the photomultiplier).
- 84 -
A more irregular distribution would have caused a gravely
problematical situation, against which the advantages of
alternative diffraction pattern,me-asuremen.t ~•de.vic:ess_wēip;h v4*y l eavily,
(e: . the 'ROA' array - a commercially available solid-state.';' 'detector comprising arrays of wedge-snared and ,annular..elements:)'
2.4.3 Automation and Real Object Tests
The extension of diffraction pattern measurements to
the analysis of 'real' (remote sensing) imagery took place
chronologically in parallel with the conversion of the
directional sampling system to semi-automatic operation;
it is deemed convenient to deal fully with the latter subject
before proceeding to the former.
The automation of diffraction-plane scanning and
measurement was accomplished by the addition of three.
instruments to the basic system of Fig..(2.4)1, viz; a
stepping motor to provide the mechanical drive to the sector
disc;: a tape punch to transfer the output information of
the digital panel meter onto paper tape; and a control unit
to co-ordinate activities within the complete system, which
thus appears systematically as in Fig.(2.4)'12. The detailed
design and construction of the control box, together with
the integration of these instruments into the system was
undertaken by a colleague, Mr. G. Talbett, of the Appliedi
Optics Section, Imperial College; the following account is
therefore intended to briefly summarise their operation «
-85-
The stepping motor was of a stock design, requiring
200 steps per revolution of the drive spindle;; with the gear
reduction used, this entailed 35,000 steps per revolution
of the sector disc, implying a possible angular resolution
(i.e. of 1 step) of about 0.01° of arc or 0.2 milliradians.
In fact this was much less than the frenplay in the gear
train, which thus set the limit to angular accuracy; the
starting position of the sector could be set by eye to an
accuracy of about 0.1° of arc (2 milhiradians)-. The tape
punch, also a stock item, was used to generate 8-hole paper
tape in a code suitable for acceptance by a remote terminal of
the college computer, the coding operations being performedh
by the control box as explained below. The basic functioning
of the control box itself is shown schematically in Fig.(2.4),13
and proceeds as follows:
Once the starting button is pressed, the stepping motor
drive board commences sending pulses to the motor, which steps
accordingly;; the pulses are-counted by the control electronics
and terminated when they reach a number (preset by the operator).
equivalent to the required angular sampling interval. Although
the photomultiplier output follows the light level during the
sector movement, the panel meter is kept locked at the previous
reading until the stepping terminates; it is then unlocked,
allowed to reach and display the photomultiplier signal
level, and after a time interval (preset by the operator) is
relocked at this new reading. The time interval required for
settling of the meter is usually less than one second, but can
be increased_if there are extremes of variation in signal level
between successive readings. After relocking, the signal from
-86-
the panel meter is coded_by the control;_ electronics and fed into
the tape punch; when punching of the reading ceases_, the
control box checks to see if the number of readings taken has
reached the value (preset by the operator) equivalent to the
required total angular range (usually 360°). If it has
not, the cycle is repeated by reactivating the stepper,
which moves on to the next reading; if it has, the control
box resets itself, ready for restarting by the operator.
Typically, the entire. sequence of operations of sampling
a 360° range at 2° intervals takes about 5 minutes and generates 3 metres of paper tape. This speed is comparable to .
that at which the tape can be read in to the local terminal of
the college computer. 180°-averaging is then applied, and
hard-copy (generally in the form of linear or polar plots) iia-
producediin a few minutes (limited by the output speed of the
terminal). Typically, the minimum time interval between.
the start of sampling and the completion of hard-copy is about
15 mins. The complete directional sampling system thus
embodies, a'slow, interactive/non-interactive, technique,
(interaction with the data being via instructions typed on
the terminal), which complements the 'fast interactive' video—
processing option of Chapter 2.3, its advantages over the
latter being better sensitivity, linearity and geometric fidelity..
(NOTE: The computing . respō biliti46 ,iēre` h sb. ūiide'rtaltēn
-87-
The aim of the following series of angular scans of the
diffraction patterns of 'real' objects (remote sensing
imagery of some form) was to attain some initial feeling for
the relationship between the subjective assessment of the
directionality in a scene, and the corresponding 'objective'
measurements provided by the sector disc._ The principal
scene used for these scans was_- the seabed sonargraph shown in
Fig.(2.218 and here repeated as Fig..(2.4114. This was chosen
partly because it displayed an obvious directional trend;
partly because the diffraction pattern had already been
photographed and was thus conveniently available for comparison;
and partly because, (being an image composed of regular scan-lines).,
it was desired to obtain some quantitative idea of the effect
of the scan-lines on the shape of the directional plot.
The first scan shown used a sector of 10° angular width
with 10° sampling intervals, utilising the full spatial.
frequency range of the system. 2.5-50c/mm; Fig.(2.4)'15 is a
linear plot of the results and Fig.(2.4)16 is the somewhat more
informative polar plot (rose diagram). The large lobe extending
between roughly 010° and 045° of this plot clearly associates.
with the predominant rock bedding in the object scene.
Information on directional strengths is represented by the whole
of the 180° envelope, but for a 'unilobal' shape such as this,
we can take the ratio of the major to minor ordinate radii as
a crude empirical measure of the 'directionality " of the scene
(in this plot the value is about 4:11; the significance of
doing this will be appreciated from later results in this section.
Fig..(2.4)17 and Fig.(2.4)-18 are further scans of the same
-88-
pattern, taken using 5° and 2_° sector angles/sampling
intervals, respectively. The intensity of the object
illn in ating:beam was multiplied by factors of 2 and 5
respectively relative to its value for the 10° sector scan,
in order to compensate for the smaller sector angles, thereby
'normalising' the scale of the plots. As one would expect,
these scans show the effect of increased angular resolution
in defining subsidiary lobes within the main envelope;
the 'horizontal' lobe (at 273° since the original transparency
was slightly askew: in its mounting) corresponds to the
'vertical.' scan-lines of the sonar picture. The overall
directionality of the plot is of course unchanged by the
increase of angular resolution.
The next two figures are included to demonstrate the
severity of emulsion-grain scattering effects in 'real'
imagery.• Fig.(2.4)19 shows 2° sampled scans over the range
2.5-50c/mm of the diffraction patterns from oil-immersed and
non-immersed., copies of the seabed: sonar
transparency (cf. Figs.(2.3):1&2),. The same intensity of
illuminating beam was used for both scans, so if one neglects
the small difference in transmission losses between the two
objects, one can regard the plots as comparable in absolute terms.
The figure shows that within the spatial frequency range 2.5-50c/mm,
taken as a whole, there is a higher level of diffracted light
from the non-immersed object; this is presumably balanced by
a corresponding loss of light energy from the frequencies below.
2.5c/mm, relative to the oil-immersed object. The more
significant difference however lies in the 'smoothing out' of
-89-
the finer lobes for the non-immersed; object as opposed to the
oil-immersed one. This can be shown more clearly by artificially
adjusting the 'oil-immersed' plot in the following manner.
By making the assumption that the diffraction effects due to the
emulsion grains in the transparency are to a first approximation
isotropic in the Fourier plane, one can compensate for the major
size difference in the plots by adding a 'D.C. level' (i.e.
isotropic increment) to the values of the 'oil immersed.' plot.
(c=omparison between the 'modified oil-immersed:' and .!non-immersed' in
plots is madekFig.(2.4)20, which thus highlights the loss; in
angular detail which results from omitting to immerse the
transparency (and confirms that the assumption of isotropy
mentioned above is only approximate). It should be mentioned
that the photographic emulsion, used in these tests was
'Ilford pan F', which although not as fine-grained as the recording
emulsion of ERTStransparencies, was taken as representative
of the wide range of input materials that might conceivably be,
used on the bench.
The next series of scans made explored the variation in
directionality with respect to spatial frequency, in the
transform of the sonar scene. Consecutive 20 sampling scans
were taken over three bands of spatial frequency (i.e. annuli
in the Fourier plane), defined by stops over the sector, at
2.5-5c/, 5-10c/mm and 10-50c/mm. The total light energy in
each of the bands was measured using a photocell, and the
intensity of the illuminating beam correspondingly adjusted:
in order to normalise the scans relative to each other
with respect to total_ intensity in each band). By dividing
- 90
through with the normalising factor, the readings could also
be expressed in absolute form (i.e. including the effects of
the differing total energies from the different bands)-. The
absolute. plots are shown in Fig.(2.4)21 and the normalised ones.
in Fig.(2.4)22.
The ratio of total intensities between the 'high' 'medium'
and 'low' frequency bands was 1 t 3.3 5 10, the dominant
concentration of light in the low frequencies causing that
scan to be similar in shape to the previous 2.5 - 50 c/mm
measurements. The medium and high frequency bands, however,
show significant departures in the lobe distribution; as
expected, the scan-line lobe becomes- relatively very prominent
at high spatial frequencies.. The overall envelope shape also
varies somewhat with spatial frequency, the basic 'direction-
ality' (as defined previously), ranging from 6 at 2.5-5c/mm,
through 4 at 5-10c/mm to 2 at 10-50c/mm, indicating a
plausible (indeed rather expected) increase in randomness.:
of feature direction between the coarser and finer details of
the scene. The relevance of the high frequency scan is a little
suspect e b croix?ē 'the . fundamental scan-line frequency of
30c/mm is included-in-its range (although there are also many sub-harmonics), so there must be some, contribution from the
side-orders; however, since these are much dimmer than the
zero-order, the 'overlap contribution' is probably small.
For comparison with Fig..(2.4)14, the spatial frequency bands_
should be expressed in, 'real-space' as opposed to 'bench-spacer
terms; thus 1 cycle/mm is equivalent to 10 cycles/km, and the
- 91
scan-line frequency;} corne 300 cycles=/km, corresponding
to a scan spatial period of about 3.3 metres 'on the ground'.
A_significant problem that arose during these tests was
the possibility of distortion of the readings caused by mis-
centring of the sector disc relative to the Fourier plane.
Initially, lining-up was done by traversing bodily the whole
sector scanning device, using dial guages for control
measurement, until the zero-order diffraction spot was concentric
with the central stop in the sector discs. However, it was
found that scans taken following this procedure showed:
irregularities (before 180°-averaging) that were too severe to
be attributable to the cathode non-uniformities mentioned
previously. Investigation showed that the 'central' hole
by which the stop was mounted in the sectors (see: Section 2.4..1)
had not been positioned to the specified tolerance of 25turn
(the miscentring error was in fact 120/0m)!; moreover the college
workshops subsequently claimed. that they did not possess the
facilities for maintaining the tolerance in this operation..
The short-term solution was to line up the centre of the
Fourier plane with the true centre of rotation of the discs,
so that the diffraction patterns were at least scanned
symmetrically, although the eccentricity of rotation of the
stop meant that there was necessarily a residual absolute
inaccuracy in the readings.
This problem was overcome in the permanent solution,
which entailed the construction of a centring unit to fit
between the discs and the main body of the rotating assembly.
— 92
(See!Fig.(2.4)23). This allowed the discs to be adjusted:
so that the stop coincided with the centre: of rotation
(an operation performed iteratively, observing the stop
during rotation via a travelling microscope), at which point
they were clamped permanently.. The central stop was then
lined up with the centre of the Fourier plane using
translation stages as before.
The following is an example showing the effect of
miscentring on rose diagram shape. Fig..(2.4).24 is a vertical
aerial photograph of a 2km x 2km area of the Yorkshire
Pennines, showing part of a limestone plateau. Weathering
and vegetation have helped to outline several fissuresin
the surface, including the prominent sets developed along the
rectangular jointa:that are characteristic of this type of
rock.. Fig..(2.4)25 is the un-averagedx 3600 rose diagram
for the circled. area. produced~ by sampling in the range
2.5-25e/mm (25-250 c/km 'on the ground') at 2°"resolution.
The diagram has been rotated through 900" relative to the Fourier
plane so that Lobes in the diagram should be parallel to
prominent directionality in the object. The effect of
miscentring is particularly evident in the angular discrepancy
between the lobes corresponding to approximately north/south..
In. the 1800-averaged version, this gives rise to misleading
information by suggesting the prescence of two separate sets:
of roughly NA lineations. The correctly-scanned version is
shown in Fig.(2.4)27. In contrast to the single N/S. direction,
this shows several lobes in the 0700-0850 directions, corresponding
well. with observed structure in the picture..
An example of rose diagram generation from an ERTS
transparency is provided in (BARNETT AND HARNETT 1975).
-93-
2.5.- DIRECTIONAL .FILTERING
As mentioned in section 2.1.1,-the quality of the filtered:.
imagery obtained on the pilot bench was somewhat low, (though
not unaccountably so, given the nature and quality of the
components used). However, the results obtained did provide
useful guidelines to experimentation on the main bench, and.
their presentation in this chapter allows visual comparison
with those ..achj:fiv.ld on the latter (see Section 4.3.1).
2.5.1 'Inclusion' and 'Exclusion' filtering
The principal aim of these studies was to produce images
in which directions were selectively enhanced or suppressed
as an aid to the visual. detection of linear features. The
filters used wereall. of the passive, binary, amplitude-only
type (i.e. their complext. amplitude transmissivity at any given
point was real and of nominal value 1 (clear) or 0 (opaque))..
AlL filters of this type block out some proportion of the
optical information inherent in the input scene; thus the
filtering process amounts to a selective degradation of the
image in both spatial and tonal resolution.
Hence, if it is wished to enhance linear features running
in a particular direction, the modus operandi is to degrade
resolution of features running in all other directions (or
at least in directions closely adjacent to the 'desired' one),
-94-
whilst maintaining good resolution of features running in the
'desired:' direction.. The archetypal filter for this operation,
hereafter termed a 'directional inclusion filter', is shown
in Fig.(2.5).1, together with its practical derivatives;: the
latter either include or excludb the zero-order and very low
frequencies isotropically, since practical experience has
confirmed that directional filtering of 'near-zero' frequencies
causes(,usually undesirable). severe changes in the appearance of
major structures.in the picture, rather than the (desired.),
adjustment of local. detail..
The complementary 'directional exclusion' filters, also.
shown in Fig..(2.5)1, degrade resolution of structures aligned'
within a limited range of directions, whilst maintaining
resolution in other directions;; the purpose of such filters
is to block dominant directional trends in a scene to allow
easier visual inspection of weaker directions. Note that there
is no distinction between 'inclusion' and 'exclusion' for angular
band-width (Y):=900
The fact that use of. these filters produces an image built
up from 'degraded.' point-spread functions, is of significance
when the nature of the input imagery (in particular its contrast),
is considered, since the degradation may cause a loss of local_
contrast in the scene. Thus, although impressive results can
be obtained from 'binary' images (clear features on an opaque.
background or vice versa), or high-contrast continuous-tone images,
those derived from lower contrast continuous-tone images- are
somewhat less striking. In the published literature, there are
several examples of directional filtering applied to true binary
— 95 —
images such as magnetic contour maps (ARSENAULT et.al. 1974),
and lineament overlay traces (PINCUS AND DOBRIN 1966)., or to
high-contrast continuous,tone images such as seismograph records
(DOBRIN et.al. 1965),, (DOBRIN 1968), rock-section photomicrographs
(PINCUS. 1969), and aerial photographs of glaciers (BAUER et.al. 1967)..
(CHEVALLIER et.al.. 1970) provides an example of exclusion...
filtering on an aerial photograph of moderate contrast, but
in this case the structures involved are particularly well-
defined ones (later urban development on Roman field systems)..
Moreover, in the example of inclusion filtering which appears.
in the same reference, zero_-order blocking has been applied
(almost certainly of necessity)- to boost the contrast; thin
is an entirely legitimate exercise for the subject under study
(an archaeological one), but the loss of initial grey-tone
information involved might prove undesirable in a geological
context... Almost the only example of geologically relevant direct-
ional filtering on an aerial photograph of moderate contrast
is provided.-by (FONTANEL et.al. 1966). In view of this deficiency,
it has been decide&to devote the illustrations in this chapter
to examples of filtering involving continuous-tone images of
geological interest.
Initial experiments utilised a narrow slit as a directional
(inclusion) filter, but this was soon replaced by a small
/library' of carefully-cut card wedges, embodying several
different values of (inclusion and exclusion). The zero-order
was either passed through a pinhole in the card or blocked by
a spot of pa;inue deposited on a glass slide (placed adjacent to
- 96 -
the wedges along the optical axis).. The filters were
mounted in a rotational stage. After checking that the
filters operated satisfactorily upon simple test objects:
(such as.: the gratings of Fig..(2.1)19)., they were applied:
to a variety of geological image transparencies.
2.5.2 Examples (zero order passed:).
Fig..(2.5)-2b shows a portion of an unfiltered negative of
the Hartland Point' sonar scene, (which was chosen as a
representative high-contrast object);, as viewed through the
system, (i.e. including double-reflection and coherent scattering
effects). The degree of deterioration due to the latter is
apparent from comparison with the input .positive,
Figs..(2.5)2ct-h are filtered versions of the image_, using a
zero-pass inclusion filter of angular bandwidth Y =20°.
The centre direction of the included range (indicated by arrows)'
is as follows (taking the vertical direction as 000°)s—
c :000° d:030 a x060° f :090x° g 120° h :•150°. It can be seen that
in this scene, the filtering operations have emphasised the
various systems of linears quite effectively, particularly the
long faults in c and lineaments at 080° and 100° in f. Note
also the preponderance of lineation around 120° in g, compared
with the scarcity aroundz030°-060° in d. and e; this is in
agreement with the rose diagram for the region (see Figs.(2.4)16-2z).
- 97 -
An example employing an image of moderate contrast is.
provided-by Figs.(2.5)3a,b.. Fig..(2.5).3a is a negative copy
of the unfiltered: aerial photograph shown in Fig..(2.4)24;:
Fig.(2.5)3b is a directionally filtered version of the image,
using a q1=20°, zero-pass, inclusion filter, aligned;. for
0300. This has enhanced the two long linears:(arrowed);
however, one can see that the general deterioration of the
scene, brought about by filtering, is fairly severe, and may
touch on the limits of acceptability to a photo-interpreter:-
i.e. the gain in direct, 'locational' information due to
optical enhancement of the linears, may well be balanced.by
the loss of indirect,.'contextual' information pertaining to
them, (relative to the unfiltered image). ERTS images are
particularly vulnerable in this respect, owing tō their
excellent spatial and tonal resolution; under these circumstances,
directional exclusion filtering becomes preferable to inclusion.
Fig.(2.5)4a is an unfiltered ERTS image showing aportion
of S.W.: Angola gatalogue no. E1007 0036 (this is a negative
copy derived from a colour composite original). The rose✓
diagram obtained-by scanning at 1.5 - 40c/mm, (0.16 - 4.40 cycles/km
'on the ground'), is shown as Fig.(2.5)5, and Figs.,.(2.5)4b-d.
were produced by using a y =20°, zero-pass, exclusion filter. In Fig.(2.5)4b, the sector blocks directions 070° - 090°
(eliminating the major lobe of the rose diagram at 0800);
directions showing particular enhancement are around 0550 and 100°.
For Fig.(2.5)4c, the blocked range of directions is 1450 - 1650
and there is enhancement of linears in directions 125° and 180°
Finally, for Fig.(2.5)4d, blocking is at 040° - 060°,
enhancement at 0200 and 0750.
-98-
It is evident from this example that enhancement occurs
chiefly in those directions that lie adjacent to the 'blocked:'
directions in the scene. This observation was confirmed]on
other scenes, (and is in agreement with the appearance of the
filtered image that may be expected from a consideration of
the filter point-spread function, see Section 4.3.1). In
this situation, the rose diagram is a very useful guide in
choosing the alignment(s) of the filter (Sea BARNETT AND HARNETT 1975).
2.5.3, Examples (zero-order blocked)
Inclusion or exclusion filtering with a blocked
zero-order, is not commonly reported in the literature,
although it does occur in (CHE3TALLIER et.al. 1970);. The
'edge-sharpening' effect of zero-order blocking (due to the fact
that the high-frequency components forming edges are no longer
'masked' by the lower frequency components) is well-known, and
proves advantageous in the 'archaeological' imagery of the
above reference. However, when applying this technique to
geological images on the pilot bench, the result was generally
of dubious utility. A typical example is provided in
Figs.(2.5)6a,b, showing respectively, unfiltered and filtered'
versions of the sonar image used previously. The operation used:
te —10°, zero-block, inclusion filter, aligned:to pass features
running in directions 130° - 140°.
- 99 -
In common with many filtering operations, this form of
image presents a somewhat unfamiliar object'of speculation.:for
photogeologists. It is thus highly desirable to view such
images in parallel with their unfiltered versions, a
recommendation for the main bench design stressed in Section 2.2.2.
(Although this chapter is restrictedito discussion of
directional filtering, it should be mentioned that some work
on non-directional filtering (e.g. plain zero-blocking, without
wedges) was also carried out. The main bench studies that arose
from this are reported. in Section 4.3.2).
- 100 -
3.1 LAYOUT
As with the pilot bench, the design of the main bench
was based on the 'classical' system illustrated in Fig.(2.1)17,
but with certain modifications to the geometry and components_
used in order to meet the conditions imposed. at the start of
the project or developed during the pilot bench studies.
The major factors affecting the eventual choice of layout
can be summarised as follows:•
1): Minimisation of overall system length
The original specifications for the object and Fourier planes_
ledi to a telephoto lens design (see: Section 3.2.2), which gavee
an object plane to image plane distance of about 1..7 metres-
for a focal length of 0.7 metres. The possibility of further
economies in the overall-system length were therefore confined
to the illumination and collimation part of the bench..
2); Provision for holographic matched filtering:-
It had been decided at an early stage in the project to
include facilities for holographic matched filtering on the
bench (see:Section 1.3.1).
In this technique a collimated coherent reference beam
is arranged to interfere with the diffraction pattern of an
object scene o1(x,y)., (see Fig. (3..1)1) . . A-recording of the=
interference pattern on either a photographic or some other
medium constitutes a hologram of the diffraction pattern.
If the hologram is itself illuminated by the diffraction pattern
- 101 -
of either the same object scene=o1(x,y), or some other scene.
o2(x,y), (see. Fig.(3.112)., then the optical output of the
hologram in the direction of the original reference beam,
when Fourier-transformed, becomes the autocorrelation
o1(x,y1! @ o1(x,y), or the cross-correlation oa(x,y) o*(x,y)
of the input object scenes. This function has a sharply-peaked:
maximum if o1(x,y)i and o2(x,y) are very similar, ('well-matched');
in general, the height and width of the peak are measures of
the degree3 of correlation or 'matching' between o1 (x,y) and
o2.(x,y); hence the hologram is said to act as a 'matched
filter'.
In ordier to accomodāte this technique on the bench, it
was necessary to provide a reference beam, offset at an.
angle to the main axis of the bench, and a means of swinging
the second transform lens off the main axis, (using a vertical
line through the centre of the Fourier plane as the axis-
of rotation).
3) Stability of components:-
In view of the exceptional size and weight of the transform
lenses, the resultant supporting components were of massive
construction, to ensure rigidity and stability of the bench..
In addition, the matched filtering facility imposed the require-
ment of vibration stability to holographic standards.
It was decided. to mount as much of the optical equipment
as possible on a cast-iron surface table, the legs of which
rested on air•-cushions (inflated inner tubes)—a proven method:
- 102 -
of providing satisfactory vibration damping, used frequently
in Imperial College Optics section and elsewhere..
For the illumination system eventually chosen (see°Section
3.2.1) it was found desirable to provide an extension in the
form of a II-section girder which was bolted to the underside
of the table-top. The disposition of the various components
of the system on the table and extension is shown in Figs.(3.1)3
and 4. The arrangement of Fig.(3.1)3 is suitable for CCTV
examination of the diffraction pattern, filtered and unfiltered
images, and for producing rose diagrams from the azimuthal
diffraction pattern scanner. Fig.(3.1)4 shows the arrangement
used in holographic matched filtering, with the CCTV systems
used to display a test image and its cross-correlation with
a 'target' image.
For clarity, Figs.(3.1)3 and 4 omit to show the
supporting benches for the lenses, mirrors, beamsplitters, etc;
these are however covered in the appropriate sections of
Chapter 3.2 together with detailed descriptions of the other
components in the figures.
-103-
3.2 COMPONENTS
3.2.1 Illumination System
The light source chosen was an argon gas laser having
& continuous output of about 200 mW in its most powerful
lasing line (488nm.), the transform lenses therefore being
optimised to work at this wavelength. A laser of this power
was chosen to allow rapid measurement with good Fourier
space resolution using the photomultiplier/sector sampling
equipment developed on the pilot bench. The power requirement
had to take into account losses in the illuminating optics:
(see below), the likely variation of intensity with spatial
frequency (Section 2.4.1), and the sensitivity of the
photomultiplier (Section 2.4.1).
The coherence length of the laser beam was determined
by measuring the visibility of the interference fringes
formed in a: Michelson interferometer, as a function of the
optical path difference between the interferometer arms..
The visibility remained good for a path difference of up
to ±25mm (the first zeros of visibility were at +?5mm), so
it was decided to adopt the former figure as a tolerance for
the reference beam-object beam path difference in the design
of the holographic matched filtering aspect of the main bench.
- 104—
The laser was not fixed to the surface table but its position
and orientation were maintained by abutting the laser housing
feet against metal strips bolted to the table top. In the
event of it being necessary to move the laser for maintenance,
or for installation of further bench components, this arrangement
allowed the laser to be instantly re-aligned with the rest of
the illpm;nation optics.
The size of the transform lenses and their associate&
supporting unite;required the optical axis of the bench
to be in a plane some considerable height (30Smm was chosen),
above the table top. The beam from the laser was brought up to
this level via two guidance mirrors as shown in Fig.(3.211
and Fig . (.3.2) 3.. Studies on thermoplastic holograms (P.. GRAY - private
communication) indicated that reference beam angles of about
30° should be designed for in the main bench, and that, therefore,
a 'beside-the-lens' reference beam system was necessary, as
shown in Fig.(3.2)6, in contrast to the 'through-the-lens'
system of Fig.(3.2)5. The options that presented themselves
were
(a) splitting the unexpanded laser beam, expanding
and collimating object and reference beams
seperately.
(b). expanding and collimating the beam, using a small.
aperture collimating lens, and splitting off the
reference beam from the expanded object beam..
- 105 -
(c) expanding and collimating the beam, using a large
aperture collimating mirror, taking seperate
expanded-outputs from the mirror face for object
and reference beams.
(a) was clearly eliminated as requiring far more equipment
and space than the other options. (b) would have entailed
obtaining two high quality optical components (lens and
beamsplitter) versus the one (mirror) of (c).; moreover,
(b) would have placed several optical surfaces in the path of
the expanded beam in contrast to the single one of (c),
(i.e. (c) was a better choice on grounds of low coherent noise
from dust scatter); another advantage of the mirror system'
was that its inherent 180° fold could be used to make a much
more compact illumination system than (b);: in addition, large
aperture, high quality paraboloid:: (collimating)' mirrors were
available as stock items (and therefore relatively inexpensive.).
from astronomical telescope manufacturers. Option (c)- was
therefore adopted, the mirror being mounted in a support unit
bolted to the girder extension, and masked off to expose only
those parts of the surface required for the object and reference
beams, (Fig.(3.211).
For aligning the system, the mounting allowed fine tilt
adjustment of the mirror via three screws (Fig.(3.2)9);;
focussing was accomplished by mounting the self-contained beam
expander unit on a traverse table (Fig.(3.2)8), which allowed . it
to be racked along the mirror axis. A conventional beam expander
unit, consisting of a microscope objective and pinhole filter
(for beam 'cleaning') was used, (Fig.(3.2)2)..
-106-
For constructing holographic filters, (when both object
and reference beams were required>, a x40 objective was used
to spread the beam over both apertures in the mask, as in
Fig.(3.2)4. In other modes of use, (when only object illumin-
ation was required)-, a x10 objective was substituted and the
beam guidance mirrors were-adjusted: to confine the beam spread
to the 'object aperture' of the mask, i.e. off the mirror
axis, permitting a higher intensity object beam to be obtained,
as in Fig..(3.2)1.
In either arrangement, there was a variation of intensity
across the collimated beam(s), from the mirror, and the choice
of objective powers mentioned above was based on a compromise:
between the size of this variation and the amount of light
wasted at the mask. It was realised that in many applications-,
a significant intensity variation across the object plane
(e.g. ±50% ".of the central intensity) could be tolerated; this
is because:
(a) When recording images in the image plane of the
bench, the logarithmic response of photographic
emulsionspreducesthe intensity variations to
relatively small density variations..
(b) For Fourier-transformation, the object plane can be
considered to contain a product of the object amplitude
distribution with a slowly-varying illumination
amplitude distribution.. The Fourier plane thus:
consists of the transform of the object distribution
convolved with a modified point spread function
- 107 -
that corresponds to the transform of the
illumination distribution.. Since the latter is_
slowly-varying, most of the energy in the point
spread function remains confined to low spatial
frequencies;. hence there is no significant alteration
in the 'scale' of the point spread function. Thus
for most objects of interest, the 'envelope' of
the convolution is virtually identical to that which
would be obtained if using illumination of uniform
amplitude across the object.
It was, however, possible to provide more uniform object
illumination by using a higher power objective (e.g. x40)
off-axis, for applications where object/image photometric
accuracy was important.
The single angled reference? beam mirror shown in Fig.(3.2)6
suffers from several disadvantages which made it unsuitable for
incorporation into the main bench, namely:-
(a) There is no provision for equalising the reference
and object optical path lengths for holographic
recording.
(b) The shallow reference beam angle, (i.e. large angle
of incidence) requires the optical flatness of the
mirror to be maintained over an unusually large
length, compared to the other mirrors and beamsplitters
used in the display system (Section 3.2.4), which were
of a much more manageable size. Optical flatness
- 108 -
is needed.to maintain a sharp point-spread-function
in the auto/cross-correlation plane..
(c) The large area of mirror exposed to possible dust
accumulation, combined with the large angle of
incidence/reflection encourages beam noise from
dust scattering. This can adversely affect the:
signal-to-noise ratio in the auto/cross correlation..
In order to overcome these problems, the system shown
in Fig.(3.2)7 was used in practice. The individual mirror
lengths and angles of incidence were much smaller than that
of the single mirror of Fig.(3.2)6. In addition, the reference
beam path length could be adjusted by tilting and translating
the second mirror (on a sliding mount)) relative to the first,
as indicated. The mirror support unit could be bolted to the
table at several positions along the beam from the collimator
to supply a. wide range of reference beam angles= (approximately
300-60°)i, and is shown in Fig.(3.2)3 and Fig.(3.2)4. The
mirror mounts were of the designs described_ in the display
system (Section 3.2.4),.
It will be noticed that the geometrical path length of
the reference beam was considerably larger than that of the
object beam. This was necessary in order to equalise the
optical paths, since the object beam passed through a
considerable thickness of glass (transform lens and liquid: gate
windows) and index-matching liquid (in the gate).
- 109 -
3.2.2. Transform lens System
The collimated coherent object beam from the paraboloid
mirror passed-to the object plane along the principal axis of
the bench, defined by the transform lens system. The latter
is taken to consist of the lenses themselves together with
their associated_ mechanical support assemblies; discussion of
the object plane, Fourier plane and image plane stages is
deferred to Section 3.2.3.
The: original specification for the transform lenses is
given in Fig.(3.2)10. The design adopted as an initial model
was the six-element symmetrical system proposed: by (BLANDFORD 1970).,
but significant modifications (in the choice of glass types
and in the replacement of.cemented_by air-spaced doublets)- were
necessary in order to meet the specification. The design
chosen is shown in Fig.(3.2)11a.
An initial computer optimisation was made using catalogue'
glasses and this was followed by further optimisations as work
on the glassware proceeded, to take account of the real melt
refractive indices, test plate radii of curvature and element
thicknesses. Stringent inspection of the glass for bubbles and
of the worked elements for striae. was carried out in order
to minimise sources of coherent noise in the lenses, and a high-
quality stock antireflection coating, optimised to the design
wavelength of 488nm., was applied.
Fig.(3.2)11b shows a longitudinal section of a complete
mounted transform lens. It can be seen that the glass:
elements were precision mounted in a series of cells making
- 110 -
up an inner barrel, fitting into a thick-walled three-piece
outer barrel to give strength and rigidity to the assembly..
Naval brass was chosen as the barrel material in view of its
good stress resistance, thermal expansion and machining
properties.
Twyman-Green interferogram tests were carried out on
the completed lenses, .verifying them to be within specification
and therefore diffraction-limited over the desired object/image°
and transform fields.
Design of the lenses was supervised by Prof.. C..G.. Wynne
of the Optics Section at. Imperial College, and their mounting
and testing also took place in the Optics Section, primarily
under the guidance of Mr. F.D..Reavell.
It was realised that the relatively massive construction
of the transform lenses required that translation and tilt
adjustments be accomplished via a system of support units and
benches of a size and stability beyond that provided by
laboratory equipment manufacturers 1 standard items. The
solution arrived at utilised a combination of stock engineering
components and units designed and built in the Physics
department at Imperial College.
Each lens was supported by a matched pair of stock
V-blocks, the lens + V-block combination being treated as a
single unit to which the three orthogonal translations and three
orthogonal tilts were applied. The intention was to provide
a means of adjustment for intermittent rather than regular
use to allow initial precision alignment of the optical
system which would then be locked in position unless/until
realignment became necessary through possible future modifications
or additions to the system.
An identical lens support unit, shown in Fig.(3.2)12,
was used_for each transform lens. The V-blocks rested on a
flat steel plate and were kept in alignment by straightedges
(and the lens);. The horizontal adjustment screws, mounted in
one of the edging strips, provided transverse translation and
tilt in the horizontal plane.. Locking was performed by screwing
up against the opposite edging strip, using spacer blocks and
shim to give the correct alignment Of the lens to the axis,
defined by the illumination system. Vertical translation and
tilts in two orthogonal vertical planes was providediby the
three vertical adjustment screws, relying on the weight of
the lens to self-lock these adjustments. The ball,-ends of
these screws bore into slots in base plates attached to either
the fixed or the rotating optical benches respectively.
A: stock milling-machine table, bearing several precision--
parallel T-slots and V-slots, (which proved to be very useful
for mounting components)., was used as the fixed optical bench,
and was chosen to be of sufficient length to accomodate the
object and filter stages in addition to the first transform
lens assembly. Longitudinal horizontal translation of the
latter was attained by allowing its base plate to slide along
the milling-machine table, located by guides running in one of
- 112 -
the T-slots; the base plate could be clamped by a nut and bolt
also engaging in the T-slot, see Figs.(3.2),13,14. The milling
machine table stood on rubber pads on the cast-iron surface-
table; the large frictional force due to the supported load was
sufficient to make it unneccesary to bolt it to the surface.
Longitudinal translation of the second transform lens
assembly was accomplished by attaching its base plate to a stock
lathe top-slide, Fig.(3.2)15. The latter was mounted on a rotating
platform assembly, the function of which was to swing the second
transform lens horizontally off the main optical axis of the
system, when required: for holographic matched filtering. For
this operation, the axis of rotation would be defined: by a vertical
line through the centre-of the Fourier plane, and thus passing
through the fixed bench. It was therefore: decided to undercut
part of the milling-machine table to make room for a bearing
pivot beneath it. The removal of the bottom of the suds well
in the milling machine table left a hole by which the bearing
pin could be inserted.
A-full description of the rotating platform assembly is
given in Figs.(3.2)16-21. Additional points to note are
(1). The assembly, with top slide, less support unit and lens
attached, was designed to approximately balance on the line of
contact between the wheels and the surface of the cast-iron
surface table, thus avoiding excessive vertical thrust on the
bearing.
- 113 -
(ii). A detachable sighting pin could be fittest into a
vertical socket machined concentrically in the bearing pin..
During alignment of the system, the adjustment screws-in the
bearing base were used to translate the bearing pin until the
tip- of the sighting pin coincided with a focussed point of
light at the centre of the Fourier plane.
(iii) At the on-axis 'normal' and off-axis 'matched filtering'
positions, the rotating bench was locked to the surface table
by means of stock magnetic bases-:.
-
3.2.3 Object/Filter/Image stages.
Experimentation on the pilot bench (Section 2.4.2) had.
confirmed the desirability of enclosing object transparencies
in a refractive index matching liquid in order to reduce the
effect of random light scattering by the grains of the photo-
graphic emulsion. Measurements of the intensity distribution
of a slit image, made in the Optics Section; (F.G.. LEAVER:-
private communication) showed a reduction in scattered light
intensity of an order of magnitude in the case of a medium-grain
emulsion (Ilford N5.31) and by a factor of 2 or 3 for a holographic
emulsion (Agfa 10E75);. The benefits of index matching were
also reported in more detail by (WOJTOWIGZ 1971) who used an
inert silicone oil as the matching liquid; silicone oils were
also used in the liquid gate for a diffractometer described by
(HARBURN AND .RANNIK0:1971)), and it was decided to use one of
these oils for the liquid gate in this project.
The gate design chosen consisted of a tank supporting two
optical flats (windows), enclosing a slide mechanism to accept
single 70mm x 70mm mounted transparencies. The slides were
inserted andextracted: via a slot in the roof of the gate which
could be covered to minimise contamination of the liquid by
airborne dust, (Figs.(3.2)22,23):. One of the windows was.
mounted between rubber 0-rings and clamped to the gate body
by three adjustable screws:s this arrangement permittech the
window to be aligned parallel to the opposite window, of the gate,
since the elasticity of the 0-rings allowed an adequate: range
of movement, whilst maintaining _ 'ail- oil-tight seal, (Fig.(3.2)24),.
-115 -
The windows were aligned parallel to each other by
fluffing out wedge fringes in the reflections from their
inner faces of the collimated beam, before filling with oil..
The defluffed field was monitored as the gate was filled:to
check that no significant displacement of the windows took
place due to the variation in pressure of the oil at differing
depths in the gate. Only very weak reflections occurred in
the filled gate, due to the index match between oil and glass.
The outer faces of the windows were given an antireflection
coating similar to that used for the transform lenses.
it was envisaged that, should the bench be required for
batch-processing of images, an object stage that could
accomodate roll film spools, (cf. the gate manufactured by
Space. Optics Research Laboratories of Chelmsford, Massachusetts),
would be necessary: hence the tank was made thick enough to
hold spools in place of the slide mechanism.. The large
- thickness of oil and glass caused; a considerable shift between
the real and apparent object planes (as seen by the transform
lens) and also some aberration due to the variation in length
of the optical path through the gate experienced by rays within
the 'diffraction cone' from each point on the object.
Calculation showed however that the small_ angle of the diffraction
cone allowed: this to be compensated by defocussing, so that
diffraction - limite& performance could be maintained with
the gate. The large optical path increase introduced by the
gate between collimator and Fourier plane also had to be taken
into account when designing the off-axis reference beam for
holographic matched filtering (Section 3.2.1).
- 116-
The liquid gate was mounted on the fixed optical bench
via a support unit and sliding base plate designed along the
same lines as those used for the first transform lens, and
incorporating alL translation and tilt adjustments.
On extraction from the gate, a mounted object transparency
would be drained of most of its oil film in a dustproof box-.,
and then transferred to a further dustproof box for storage;
no attempt was made to remove all the oi1_from the transparency.
It was found in use that transparencies re-inserted in the gate
introduced only very slight amounts of dust, and it was thus=
possible to use the gate with a single charge of liquid for
many months. The gate was provided:: with a bottom drain hole to
allow easy replacement of the liquid when this eventually
became necessary..
It is not proposed to record here the many types and
modes of construction of spatial frequency filters, a subject
that has been well covered in the works of (BIRCH 1972);
(GOODMAN 1968), and (PRESTON 1972)..
The main intention in this project was to use passive
binary amplitude filters of directional (wedge-shaped) and
textural (annular) form, in response to their apparent utility
in geophysical image processing tasks, as mentioned in Section 1.2.2.t
t It should be mentioned, however, that the bench was also used extensively for holographic matched filtering; and that further developments, particularly in the installation of a Mach-Zender interferometer between the transform lenses, have also allowed. phase filtering operations to be implemented..
Experimentation on the pilot bench had shown that
low-pass: filters, (Fig.(3.2)25)., made by piercing sheets of
foil or thin plate were quite satisfactory.. Drops of paint
on microscope slides were testecb as_ high pass:filters, but
these were soon replaced by filters on photographic film
using 'Kodalithe high contrast emulsion. These were made
by drawing out and photographing large versions of the
desired filters. The disadvantage of these filters was that
fixed, emulsion remaining in the clear areas (after photographic
processing) caused considerable scattering of the light in
the Fourier plane, i.e.. introduced much noise into the system.
This was overcome by using a reversal bleaching process in place
of the conventional photographic processing; in addition to
producing positives rather than negatives from an original
drawing, the bleaching process.strippech the emulsion from the
clear areas, so filters made in this way contributed only an
acceptably small increment to the optical noise-,level. Using
this procedure, suites of filters based on the forms. shown in
Fig.(3.2)25 and Fig.(2.5)1 were produced.
The filters were mounted in slides which were supported.
by a translation stage made up from stock optical bench
fittings, to allow precision positioning in the Fourier plane,
Fig.(3.2)-26. The unit gave horizontal and vertical translation
within the plane and also rotation about the optical axis
(for directional filters). It was mounted on a sliding base,.
engaging with a T-slot of the fixed.. optical bench, to permit
focussing of the diffraction pattern onto the filter; se& Fig.(3.2)20.
•
...
- 118 -
Much of the observation in the image plane was performem
via one_ of the CCTV systems; but it was also found convenient
to view the plane directly on the ground glass screen of a
4" x 5" sheet film camera back, Fig.(3.2)27. This providedi a
convenient means of generating hard copy output, using a
shutter at the laser to control exposure.. The camera back formed
a free-standing unit on the table top, but could be connectem
to the rotating optical bench to prevent any relative movement
between the second transform lens and the film plane.
3.2.4-Display and Sampling System
Following the pi10t bench research of Chaper 2.2, the
display system utiliaed two closed-circuit televis_ion . systemS',
each consisting of a camera, video-processing unit and monitor •.
The use of these CCTV channels fulfilled all of the recommendations
put forwar~ in that chapter, including independent ranges of
magnification of the Fourier and object/image planes, and
simultaneous side-by-side viewing of the object and filtered
image_., As described; bel-owj, the main bench facility also
allowe'd superposit~on of a 'test' object onto its cross-
correlation with a 'referenc~' object, when the bench was used
for matched- holographic-filtering •
The monitors, (which were interchangeable between the
cameras) comprised one monochrome and one colour set.. In the
latter, the v~deo-processed signals were used to display the
density slices in a range of distinct colours. Thus it was
- 119 -
possible to generate 'false-colour' images, or more specifically-,
to display colour-contoured maps of intensity of the image
viewed-by the camera. This had been found to provide a
valuable extension to the monochrome video-processed images
when dealing with complicated. or 'highly textured:' images
(i.e. those including relatively large amounts of high spatial
frequency information).
In order to retain photometric accuracy, both cameras
required field lenses to collect light from the physically
large aperture images in the optical bench and transfer it
through the small_ apertures of the stock T.V.. camera lenses..
The performance of the CCTV systems (particularly as
regards resolution) as summarised in Section 2.2.5, acted as a
base for specifying the mirrors and beamsplitters needed for
the various display paths, but consideration was also given to
the recording of hard copy, and direct visual observation of
the images in the display 'paths, which in general led. to a preference for spatial resolution in excesssof that which could.
be passed by the CCTV systems. The upper limit of spatial
resolution was set by the size of mirrors and beamsplitters
that it would be practical to use; for a given object size,
projection of the 'cones' of diffracted light with a semi-angle
corresponding to a particular spatial frequency, defines the
effective aperture occupied by the diffracted light at any plane
along the display paths, and hence the requiredzbeamsglitter
or mirror aperture= required to pass- that spatial frequency
over the whole of the given object format. Thus, for instance,
referring to Fig.(3.1)3, for a spatial frequency of 40c/mm
(i.e. diffraction cone semi-angle = 0.488 x 10-3 x:40 rads..
= 0.02 rads.). and object field of 60mm x 60mm, the required.
- 120 -
aperture for mirror Ml, distant 750mm from the gated object
plane, would be: (60+ 2 k.750 x` 0.02).mm =- 90mm, in the
vertical direction, and approximately 90 ;sin 45° = 130mm,
in the horizontal direction; the same aperture would also
transmit a 30mm x:30mm object field at 80c/mm;:(these figures
were the ones actually adopted in practice for this path)•.
Similar calculations were.used.to specify the apertures
of all the mirrors, beamsplitters and lenses used in the display
and sampling paths; those. applied to the diffraction pattern
covered the full. spatial frequency range passed by the transform
lenses.
Consideration was given to the possibility of employing
pellicle (membrane) mirrors and beamsplitters, but these were
rejected on the grounds of: (a) insufficient thickness:
uniformity of the beamsplitters (tolerances quoted amounted to
several fringes over the required apertures); (b) possible
susceptibility to vibration (from sound waves)• - undesirable-_:
in holographic matched filtering.. Therefore, optical flats
of good quality were used for the mirrors and beamsplitters,
to keep aberrations to a minimum; it was decided however,
(referring to Figs.(3.1)3,4) to mount at least the elements
B1,B2 and M4, (which interpose in the main axis of the transform
lens system)•, on sliding mounts, so that they could be retracted
when not in use to give the true diffraction-limited path
through the transform lenses.
In practice, all of the elements were mounted on specially-
designed sliding saddles of a uniform pattern, which fitted onto
- 121 -
a system of lightweight optical benches, bolted to the surface
table top, and running perpendicular to the transform lens
axis. The saddles could be locked in position, but allowed some
translation and rotation adjustment to aid alignment of the
system;: many of the mounts were of a simple type in which the
mirror or beamsplitter was lightly clamped in position by nylon
screws. against: rubber cushions, (Fig..(3.2) 28, 29) ; however, some
of the mirrors were supported in kinematic mounts to allow
fine adjustment of horizontal and. vertical tilt, (Fig.(3.2)301.
The mounts were distributed such as to ensure that sufficient
degrees of freedom were provided in each of the display/sampling
paths, to allow accurate alignment.
The beamsplitters were antireflection coated on their rear
surfaces and the front surface treatment was as described below,
(the following descriptions all_ refer to Figs.(3.2)3,4);-
(a) Fourier Plane Display - via beamsplitter B2: this had
an uncoated front surface so that only a small_
fraction of the light from the (bright). diffraction
pattern would be diverted into the T.V.. camera. This
helped to protect the camera and also caused only a
small lose of light from the filtered image viewed,
by the other camera. When viewing very low spatial
frequencies, an additional beamsplitter could be
used, as shown in Fig.(3.2)-31, for .a further reduction
in intensity at the first camera, whilst simultaneously
providing an extra image of the diffraction pattern
for e.g.. hard-copy recording.
- 122 - .
(b). Fourier Plane Sampling - via mirrors M4, M5 and
transfer lens L4, (see Fig.(3.2).32). By changing
the power and position of L4 (normally, telescope
doublets were used)., a range of magnifications of
the Fourier plane could be obtained at the sector
disc, to facilitate sampling at differing spatial
frequency ranges, particularly low spatial frequencies..
(gee.also Figs.(3.2)33,34)..- (c)" Object/Image plane Display - via beamsplitter BI,
mirrors M1,M2,M3 and re-imaging lens L3, (see?
Figs.(3.2)35,36,37,38). Beamsplitter BI was coated.
for 55% transmittance, 4% reflectance, at its working
angle of. 45°;,the departure: from 50%/50% was intendedi
to compensate for losses in the transmitted beam at
B2. and at the large number of (albeit coated). surfaces
of the transform lenses and liquid gate, so that in
the absence of filters, images of approximately equal
intensity could be viewed-side by-side at the image
stage I. The effect of filtering operations could
thus be monitored: in direct comparison with the
adjacent unfiltered image of the object provided:
by this display path..
Initial experiments used a single doublet lens
for L3, but it was decided-to replace this by two
separate matched-doublet lenses'`, arranged to place
the object in the front focal plane of the first
lens and the image in the back focal plane of the
fi The double lens system for L3 was tried experimentally but permanent mountings for the lenses had not been constructed at the time of the authorts"departure from the project.
- 123 -
second. The advantage of this system was that axial
movement of the second lens relative to the first
allowed the re-imaging path length to be altered
for (d) below..
(d) Object/Cross-correlation Plane Display - via
beamsplitters B1, B3, mirrors -M1 1 M2 and re-
imaging lens L3. (See Figs.(3.2)39,). By
shortening the separation of the two lenses
comprising L3, an unfiltered image of an object
could be focussed in the auto or cross-correlation
plane J. The beamsplitter B3 had an uncoated
front surface so that a 'reduced-intensity' image
could be superimposed on a 'full-intensity' auto/
cross-correlation pattern, the intention being to
allow the object to be simultaneously visible with
its auto/cross-correlation, in registered superposition.
In practice, it was usually found necessary to use
neutral density filters to balance the beam intensities
in order to acheive this.
A general view of the main bench is given in Figs.(3.2)41,42«
- 124 - 3.3 SUPPLIERS
Many of the components described in Chapter 3.2 were
manufactured in the Optics section and PhysicsDepartment workshops.
A list of the outside suppliers of items mentioned is included
at this stage.
'Crown' 8' x 4' Cast Iron Surface Table..
'Bridgeport' 42!' x. 9" Milling Machine Table
'Mascot' 12" x.5" Lathe Top Slide
Roller Bearings for, Rotating Optical Bench and. Sampling Unit .
Model 54 Argon Ion Laser
Beam Expander and Pinhole Filter Unit
10" aperture, 40" focus Paraboloid Mirror
Windley Bros. Ltd. Crown Works; Beach's Drive= Chelmsford Essex:
- Adcock-Shipley P.O. Box: 22_ Forest Road Leicester _LE5 OFJ
Colchester Lathe Co.. Hythe Colchester Essex_
I.N.A.. Bearing Co. Ltd. Maybrook Road,. Castle Vale Industrial Estate, Minworth Sutton Coldfield " Warks
- Windley Bros. Ltd. (as above)
Delta (Manganese Bronze) Ltd. Handford: Worker Hadleigh Road Ipswich
- Suffolk
- Coherent (UK) Ltd. 13 The Mall Bar Hill. Cambridge CB3 8DZ:
Scie-Mechs 8a Wheatash Road Addlestone' Surrey
- Astronomical Eauipment Ltd. 26 Guildford Street Luton Beds.
Vee Blocks 4" Height, 4" Gap 2 Matched Pairs
Rolled Naval Brass for Transform Lens Barrels
- 125-
Liquid Gate Windows:, Transform Lens Elements, Mirrors, Beamsplitters
Coatings for windows, lenses and beamsplitters
Liquid Gate medium:. Dow Corning 710 silicone oil
Stepping Motor for Sampling Unit
Photomultiplier
Power Supply
Digital Panel Meter
Tape Punch
Link Electronics CCTV Cameras
- I.C.- Optical Systems Ltd. Franklin Road., London SE20 8HW
- Balzers High Vacuum Ltd:. Northbridge Road Berkhamste& Herts.
- Hopkin and Williams Freshwater Road:. Chadwell.Heath Romford Essex
- Unimatic Engineers Ltd. 122 Granville Roadh London NW2
- E.M.I.. Ltd. Electron Tutee Division Bury Street Ruislip Middlesex:
V.G. Electronics Ltd. Menzies Road. Hastings Sussex.
Advanced Electronics Ltd.. Raynham Road. Bishops Stortford Herts.
- Data Dynamics Ltd. Springfield Road Hayes Middx.
Studio 99 Video Ltd. 73 Fairfax; Road London NW6
Shibaden 15" monochrome= CCTV Monitor
- Studio 99 Video (as above)
Ltd.
Sony 'Trinitron' colour Television Receiver
- Modified, by Dr. T.H.- Williams Optics Section, Blackett Laboratory
- 126 -
4.1 BACKGROUND
The following chapters describe a number of 'case studies'
demonstrating the performance of the completed main bench in
operating on imagery of practical significance, using the
techniques of diffraction pattern sampling and filtering.
The purpose of this chapter is to provide a few accompanying
notes on the geophysical background to these studies, in order
to indicate the relevance of the techniques to the particular
practical situations.
4.1.1 Fracture Trace Analysis
SEE::. (HUNTINGDON 1969). ,
(NORMAN AND HUNTINGDON 1974).,
(NORMAN 1976).
In the geological sciences, the investigation of linear
features in the earth's szrfāce-- as indicators of its structure
and history is now a familiar and well;-established technique..
It is a particularly important theme in the branch of photogeology,
since in many cases, linears that may be difficult to establish
by field survey techniques can be detected relatively easily
from aerial or satellite photography..
The use of such remotely-sensed imagery in lineament
analysis makes possible the simultaneous evaluation of large
tracts of territory, including areas where prospective ground_
surveys are relatively difficult to mount, (e.g. jungle, desert,
mountain), and therefore difficult to justify unless preceded.
by indications of the importance of the area from other sources:
of data; in fact, remote sensing images are usually the major
-127-
'other source', which reinforces the importance of a thorough
analysis of the images. Another important feature of such
analyses is that they may reveal traces of fracture patterns
in formations that are buried beneath a (sometimes substantial)
covering of surface rocks. The latter frequently have their own,
unrelated, stress patterns, which may drastically obscure the
buried fractures in a ground survey.
By making composites of high-altitude aerial photographs,
or more recently, satellite imagery, extensive major lineaments
often running to several tens of kilometres. in length have been
discovered.. In contrast, lower altitude photographs can be used
for revealing the pattern of smaller scale lineaments in local
areas; these may resolve finer details of the regional stress
patterns indicated by the major lineaments and may therefore
allow detection of anomalous areas. in the pattern, which can
represent features of structural of mineralogical interest.
Of course, not all linear features appearing in remotely -
sensed imagery may be directly associated with fractures, faults
or joints, (which are the 'target' features). One of the major
tasks in traditional 'eyeballed' fracture trace analysis is to
separate fracture traces from unrelated and/or irrelevant
lineaments, such as exposed bedding planes, glacial striae',
buried drainage channels, gullying and other erosional or
depositional forms, and:. artifacts such as field boundaries..
In certain types of imagery, e.g. side-looking radar, or sonar
images, it may also be necessary to compensate for lineation
due to instrumental effects (e.g. scanning, or,movement of the
detector,1 involved in generating the image; (See section 4.2.21.
-128-
Conversely, fracture traces may appear in a variety of
forms, (in addition to obvious cracks), such as tonal (rock
or soil). and vegetal lineations;. or textural boundaries; or
may be manifested. in the shape of landforms and drainage
(e.g. the classic example of unusually straight sections in
a meandering stream)..
Consequently, the traditional 'eyeballing' procedure,
normally entails the compilation of a map of all_ 'genuine'
lineaments:, constructed by plotting the lineaments on a
transparent overlay attached to the image under interpretation.
The lineament map is a very useful representation of structural
information; it may:. allow areas having similar stress patterns
to be interrelated; aid verification of the existence of single
long lineaments from a series of separate (discontinuous) traces;
define the boundaries,of anomalous regions in the stress pattern;
or _enhance groupings of lineaments characteristic of specific
geological entities, (e.g. shatter zones over intrusion boundaries).
In addition to the. above, in areas of dense lineament data
it has been found advantageous to adopt a statistical approach
to the analysis, and parameters such as lineament density (e.g..
number or cumulative length of lineaments per unit area), or
histograms of lineament length, have proved to be useful
indicators of the geophysical situation.
Lineament overlays frequently display several superimposed.
fracture systems, each with possibly independent directional
characteristics;: directional statistics have therefore been
found to be of considerable value in separating the various
- 129-
geophysical events involved, and in assessing the relative strength
of the stress patterns, or their relative significance in
locating possible zones of mineralisation. These statistics.
are frequently expressed as rose diagrams or directional
histograms, plotting (e.g.) the total number or total length
of linears within successive compasa sectors.
It should be emphasised_ that fracture-trace analysis;
generally constitutes only one facet of a geologist's investigations
of a study area;; in developing conclusions, its results would
be combined with those from any other available data such as
geochemical samples: or aeromagnetic measurements, plus the
background knowledge of the interpreter in relating the observed'
or inferred structures to those of previous experience.
It can be deduced from previous chapters of this thesis
that coherent optical diffraction techniques offer broadly two
important prospects to fracture trace analysis:
11: Rose diagram generation, (i.e. compiling directional lineament
statistics), via azimuthal sampling in the Fourier plane.
2) Feature enhancement, (of particular directions or particular
concentrations of lineaments)• via directional or textural frequency
filtering in the Fourier plane..
Considering rose diagram generation, comparisons between
eyeballing and coherent optical methods can be made as follows:-
— 130—
a) Objectivity. A very significant weakness of eyeballedi
fracture-trace data is the inevitable subjectivity of the
interpreter. This can take the form not only of perceptual
inconsistencies, e.g. resulting in an overlay where particular
directions are over-or under-represented due to differences in
appearance (e.g. contrast, whether vegetated, whether coinciding
with tonal boundaries, etc.) of the lineaments on the remotely
sensed images; but also of spurious bias effects due to the
background knowledge of the interpreter (e.g. a tendency to
preferentially select lineaments which support hypotheses drawn
from other data in the image, or from other sources).
However, background knowledge also confers significant
value to eyeballing methods of interpretation, since it enable
the-mass,of indisputably irrelevant data (e.g. bedding planes,
field boundaries) to be rejected and can allow valid weighting
corrections to be applied to particular directions as a result .
of data from other sources. (It is well known that the prominence
of a fracture trace in an image may be only loosely related to -
its geological relevance).
B6 blc these aspects must be contrasted against the results
of the coherent optical techniques which assesses the directional
characteristics of the totality of features in an image, and
which therefore avoids interpreter bias at the expense of losing
interpreter discrimination. It should be noted that any differences
between the results obtained by coherent optical versus,
eyeballed methods will_be to some extent scene-dependent - i.e.
they will_be affected by the nature of the features making up
the particular scene or image under analysis, e.g. the proportion
-131-
of 'irrelevant' data, or the proportion of valid features liable
to be mis-interpreted. In scenes where such factors: are at
least not obviously prominent, one might anticipate some degree
of correlation between results derived: from the two methods.
Section 4.2.1 reports a pilot experiment to investigate whether
a useful degree:of correlation can be obtained in practice
under these circumstances.
b). Speed Assuming'that the coherent optical method can.be
demonstrated as capable of producing useful statistical results,
speed becomes its most obvious other advantage over eyeballing.
The superiority of coherent optical processing for the particular
task of rose diagram generation is not only due to the fact that
the data is compiled by the parallel nature of the diffraction
process: and because of the relatively rapid response of the
photodetection and measurement system, but also because of the
possibility of deriving the information directly from the remote
sensing image, bypassing the lengthy stage of fracture trace
overlay production.
The sampling system designed for the bench in this project
was capable of generating a rose diagram in a few minutes, and
it would be quite possible to modify the system to reduce-this
time to a few seconds if required. By traditional eyeballing,
the derivation of a rose diagram from an overlay might take many
hours although this could obviously be significantly shortened
by (e.g.) the use of semi-automatic plotting tables or, if
video input/output to a conventional computer is available, by
a simple line identification and measurement programme.
- 132 -
However one might notionally ad&.to this the considerable
time required to construct the overlay itself from the remote-
sensing image, although in many instances this task would be
considered an essential part of the full interpretation of the
area, irrespective of its use in generating further groupings
of information, (such as rose diagrams). Thus the speed
advantages of the coherent optical method are likely -to find
their greatest use in generating statistics for areas in advance
of full: interpretation, and therefore to provide some
guidance in selecting those areas.
Allied to this is the ease with which certain compilation
parameters, such as sector angular size and diameter of sample
area,: can be adjusted, e.g. to take account of variations in the
numerical density of lineaments or to subsample areas in order
to track gradual variations in directional trends and isolatee.
directionally anomalous regions - (see Section 4.2.2).
It should be noted that the time required for any serial
form of analysis, such as eyeballing, increases linearly with
the number of lineaments involved, but remains constant for thea
parallel form embodied by coherent optical processing. Hence
the speed advantages of the latter method increase with the
density of lineaments and the size of the area under. study, and
may make it possible to apply rose diagram compilations to a
greater extent than would otherwise be practicable «
Turning to the aspect of feature enhancement by spatial
frequency filtering, it is apparent that for linear features,
133 -
directional filtering is of obvious importance. Applications,
to fracture trace: analysis can occur both in the remote sensing
image prior to interpretation and in the fracture trace overlay.
When dealing with the 'raw' image, spatial filtering can
provide an aid to the conventional 'eyeballed' overlay
construction procedure by producing modified images in which:
(i) the application of a narrow angular pass-band filter
allows only lineaments running within a specified narrow range
of directions to be resolved, hence enhancing such lineaments
relative to the rest of the detail in the scene.
This operation is particularly useful for identifying
connections or continuations between apparently discontinuous,
sections of a lineament, or for clarifying the appearance of
'en echelon' fractures,..
OR
(ii) angular blocking filters act to eliminate irrelevant or
spurious linear features which may obscure or be confused:
with true fracture traces in the original (unfiltered) image;:
or to suppress. the stronger fracture trace directions thus
allowing easier perception of the weaker trends in the scene..
Similar operations can also be applied to fracture trace
overlays, in order to define or mag zones of similar directionality
within a scene, or to remove dominant trands if these obscure
other traces under study (as above)-.
0. An example of directional filtering, applied togremote sensing
image, using the main bench optics, is described in Section 4.3.1..
-134-
4.1.2 Terrain Classification
See: (CORBETT 1973).
(GRAEMENOPOIILOS, 1975)
(McKEITH 1974)
One of the major fields of application of remote sensing
data, particularly the LANDSAT series satellite imagery, is in
terrain or land-use classification, for such purposes as:•
crop forecasting, water resource and drainage planning, and
monitoring forest inventories, urban development and desertification..
These studies are extensively based on the techniques of
multi-spectral analysis, in which measurements of spectral
reflectance: in various wavebands are used to categorise target
areas into terrain or land-use classes, (e.g. healthy/diseased
wheat, shallow/deep water, coniferous/deciduous woodland,
bare earth/scrub etc. etc..).'
A. multitude of computer-based methods of analysing the input
data to optimise the accuracy and consistency of such classifications
has been developed, and have been described in a vast range of
literature. The success of these methods using satellite imagery
has also stimulated research using lower level (e.g. aircraft)`
imagery.
It has long been recognised that classification procedures
would be improved if textural information were utilised as well_
as tonal, i.e. that, in addition to the reflectancesat each
point la the scene, the nature of the relationship between
the reflectance at a point and that at neighbouring points,
is a valuable descriptor of terrain/land use. Indeed,defining
-135-
textural boundaries is a frequent task 'In eyeballedlphoto-'
interpretation for geological and geographical studies..
Using digital techniques, the;:general.approach is to
compare or associate point values with 'nearest neighbour'
point values, then 'second nearest neighbour' point values, and
so on, with the computing effort rising steeply as a function
of the number of points included in the association, i.e. as
the operation becomes increasingly 'parallel' in nature. The
limit of this trend is given by whole-scene operations or
transformations, where all pointsof the image are considered
in association, of which Fourier techniques are an important
example.
Since coherent optics provides the possibility of rapid
parallel whole-scene operations, there have been several invest-
igations involving its application to the field of terrain
classification. Measurements at various points in the diffraction
pattern representing the spatial frequency spectrum of an
input image can be used as the basis_.for textural signatures,
in the same manner that 'spectral' or tonal signatures are
derived from a multispectral set of imput images; i.e. spatial
frequency spectrum measurements can be manipulated using similar
mathematical tools as those regularly applied to measurements
of the electromagnetic spectrum (i.e. 'tonal' or reflectance
values of the input scene)•.
In addition, optical spatial filtering allows rapid
separation of textural classes, definition of textural boundaries,
etc, and may thus yield images suitable for mapping directly;
-136-
or as 'preprocessed-images', for further eyeballed or
computer-aided interpretation. This aspect highlights;a
notable advantage of coherent optics over digital techniques:
i.e. that of providing an optical image output directly from
an optical image input, obviating the need for optical-digital
input/output conversion stages.
Both annular and directional spatial filters, or a
combination, may be of interest in the field of terrain
texture analysis;- a report of an experiment using annular
filtering is given in Section 4.3.2.
- 137 -
4.2 DIRECTIONAL STATISTICS
4.2.1 Queensland Aerial Image
The input material used in this study (an aerial photograph,
eyeballed fracture trace overlay and manually summed rose
diagrams) was supplied by Dr. E.J.. Heidecker and Mr. T. Supazjanya
of the Department of Geology and Mineralogy at the University of
Queensland, who had previously reported promising correlations
between the cumulative length rose diagrams and the optical
diffraction patterns of corresponding areas of the fracture
trace overlay (HEIDECKER and SUPAJANYA 1975). In this paper,
they compared the general shape of the diffraction pattern
(i.e. presence and position of lobes) with that of the-corresponding
eyeballed rose, but had not measured the azimuthal energy
distribution in the diffraction pattern, and were not therefore
able to give a numerical: comparison. The first part of the
present experiment therefore used the azimuthal sampling unit
in order to provide numerical values to build up an optical
rose diagram from the overlay.
The fracture trace overlay Fig.(4.2)1 was received in thee
form of a Xerox copy from the hand-plotted original, and was
subsequently reduced onto a 70mm x 70mm format lith-film
transparency for use in the object stage of the bench. The
width of the traces on the transparency was measured at typically
- 138 -
0.05mm suggesting that its diffraction pattern should extend:
out to about 20 cycles per mm at least. The diffraction
pattern of 'Area A!' of the overlay is shown in Fig. (4.2) 2
from which it can be seen that there was considerable energy
at spatial frequencies up to and beyond 10 cycles per mm..
The diffraction pattern was sampled using a 2° sector in
the spatial frequency band 7.5-20 cycles per mm, chosen•.
by reference to video-processed images of the diffraction
pattern, which had suggested that this range would give better
discrimination between the Lobes- than if the pattern were
sampled down to lower spatial frequencies;; (this was confirmed;,
experimentally by a.. trial run including low frequencies, on
the sampling unit). The resultant optical rose diagram for
Area A is shown superimposed on the manually-summed rose in
Fig.(4.2)3.
The plots agreed well in picking out the major directional
lobe 060°-09et, but showed- significant disagreement in the
region 110°=150°,- where the optical rose gave much lower readings,
than the manual one. The explanation offered for this
discrepancy was the existence of reprographic errors in the
input, as follows:
It was noticed that the contrast and continuity of the=
fracture traces on the photocopy were somewhat dependent on
their direction, and in general, that lines running in the
range of directions 0900-180° were poorly reproduced compared
to those in the range 0000-0900.. Microscopic examination
confirmed that this condition had been transferred (and
t All direction measurements refer to True North in the object plane (i.e.-Diffraction pattern measurements have been 90°-shifted).
- 139 -
possibly exaggerated by the nature of the lith exposure
characteristic) to the transparency, which might therefore
be expected to give rise to a rose diagram with systematically
weakened readings in the range 0900-1800, (i.e. including the
observed. 1100-1500, 'weak' region).
Circumstantial evidence for attributing the discrepancy
to this cause rather than to any other factor was given by
the relatively good 'Area:. A' optical - manual correlation
obtained when using the aerial photograph (see below): as
input; (since the latter would otherwise:be expected to give
less good correlation than the fracture trace overlay)..
The more important part of this experiment concerned the
optical derivation of rose diagrams direct from the uninterpretedi
aerial photograph.
The terrain covered by the photo was a part of the Owenee
granite batholith in north-eastern Queensland, and is shown in
Fig.(4.2).4. A. reduced negative transparency (on 70mm format
continuousatone fine grain film) was made from the photographic
print and used.in the object stage of the bench.. The diffraction
pattern of 'Area A' is shown in Fig. (4.2)•5, from which it is
obvious that much of the energy is contained in lower spatial
frequencies (under 3 cycles per mm) compared to 'Area. A'' of
the overlay. This is to be expected, since the appearance~ of
the lineaments on the airphoto is in general not as fine (narrow),
nor of such high contrast, as on the overlay. Much of the
high spatial` frequency information in this pattern is due to
the fine details of the picture such as boulders and scrub..
-14o-
Both these factors suggested that successful measurement
of the directionality due to lineations in the airphoto was more
likely to be achieved by scanning the diffraction pattern at
considerably lower spatial frequencies than those employed for
the overlay, and this was confirmed in practice, as shown by
the following plots..
Fig.(4.2)6 shows the optical rose diagram derived from
'Area A' of the airphoto, prepared by scanning in the spatial.
frequency. range 3-5 cycles per mm.(corresponding to about
13.5 - 22 cycles per km 'on the ground'%, superimposed on the
manual rose from 'Area A' of the overlay. This figure-
suggested that these frequencies, although not as high as those
used in the scanning of the overlay diffraction pattern, were
still too high for a satisfactory representation to be obtainedz'
from the airphoto diffraction pattern; (there is little
correspondence in shape apart from the general elongation along
the E-Wt axis compared to the N-S axis).
Fig.(4.2)7'shows:. the 'Area A-' optical rose derived from
scanning at 0.5 --1.0 cycles per mm (about 2.2-4.4 cycles per
km 'on the ground') with the comparison manual rose.. At these
frequencies there was quite close agreement, even some of the
smaller peaks being picked out by the optical method.
To provide a rough estimate of consistency, the same
spatial frequency range was used in generating an optical rose
for 'Area B' of the airphoto, and this is shown superimposed
on the corresponding manual rose in Fig.(4.2)8. General
agreement was again fairly good, but in this case there were
also substantial differences in certain directions..
It was deduced from the above results that the spatial
frequency spectrum characteristic of 'lineament information'
in this case was such as to allow some degree of separability
of that information from the other details of the scene over
a certain frequency range, i.e. that 'lineament information'
was dominant over certain spatial frequencies, presumably
related to the typical spacing and apparent width of the
lineaments. However the degree of separability might be
somewhat dependent on the particular nature of the scene, or
portion of a scenes under analysis.. To take a hypothetical.
extreme example, in a scene consisting of fairly broad fracture
features on a background composed mainly of fine rock detritus
or scrub, it might be possible to choose a spatial frequency
band that includes almost all. f the lineament information and
almost none of the background; whereas-in a scene where the
background contains a large number of bedding-plane traces
having a similar apparent width to the fractures, separation
of the 'wanted' and 'unwanted' information in the diffraction
plane might be impossible.
Other points to be noted in connection with this experiment
were that:.
(i) The 'truth' against which the optical method was
checked was a photogeologist's subjective interpretation, and
was therefore itself subject to sources of error, which must
affect the validity of the comparison to some extent..
(ii) The choice of the spatial frequency band scanned
was essentially an empirical one, based on a 'reasonable guess'
as to the nature of the image information in diffraction plane.
- 142 —
terms, i.e. the likely scale or texture of the lineament
information relative to other detail in the scene.. This
process was aided by studying the diffraction pattern (and video-
processed versions of it) via the CCTV channel, and it was thought
that this was a factor in which the knowledge and experience
of a photogeologist should play a vital part in continuing
future studies-.
(iii) Only a particular rock type/geological structure
was considered; it was anticipated that further trials of the
technique should be applied to a wide variety of geological_
situations (e.g.. with varying degrees of superficial cover);
and other forms of imagery.
In conclusion, the experiment demonstrated that in comparing
the optical rose from an uninterpreted image and an 'eyeballs-d'
interpreted rose, it was possible to obtain a degree of
correlation of practical importance to geologists. However,
the criteria for selecting the spatial frequency range to be
scanned, and the consistency of the results as a function of
the particular geological situation under analysis, are subjects
on which considerable further work wilL be required if optical
rose diagram generation is to become a routinely accepted tool
for the photogeologist..
This work was communicated to the geological disciplines
in (HARNETT AND BARNETT 1977),..
- 143 -
4.2.2 'FAMOUS' Sonar Image
This section reports work involving a sonar image supplied
by Dr. R.B..Whitmarsh of the Institute of Oceanographic
Sciences. The image of the 'FAMOUS' area (French-American
Mid Ocean Undersea:Study) was produced as part of an extensive-
project for the study of the Mid-Atlantic Ridge in the region
of the Azores, (Fig.(4.2).9), and was generated by a long-range,
side-scan sonar system, known as
Many of the features in this image are-:thought to be fault
scarps, and their distribution and directional statistics are
of significance in contributing to theories concerning the
geological evolution of the area (WHITMARSH AND LAUGHTON 1975).
It was therefore proposed to produce rose diagrams by
azimuthal diffraction pattern sampling for several test area
in the scene, (three of which are indicatediin Fig.(4.2)9)..
A problem known to be inherent in this image was that the
features shown were distorted by yaw of the sonar source/receiver..
The effect of this was to cause a biasuin the image towards
the vessel's tracking direction (055?/235o) i.e. isolated point.
features became drawn out into short lines parallel to the
track in the image, and straight scarp lines appeared to be
modulated by fine 'wiggles' or zig-zags'. Initially, sampling
was done in the spatial frequency range 0.5.-7.5 cycles per mm (0.22-3.3 cycles per km 'on the ground')., and the yaw effect was
manifested by showing the track as the strongest direction in
the rose, (see Fig.(4.2).10a).
It was reasoned that since the distortion was a high
spatial frequency effect, a better result might be obtained by
'GLORIA', (LAUGHTON AND RUSHY 1975)..
-144 -
confining the azimuthal scan to low spatial frequencies. The
band chosen was:0.5-1.5 cycles per mm, (0.22-0.66 cycles per
km 'on the ground:')., corresponding to detail of characteristic
size/stiacing of 1.5-4.5 kms, and therefore including most of
the features of interest to the geologists in this context.
The resultant rose diagram, (Fig.(4.2)10b), showed a significant
reduction in the 'track' direction and was much more in accord
with the anticipated geological. result; the remaining test area&
were therefore scanned using the low,:pass spatial frequency
band.
Another factor affecting the results obtained from scanning
was that the various test areas specified were of differing
sizes=; thus, for a constant illumination intensity, average lineament
density, and spatial frequency spectral distribution, the rose:
diagrams. would be scaled to the size of the test area.. Therefore,
in order to normalise the individual test area roses, the
illumination intensity was adjusted in inverse-ratio to the mag-
nitude of the test area. The roses, from test area?s:2 and 3, •
for instance, (Fig.(4.2)10c,d1 could then be compared in
absolute magnitude with that from test area. l(Fig.(4.2).10b).
The resultant rose diagrams have been incorporated into
a comprehensive report on the 'FAMOUS' area in (WHITMARSH and
LAUGHTON 1976), in which the geological implications are
discussed in detail.
- 145 -
4..3 FEATURE_ ENHANCEMENT
4.3.1 Botswana 'LANDSAT' Image
The input material used in this section was a portion of
a3LANDSAT satellite image supplied by Dr. Mallick of they
Institute of Geological Sciences..
The scene consisted of a region of BotswanaĀapproximate-ly
90 x_60 miles in extent (Fig.(4.3)1). The problem here was an example of a situation that often troubles photogeologists,
i.e. that features of interest, particularly possible linears „
and tonal boundaries=, may be partially obscured by overlying
material such as glacial drift, desert sand, etc. In this case:
the superficial cover consisted of vegetated_ sand-dunes, which
interfered with interpretation over a sizeable area of the image..
Prevailing winds had caused the dunesito assume a.unidirectionaS..
form, so a directional exclusion (blocking). filter (40° of arc
with zero order pass) was used in the Fourier plane to eliminate:
the dune-crest direction, resulting in the image shown in
Fig.(4.3)2. The effect of the filtering operation can be seen
at higher magnification by comparing the unfiltered and
filtered images of Figs.(4.3)3 and 4. In addition to eliminating
the dunes, the filter has imparted a 'grain' on the scene, one
of the effects of which has been to enhance the LANDSAT scan
lines, aligned at about 20° to the (missing). dune crest direction.
This can be explained by considering the nature of the point
spread function produced by the filter, from which the filtered_.
image was built up, as follows.
- 146 -
Figs.(4.3)5 and 6 show, respectively, 10° inclusion and
exclusion filters (zero order pass) with their corresponding
diffraction patterns i.e. intensity point spread functions,
(produced by photographing the Fourier plane with the filters
placed in the object plane of the bench):. As expected the
diameter of the point spread function is 'small' or 'large='
respectively in directions at 90° to the resolved or blockech
range of directions. However, a notable feature of both point.
spread functions is the pair of sharp lobes caused by diffraction
from the 'discontinuity' corresponding to the wedge edges..
When the wedges are used as filters, the filtered image
consists of a convolution of the unfiltered image with the
modified'(filtered> point spread function.. Hence there is a,
tendency for enhancement of linears running in or near to the
direction of the long lobes in the filtered point spread:
function. This effect operates independently of any lineament
enhancement that occurs due to the preferential exclusion or
inclusion of directions over the whole angular range covered:
by the filter. The effect does not seem to have been previously
recorded: in the literature, evem though it has been observed
to be fairly pronounced in certain types of image (particularly
high contrast or 'binary' images such as fracture trace overlays);;
it appears to be= the cause of the 'directional grain' in the
filtered: images of Figs. (4.3 ).2 and 4. A significant consequence of this effect is that, whilst
it can enhance 'genuine' linear features, it can also introduce
spurious directionality, of no geological importance, by its
tendency to 'join up' features lying chance along lines in or
near the lobe directions. Whether such spurious directionality
-147-
is sufficiently innocuous as to be outweighed by the benefits
of the filtering operation (or can be easily discounted from
geological background: information), or whether it is sufficiently
serious as to degrade the value of the filtering operation to
an unacceptable extent, may depend partly upon the nature of the
image involved (contrast, etc.)- and partly upon the skill and
geological background knowledge of the interpreter.
4:3.2 Dartmoor 'LANDSAT' Image
This section reports an experiment to test the ability
of coherent optical filtering to provide textural separations,
which are meaningful. in the context of terrain classification..
A common requirement in this type of analysis is the demarcation
of boundaries:between zones of differing field size, which may
indicate differing schemes of agricultural land use. This is
particularly important in regions of the world where agricultural_
development is proceeding relatively rapidly and which are
otherwise not well_-mapped. However, for this example, a fairly
well-mapped area that of Dartmoor and its environs, has been
employed..
Fig.(4.3)7a shows a simplified map of the area)on which
the boundary between open moorland (including the 'bracken, heath
and rough grassland' category of the Ordnance Survey)., and enclosed
fields, has been taken from Ordnance.Survey 1:.50,000 scale
maps, (revised_ 1970). Figs.(4.3)7b,c show the corresponding
portion of a LANDSAT image, in MSS. wavelength Bands5 and 7
- 148 -
respectively. It can be seen that for the season of the year
at which this image was received, the moorland/enclosure
boundary was somewhat more distinct in Band .5 than.Band..7.
Normal multispectral classification techniques would
probably use data from all bands to define the boundary. For
this example the degree:of correlation between 'map truth'
(as represented by the boundary shown in Fig.(4.3)7a) an&
the Band 5 image, was taken as a standard against which to
compare the results obtained by textural separation. The latter
were generated as follows....
It was reasonedthat the moorland. area should be characterised
by relatively low spatial frequencies, (i.e. slowly-varying
tones)_ representing broad expanses of a few types of vegetation
(e.g.-bracken, heather, grass, forestry).; whereas the enclosed:
field areas wouldicontain a greater proportion of relatively
high spatiali. frequencies (i.e. rapidly-varying tones) due to
the spatially rapi&changes in vegetation type (e.g. crop/pasture/
woodland)-. This was confirmed by the appearance of the diffraction
patterns of the areas-, and is also apparent in a simple visual
inspection of Figs.(4.3)-7b,c;. it was noticed that the 'textural
contrast' appeared to be greater in Band 7 than Band 5;. hence:
the Band 7 image was used for the spatial filtering operation..
Fig.(4.3)8a, shows the Band 7 image subjected to spatial
filtering using an annular filter of pass band1.5-7.5 cycles
per mm. (1.5-7;5 cycles per km 'on the ground' since 1:• 1 million
scale imagery was used), as seen via the CCTV system.. This,
spatial frequency range corresponds to features of characteristic
size in the range 130-650 metres on the ground; therefore the
filter passes much of the 'enclosed field' detail but blocks
the low frequency 'moorland' area, resulting in an image in
0.1
z
- 149 -
which moorland appears tonally dark compared to the enclose&.
field region.
It should be noted that this filter was chosen from a
''standard! library and that the accuracy of moorland/field
separation might be improved by using a filter specifically
tailored to exploit the differences between the moorland/field,
spatial frequency spectra. Nevertheless, the moorland/field
boundary derived from Fig.(4.3).8k7_correlates quite well with
the 'map truth' of Fig..(4.3)7a.
Further enhancement of the boundary was obtained by
'intensity slicing' the image using the video-processor, with
either a.monochrome or 'false-colour' output, as shown in
Figs..(4.3)8b,c, respectively.. It should be emphasised that
the tonal slices here represent regions of differing textural
character in the original image (Fig.(4.3)7c)', and therefore
do not necessarily bear any relationship to its (low-frequency)
tonal composition.
Thus, it has been demonstrated that annular spatial
filtering combined with video-processing can generate
'textural.. slices' which can therefore be used to aid separation
of terrain classes that are distinguishable on textural criteria.
The technique has also been applied to side-looking-radar imagery,
as reported in (HARNETT, MOUNTAIN and BARNETT, 1978);.
- 150_ -
4.4 CONCLUSIONS
Following the successful completion of the main bench, the
latter chapters of this thesis have demonstrated its operation
on remote sensing imagery in the manner originally planned..
These concluding remarks are therefore devoted to a brief
assessment of the extent to which the proposed advantages of
coherent optical techniques have been (or may be) displayed:
in the-real optical processor..
Spemd: The processor has so far been developed to the status-
of a 'research tool.', providing filtered images in seconds
and rose diagrams in tens of seconds, but with manual
setting-up of the input, output and filter stages adding somewhat
to these times. However, should it be required to use the
system for batch processing (e.g. to generate an array of
'subsample' rose diagrams from a single. input image, or to
apply a fixed spatial filtering operation to a series of input
images),, then the conversion of these stages to semi-automatic
operation should be a:fairly straightforward task. A point
to be noted in this connection-is that recent work
(G.D. MOUNTAIN - private communication) has suggested that for
input records on ultra-fineegrain photographic emulsion, the
emulsion grain noise level over the spatial frequency range
of interest may be low enough for the use of a liquid gate to
be unnecessary.
- 151
It should be remembered that the speed of coherent optical
processing compared to serial processing methods should be judged:
in relation to the density of image information in the scene
under investigation. For scenes such as LANDSAT and much other
remote sensing imagery, the amount of data to be handled in
parallel is sufficiently high for the present processor to
maintain an advantage over digital processors in this respect,..
for the immediate future..
Objectivity:. With regard to the compilation of directional
statistics, studies using the main bench have shown promising
agreement between results derived optically and those from
eyeballedd interpretation However, there is: a need for
considerable further testing, using input imagery that includes:.
aAvaried,selection of geological situations,, if the validity
and degree of accuracy of the coherent optical technique is to
be established with sufficient confidence to become a, routinely
accepted tool.
Should this prove to be the case, then it can be envisaged,:
that the coherent optical processor could perform a task that
by present eyeballed methods is arduous, time-consuming and
open to subjective influence; thus allowing a greater proportion
of the photo-interpreter's effort to be concentrated on those
aspects of the work which are less amenable to machine analysis
i.e. association of ideas, and judgement on the basis of
geological knowledge and experience.
- 152 -
Similar remarks can be attached to the results of spatial
filtering operations on geophysical imagery.. It should also be.
borne in mind that spatiaL filtering is equivalent to modifying
the point spread function of an image and may therefore introduce
undesirable optical artifacts into a scene.. A comprehensive
photo-interpretive assessment of the benefits and hazards of
spatial filtering is now desirable=..
Relevance:. It is felt that the most important factors govern-
ing the degree to which the coherent optical processor described
in this thesis: may provide meaningful contributions to image
analysis, both in the geophysical sciences and elsewhere, are:
). C:ontinued testing of the techniquesdescribed:in
the foregoing chapters, their assessment by experienced_.
photo-interpreters and other specialists in the
disciplines•,for which the results are intended, and
possible modifications of the techniques in response
to such assessment.
b) Continued improvements to the input, filter and
output stages, in order to increase the speed and
convenience of use of the apparatus..
c) Increased emphasis on the interaction between
'users' from other disciplines and 'operators' familiar
with the optical technology involved. It is important
that 'operators' understand clearly the nature of the
information that 'users' try to obtain from the imagery,
in order tc develop appropriate techniques for those tasks..
- 153 -
Conversely, 'users' may be able to benefit by the incorporation
of optical concepts such as 'spatial frequency spectra' into
their specialist notions of image descriptors (such as
'granularity', 'directionality', etc.), since they provide a
precise quantitative definition of image properties.
- 154 -
APPENDIX - Convolution The convolution of the two functions f(x). and g(x) is
another function h(x) defined by the relation: +40
h(x). _ S f(x!).g(x-x!)dx'
for which the symbolic shorthand is h(x) =f(x) © g(x).
The convolution operation can be comprehended in terms of the
following pictorial representation;
Suppose that we start with the functions:-
Using the above definition, we see that we first need, to plot
the function 800) .g(x-x/17.
Now g(x'1 looks like this: 9 Cxi)
But g(-x') is simply this function reversed, hence g(-30) looks,
like this:
- 155 -
But g(x-x'): is simply this function displaced by an amount
+-x along the x!' axis, hence g(x-x') looks like this:
9(x-x')
Also f(x') looks like this:.
Thus f (x')jg(x-x' ); looks like this:.
Note that this product function is finite only over the regions:
where f(x') and g(xi-x!) are both finite;, the value of h(x) is:
the integral of the product function with respect to x' between
the limits ± i.e. simply the area:. under the product function:
50x9.'Cx x.')
h(x)
N!
Referring to the above diagram, we can see that as .x changes, so
the function g(x-x.'): 'slides across' the function f(x'), resulting
in a continuous change in the shape of the product function f(x').g(x-x')
and hence of the area-under it.. Note that in general, the
convolution function h(x), is large for values: of m that provide a
high degree of overlap between the functions f(x') and g(xrx'),
I- x
function curves corresponding to
the above-mentioned values of xl.
3(x )e)
Cx') D
• •
•• •• 4.r••
es. xFY tt
-156-
and falls to zero at values of x_that provide no overlap between
these functions. For example;-
A, B, C, D, label positions of
the function g(x-x')
corresponding to the values
x =.0e, 0, , ō , respectively: A
x=-d X=o
A, B, C, D,. label the product
A, B, C, D, label the values of the
convolution function h(x). at the hGH)'
above-mentioned values of xw B
—ōc 6
If f(x) and g(x) both have finite widths Wf and Wg respectively,
we can see that the width of h(x) is given by Wh == Wf + Wg.
From the above, one can consider the convolution operation
to be a form of 'blurring' in which each discrete'point along
the curve of the function f(x) is replaced.. by a 'blur' whose
shape is the reversed curve of the function g(x); h(x) is the
function resulting from the superposition of all_ these 'blurred'
points.
- 157 -
REFERENCES
ARSENAULT, U.H., SEGUIN, M.K. and BROUSSEAU, N
Optical Filtering of Aeromagnetic Maps.
Applied Optics, 13, pp. 1013-1017
. (1974)
BARBER, N.F. (1949) Diffraction Analysis-of a Photograph of the Sea..
Nature, 164, p. 485
BARNETT, M.E. and HARNETT, P.R. (1975 ). Diffraction Pattern Sampling and-. its Application to
Directional Enhancement -4 Geological Image Transparencies.
Trans. I.M..M.;, 84z pp. B53-B55
BARNETT:_, M.E., HARNETT, P.R.., WELFORD, W.T. and WYNNE, C.G. (1976)
An. Interactive Hybrid Processing Facility for Geological
and Geographical Applications.
Proc. S .P.S.E..., 74, (Image. Processing)•, pp. 130-136
BARNETT, M.E. and HARNETT', P.R. (1977).
Optical Processing as an, aid to Photo-Interpretation
in 'Environmental Remote Sensing 2: practices and problems'
(eds. Eric C. Barrett and Leonard F. Curtis); 2nd Bristol Symposium on Remote Sensing, Dept. of Geography, University
of Bristol; Edward Arnold.
BAUER, A.., FONTANEL, A.. and GRAU, G. (1967)
The Application of Filtering in Coherent Light to the
Study of Aerial Photographs of Greenland Glaciers.
Journal of Glaciology, 6, pp. 781-793
BIRCH, K.G.. (1972)
Spatial Filtering in Optical Data Processing.
Rep. Prog.. Phys:, 35, pg. 1265 - 1314
'BARN TT-, N.E. and-WILLIAMS,. T.H.(19797 Video Rate' Image Processing, in •'Rank Prize: Fund 'Symposium on 'E]:ec ron-ia ieds. Schagen apd`ticLean), Press,
- 158
BLANDFORD ,. B- (1970 ) A New Lens System for use in Optical Data Processing, in 'Optical Instruments and Techniques', (ed. J. Home Dickson),
Oriel Press, pp. 435 - 443
BORN, M. and WOLF, E. (1970).
Principles of Optics, (4th Edition) Pergamon,
BRACEWELL., R.. (1965)
The Fourier Transform and its Applications. McGraw-Hill_.
CHEVALLIER, R., I+'ONTATIE L., A., GRAU, G.. and GUY, M.. (1970). Application of Optical'_ Filtering to the Study of Aerial; Photographs..
Photogramme_tria, 26, pp. 17 - 35
COLLIER, R.J., BURCKHART, C.B. and LIN, L.H. (1971) Optical Holography. Academic Press. a ch.7, pp. 164 - 166
CORBETT, F.. (1973): Terrain. Recognition in ERTS-T Imagery by Diffraction Pattern Analysis.. American Society of Photogrammetry, Fall Convention and. Symposium
on Remote Sensing in Oceanography, pp, 431 - 436
CUTRONA:, L.J. et.a1N.. (1966) On the Application of Coherent Optical Processing Techniques to Synthetic Aperture Radar. Proc. I.E.E..E-, 54, pp. 1026 - 1032
DAVIS, J.... and PRESTON, F.W.. (1972)
Optical Processing: An Alternative to Digital Computing.
Geological Society of America, Special Paper 146, pp. 49-68
DE VELIS , J . B .. and REYNOLDS, G.0- (1967 ) Theory and Applications. of Holography. Addison Wesley.
- 159
DOBRIN, M..B.., INGALLS, A.L . and LONG, J.A. (1965)
Velocity and Frequency Filtering o.f Seismic Data using Laser light.
Geophysics, 22, pp. 1144 - 1178
DOBRIN, M.B. (1968)
Optical Data Processing in the Earth Sciences.
I .E.E..E Spectrum, 5, (9) , pp.. 59 - 66
FONTANEL A., GRAU, G.., LAURENT, J. and MONTADERT, L.. (1967)
Etude et Depouillement des Photographies Aeriennes par
Diffraction de la Lumiere Coherente-issue d'un Laser.
(Actes du II e Symposium International de Photo-Interpretation,
Sept. 1966)1..
Archives Internationales de Photogrammetrie, 16, (III), pp. 13 - 22
GOODMAN, , J .W. (1968)? Introduction to Fourier Optics.. McGraw-Hill.
-. ch.7, pp. 154 - 155 b ck74 pp, 171 184
GRAEMENOPODIiO.S , . N._ (1975)
Automated.Thematic Mapping and Change Detection of ERTS.A.Imagess..
Final Report, Itek Corp., N?5-20797
GRASSELLT2, A.., ed. (1969)
Automatic Interpretation and Classification of Images..
Academic Press..
HARBURN, G. and RANNIKO,. J.K. (1971)
Details for an Optical Gate..
Journal of Physics E: Scientific Instruments, 4, pp 394 - 395
HARNETT, P.R. and BARNETT, M.E - (1977)
Optical Rose Diagrams for Lineament Analysis.
Trans. I.M.M., 86, pp. B102 - B106
HARNETT, P.R, MOUNTAIN, G.D. and BARNETT, N.E.. (1978)
Spatial Filtering Applied to Remote Sensing Imagery.
Optica Acta, 25, (8), pp. 801 - 809
-16o -
HEIDECKER, E.J. and SUPAJANYA, T. (1975) A Simple Optical Method for Routine Analyses of Fracture Traces-.
Trans. I.M.M.., 84, pp. B56 - B58
HUNTINGDON, J.F.. (1969) Methods and Applications of Fracture-Trace Analysis. in
the quantification of Structural Geology..
Geological Magazine, 106, pp. 430 - 451
JENSEN, N. (1973) High Speed Image Analysis Techniques.
Photogrammetric Engineering, 22, pp. 1321 - 1328
LAUGHTON, A.S. and RUSBY, J.S.M. (1975). Long-Range Sonar and Photographic Studies3of the Median Valley
in the FAMOUS Area of the Mid-Atlantic Ridge near 37°N. Deep Sea Research, 22, pp,.. 279 - 298
LENDARIS:, G.G ► and; STANLEY, G.L... (1970) Diffraction Pattern Sampling for Automatic Pattern Recognition. Proc. I.E.E,, 58, pp. 198 --;216
LIPSON, H., ed. (1972): Optical Transforms. Academic.. Press..
McCULLAGH,. M..J . (.1971): Optical Data Processing: A-New Geographical Tool.
Unpublished report for Kansas Geological Survey/Department
of Geography, University of Kansas_
McKEITH, P.L.C. (197 .)• Texture and Pattern in Earth Imagery.. MSc. Thesis, University of London..
- 161 -
NOBLE, V.E. (1970)-
Ocean Swell Measurements from Satellite Photographs.
Remote Sensing of Environment, 1, pp.. 151 - 154
NORMAN, J.W. ands HUNTINGDON, J.F. (1974): Possible Applications of Photogeology to the Study of Rock Mechanics..
Quarterly Journal of Engineering Geology, 7, pp. 107 - 119
NORMAN, J.W.. (1976)_ Fracture Trace_Analysis as a Subsurface Exploration Technique..
Trans. I.M.M.., 85, pp. B52 - B6a
NYBERG , S:.`, ORHAUG , T and S VENSSON , H.. (1971)
Optical Processing for Pattern Properties..
Photogrammetric Engineering, 7, pp.. 547 - 554
O'NEILL:, E.Iw.. (1956)'
Spatial Filtering in Optics..
I..E.E..E.. Trans. Inf.. Theory, (2), pp. 55 - 56
PINCUS, and DOBRIN, M.B. (1966);
Geological Applications of Optica]. Data Processing.
Journal of Geophysical Research, 71, pp. 4861 - 4869
PINCUS, H..J .. and ALI, S.A.. (1968) Optical Data,Processing of Multi-Spectral Photographs•.
of Sedimentary Structures...
Journal of Sedimentary Petrology, 38, pp. 457 - 461
PINCUS, H.J. (1969)
Sensitivity of Optical Data.Processing to Changes in Rock Fabric.
International Journal of Rock Mechanics and Minine Science,
6, pp. 259 - 276
PRESTON, F.W.. and DAVIS, J..0 . (1972)
Application of Optical Processors to Geological Images, in
'Machine Perception of Patterns and Pictures', (ed. P.A. Walker) ,
Institute of Physics, pp. 223 - 232
- 162 —'
PRESTON Jr., K. (1972).
A Comparison of Analog and Digital Techniques for Pattern Recognition..
Proc. I,E.F.Ef, 60, pp. 1216 - 1231
PRESTON Jr., K. (1972).
Coherent Optical Computers. McGraw-Hill:.
a —ch. 6, pp. 195 — 205 b - ch. 5, p. 116
SHULMAN , A.R. (1970 )_ Optical Data Processing. Wiley.
a - ch. 4
STILLWELL, D. (1969)
Directional Energy Spectra of the Sea, from Photographs..
Journal of Geophysical Research, 74, pp. 1974 - 1986
TAYLOR, C.A. and LIPSON, H. (1964)
Optical Transforms.. Bell..
TIPPETT, J.T-. et.ali. (1965)
Optical, and. Electra-Optical Information. Processing. MIT Press...
VAN DER.LUGT,.A (1964).
Signal Detection by Complex Spatial Filtering.
I.E.E.E. Trans. Inf. Theory, IT-10, pp.. 139 145
VON BIEREN, K. (1971)
Lens Design for Optical Fourier Transform Systems..
Applied Optics, 10, pp. 2739 — 2742
WHITMARSH,. R.B.. and LAUGHTON, A.S.. (1975)
The Fault Pattern of a Slow-Spreading Ridge near a Fracture Zone..
Nature, 258, pp. 509 - 510.
`4HITMARSH, R.B.. and LAUGHTON, A..S- (1976) A Long-Range Sonar Study of the Mid-Atlantic Ridge Crest
near 37°N. (FAMOUS Area) and its Tectonic Implications.
Deep Sea Research, 23, pp. 1005 — 1023
- 163 -
WOJTOWICZ, T. (1971); A. Study of some opticaa properties of photographic emulsionsi
with particular reference to rapid data processing.
PhD. Thesis, University of London..
WYNNE,. C.G. (1974). Simple Fourier Transform Lenses.-..
Optics Communications, 12, pp 266 —274
YASUHIRO SUGIMORI (1975): A study of the application of the holographic method to the
determination of the directional spectrum of ocean waves. Deep Sea Research, 22, pp 339 - 350
rn : Totally-Vignetted " it rt
CONTENTS
VOLUME I - TEXT
CONTENTS OF VOLUME II
VOLUME II -- FIGURES
CONVENTION: PART P
CHAPTER P.Q.. FIGURE FIG(P.Q)S
Optical Diffraction (Fourier Transform) Image Analysis
Showing Effect of Dominant Directionality
tr It r tr. Granularity."
Directional Filtering
FIG(2.1)1 One-Dimensional Fourier - Transform Pairs
2
3 Two- 4. tn
- 5 Diffraction from an infinite screen
6 Focussing of diffracted light by a lens
7 Basic Coherent Optical Fourier Transform Spatial Filtering Bench
8 Spatial Frequency Synthesis of a square wave
9 Illustrating Optical Fourier Analysis
10 .Infinite Aperture System: (Finite Object/Image Planes; Infinite Fourier Plane3)
Finite Aperture System: Nen-Vignetted Spatial Frequencies
ft tf:
" : Partially-Vignette& "
15 Aberration Correction Requirements for Transform Lenses
16 Typical Illumination System of a Coherent Spatial Filtering Bench
17 'Classical' Coherent Spatial Filtering Bench Arrangement
18 Optical Examples of Transform Pairs
19 Directional Filtering (Separation of particular direction)
2Q. Annular ft " frequency)
rn " ft
it
It
tt:
"'
it
ft "' " Fourier Plane Spatial Frequency StLP
tr
tr
FIG(2.2),1 Pilot Bench Layout
3 " if Display Functions
4
5 Display Requirements
6 CCTV Performance: Object/Image Plane
it s Fourier Plane Display
8 Sonar Image of Seabed off Hartland Point, Devon
9 Direct photography of diffraction pattern at
10 two exposure levels
11 Photography of diffraction pattern on CCTV monitor
12 at two contrast settings
13
14 Microdensitometer traces of a step-wedge
15 photographed directly and via a CCTV system
16
FIG(2.3);1 Diffraction Pattern of Oil-Immersed.(Gated.) Sonar Seabed Image
2 Diffraction Pattern of Sonar Seabed Image in Air
3 Video Processor 'Intensity-Slicing'
if LANDSAT Image of Grand Canyon Area
5 Sketch Map If' rr n n°
6 Unprocessed Diffraction Pattern
7 Intensity-S-liced: "
8 Relief Mode
9 Contour Mode
FIG(2.4)1 Diffraction Pattern Sampling - Schematic Diagram
2 Sector Specifications-
3 Sector Disc Construction
if Sector Sampling Unit - Schematic of Mechanical Aspectsr
5 rr - n• rr — It " Optical "'
6a " "' " - Master Assembly Diagram b
All Diffraction Patterns from LANDSAT Image
c rr n It — Dimensioned: Working Drawings
d..
7 Response to slit object: unaveraged linear plot
8 Illustrating effective 'imaging' of object onto photomultiplier diffusers
FIG(2.4)9 Photocathode Sensitivity Map (Unaveraged)
10 " " " (180°-Averaged)
11 Response to bar object: linear plots
12 Schematic Diagram of Semi-Automated Diffraction Pattern Sector Sampling System
13 Schematic Diagram of Control Box Operation in the Sector Sampling System
14 Sonar Seabed Image, Hartland Point, Devon
15 Linear Plot of Sector Sampling System Readings from Seabed Sonar Image.
Polar Plots (Rose Diagrams). of Sector Sampling System Readings from Seabed Sonar Image
18
19 Rose Diagrams from Seabed Sonar,Image.
20 illustrating the effeēt of omitting Oil'-Immersion
21 Rose Diagrams from Seabed Sonar Image?: Various Spatial Frequency Bands;- Absolute Values_
22_ Rose Diagrams from Seabed Sonar Image=: Various Spatial Frequency Bands - Normalised_Valuesj
23a- Sector Disc Centring Unit - O-verall Assembly Diagram
b in ri. ni " - Dimensioned. Workshop Drawings;
24 Aerial Photograph of Limestone Area, Yorkshire Penninesi
25 Rose Diagram for Pennine Limestone Area.: ' Unaveraged Plot - Miscentred Sector
26 Ross Diagram for Pennine Limestone Area: 180 — Averaged Plot - Miscentred Sector
27 Rose Diagram for Pennine Limestone Area: 180°— Averaged Plot - Centred,Sector
FIG(2.5)1 Directional Spatial Filter Types
2 Directional Inclusion Filtering of Seabed. Sonar Image ('Hartland Point')
3 .Directional Inclusion Filtering of Limestone?Area Aerial Image ('Yorkshire Pennines')
4 Directional Exclusion Filtering of ERTS. SatelMi.tee Image E1007 00362 (S.W . Angola)
5 Rose Diagram from portion of ERTS Image E1007 00362.
6 Directional Inclusion Filtering on Seabed Sonar Image ('Hartland Point')
16
17
FIG(3.1)1 Holographic Matched Filter Construction
2 Filtering Using the Holographic Matched Filter
3 Main Bench Layout - Display, Sampling,
Passive Filtering Modes
4 Main Bench Layout - Holographic Matched Filtering
Mode
FIG(3.2)1 Beam Expander and Collimator
2 " " Unit
3 " " and Reference Beam Mirrors
if C ol'l imat or " " "' "
5 'Through-the-Lena' Reference Beam System
6 'Beside-the-Lens' It ". "'
7 Practical " tr II
8a Traverse Table - Assembly Diagram
b. " "' - Full Workshop Drawings
9a Collimating Mirror Support --General View
b "' It "' - Detail of Adjustable=
Support Unit
10 Specification for Fourier-Transform Lenses
11a.. Transform Lens - Specification of Glass Elements
b m "- - Lens Barrel Construction
12a-- Lens Support Unit - Assembly Diagram
b It " " - Full Workshop Drawings
13a Sliding Base Plate --Assembly Diagram
b H rr "' _.Full Workshop Drawings
14 First Transform Lens and Supporting Units
15 Second " " II' II' tr.
16 Rotating Platform Assembly - Notes-
17 rr it it - Completed. Assembly Drawing
18a-c tr It It - Assembly Drawings
19a-g if II It - Full Workshop Drawings
20 Rotating Optical Bench: Bearing
21 It It 'r r Wheels
22 Liquid Gate:• Object Slide out
~3 It n. ; It m in
24 " "' : Full Workshop Drawings
25 Textural Spatial Filter Types
26 Filter Stage
27, Image Stage
FIG (3.2) 28 Mirror Mount - Full. Workshop Drawings
29 Beamsplitter Mount - Full Workshop Drawings,
30 Kinematic Mount - Main Assembly Drawings
31 Diffraction Pattern Display Path
32 " " Sampling Path
33 " " " Unit Front View
34 " It " " Top View
35 Imaging Display Path —Beamsplitter
36 rr rr 'r - Lens
37 " " " - Mirrors
38 rr '1; " - Images:
39 Auto/Cross-Correlation Display Path - Beamsplitter
4o m rr IT " " — Auto/Cross- Correlation Plane
41 General View of Bench from 'Image Plane' End.
42 " m " " " 'Object Plane' End
FIG(4.2)1 Fracture Trace Overlay
2 Diffraction Pattern from Overlay Area.A
3 Optical Rose Diagram " it " It
4 Aerial Photograph of Fracture Trace Overlay Area
5 Diffraction Pattern from Airphot a Area A-
6 Optical Rose Diagrams " rr I' rr
7 8 "' " Diagram " It " B
9 'GLORIA' Sonar Image of 'FAMOUS' Area. — Mid-Atlantic Ridge
10 Optical Rose Diagrams from Sonar Image
FIG(4.3):1 Botswana 'LANDSAT' Image - Unfiltered
a m m " -Filtered:
3 " "c " — Unfiltered (Enlargement)
4 "' tr "' Filteredi It
0 5 10 Directional Inclusion Filter (Zero-Order Pass)
with corresponding Diffraction Pattern
6 100 Directional Exclusion Filter (Zero-Order Pass) with corresponding Diffraction Pattern
7 Dartmoor 'LANDSAT' Unprocessed Images:
" Processed: "' 8 rn
[I Cr ( 1. 2) I
\ \ \ \
OPTICAL DIFFRACTION (FOURIER TRANSFORM) IMAG-E ANALYSIS I
o.B:JECT TRANSFoRM
,"" --- ............ ,
' .
' .....
/ / / v ~~ ' b,,,\e
I p \ \
'I r~ u. 1-'-
~/ I \ , p I ' , I V' /' ' // ......... ....__-""
Ft&-(1·2) 2 SHoWING'-- EFFEC.I OF OoMI NANT OIR.EC.IIONALfT'(
OB.:TE.c..T
FtG-(1·2)3 SHOWIN<r EFFEC..T OF DOMINANT G-R.A.NVLARITY
OS:TE:C:.T
TRANSFORM
FILTER BLocItS oFF ALL OF TRAAISFORM EXCEPT THAT WHICH CORRESPONDS TO NEAR-V R- mkt_ LINES
FIG- (1.2)4.
DIRECTIONAL FILTERING-
FILTERED IMAGE
61
O.
6.
e-7119 ae 9auss in rt 54u.ss io r1
ru - q
FIG (2.1) 1 ONE-DIMENSIONAL FOUR/ER--TRANSFORM PRmRS
f(x)
1 FCu)
'rect' func o4
i
I.0
q. 2
Co rlsf0.nt
i•0
>u
Ar x
-
FtW
•••
IL
+2 +4- -z ā -z -It -+ -L 0 +i 41 tit 4L tt:+;>-
0
x
F1G-C2 . I) 2 ONE -'DIMENSIONAL FOURIER-TRANSFORM PAIRS
COMB FUNCTION
+.500 e- A 664-1)
COMB FUNCTION
Y
(
coo
Fim) A
1 1,111111 1;z..-{-
1
RECTC'9 -I -. 3. ti 41
4 4
SQUARE +o0 WAVE L
+0r)REcTCx) @ M S(x_2J )1 1sINc. x 7 Sc,_ 2)] MCo LAAT EP
REcr(x).S(y)# SiNc(u) .
RECT(XĪ. I SINc(u) . S(v)
PILL (X,y) AIR y (u)v)
FF(G(2.1)3 Two-DIMENSIONAL FOURIER- TRANSFORM Pi IRS,
FIG-(2.1)4- Two-DIMENSIoNAL FoURIER—TRjNSFoRH PARS
f(x19 ailf RAW)
i
f R CT(x) SN —24]. 0LS ilk/ CC4) ao .coa(t- i )J • S(v)
9
got
re !
eivir
j> 1~ - / r 1 % it t,
<f ~
PILL (4y) Q-± g(x-n,y-m) e#- AIRY&Wv) ._Z S(Lk- n,v-m) .4 i - ■
COLLIMATED COHERENT 1.164-IT
COMPLEX AMPLITUDE A3
DIFFRACTING. SCREW ELEMENT AMPUTVpe TRANSMITTANCE ii(x)
F1G(2 •I)6 FOCUSSING OF DIFFRACTED LIGHT BY A LENS
I<
LENS DIFFRACTIWCr SCREEN
F1G(2.1) 5 DIFFRACTION FROM AN INFINITE SCREEN
Ix I
BACK FOCAL PLANE OF LENS
f 1.4 f -1• f
coL.LIMATD
COHERENT U4it T
WAVELENlrTH X
yz
T
°6TEGT PLANS
FIRST TRANSFORM LENS
FOURIER PLANE
f
FIG(2.I)7 BASIC COHERENT OPTICAL- FOURIER TRANSFORM SPATIAL FILTERING- BENCH
SQUARE WAVE
SOO
t', -1P,_ tk Cx
31
FIG C2.1)2 SPATIAL FREQUENCY SYNTHESIS OF A SQUARE WAVE,
CONSTANT iTC7)
1ST HARMONtC.
3Ro HARMoNLC
-11-WAAPAtobvt4(
SQtJARE WAVE= sum OF MoAuLATEP Carla = SUM or'
CogSTANT -- HA2wl0 $ c JTRAL -- StPE 6 FuNrc1 oKS
/
N. / 48- f u.nc bons /
fpo ints cf hi-h co r ipLe) ampLi twde strtn9 .h f wayeLen3tll o$ L jkt
A 5
Rn:
%A
NAk
FIG-(2.1)9 ILLusTRAT1NG OPTICAL FOURIER ANALYSIS
0T B- PLANE S afia~ crests i tromil
ratin9 ~of complex cutrtitucteI
TRANSFORM ~.,' ' LENS
FOUR(ER. PLANE
OBJECT PLANE
showing Q notionAL sinusoidal "5mtirg"
FOURIER PLANE
showing t msuLtant roc-functions
yr
S = spatial frejuertc5 of 5raten9 f = focal, lett6 of transform Lens
FIG (2. I) 1 0 INFINITE APERTURE SYSTEM : (FINITE OBTELT/IMAGE PLANES; INwNITE FOURIER PLANE)
f
A
FIG-(2.1)11 FINITE APERTURE SYSTEM : NON-VICrNETTED SPATIAL FREQUENCIES
FI Cr(2. I) 12 FI N I TE APERTURE SYSTEM ? PARTIALLY- VIGNETTED SPATIAL FREQUENCIES
L LZ
f f f
L, >i<
f >1
I.
Ft&(2.1)13 FINITE APERTURE SYSTEM : TOTALLY-VI&NE7TED SPATIAL FREQUENCIES
FIG-C2.1) 14- FINITE APERTURE SYSTEM : FouRIER PLANE SPATIAL FREQUENCY STOP
FlG (2.1) IS ABERRATION CoRRECTIoN REQUIREMENTS FOR TRANS FORM LENSES
f
IF j
ADERRA710N CORRECTION RE LHREP FOR: (LI) co -0'8AUC FOCAL PLANE (Li) FRoNT FOCAL PLANE-I~oo
[~.e. UNAI3ERRATEp POINT SPREAD FuNCTIoNS IN FOURIER PLANE]
• 0
V L, I F I 1..2.1..2.
ABERRATION CoRRE(TION REQUIRED FOR: (L,) FRONT FOCAL PLANE-Poo (L2) co -ar BACK FOCAL PLANE
jj.e.UNABR:RRATEP POINTSPREAp FuticrioNS IN 11 1#\GE PLANE]
0 fL,
T
t
a
FIG(2.I)17 CLASSICAL COHERENT SPATIAL FILTERING BENCH ARRANGEMENT ,
E BEAM EXPANDER LENS
P r PINHOLE FILTER
C = COLLIMATOR LENS
Li = FIRST TRANSFORM LENS
f2 = SECOND TRANSFORM LENS FocAL LENGTH aF TRANSFORM LENSES
O = Ol3ZECT PLANE. F = FOURIER PLANE I = IMA&-E PLANE
Fl&-(2 .J)I'i oPTlCA'- EXA.MPL£5 OF TR.AN.SFot<.t--1 PAIR-S
DIFFlt.A<.TlON PATTft'tN
ri&C2-I)l1 p,KECcc
(SEPARRTIoN of PMT1c0Lk1t PAC crroN)
OB 1EC7
FIGC2-1)2o ANN u(Aft F►c—TGf 1.J6.
(5'e/1W-07101V or PRftTi c uW rgo o wcy)
}
r-- TRANSF02M5 FIL7Ev it-1&G-ES
1
1a EN-is PLIT7ER.S RELR/ 3 LENS
M, oR
0 444
M I( c*, M2.
SEccr.l D Fou IER--rarNSFORM
LENS L2 ti IC(toS<oeE oa 3Ec-nVE
04A01 )FIER)
~ 5
- oBSevATI oN , Sc artni
FIc,-2.21 PILOT BENCH LAYOUT
.4
SCALE : * FULL SIZE 1
FIRST 7 Fou c a`T1I('4 f-oQM
LENS L ~
MI
LL
i
FIG. S•(2•2) 2-,I) If PILOT BENCH DISPLAY FUNCTIONS
FI Cr. (2.2) 2
Ls
FIG.C2.273 M1 ,.....
Ls
7 MAc,NIFIoe SECTION OF
FouRtIER PLANO
/ 1144NIFIED
!MAGI PLANA
•
0
SU BS ECTION MAGrNIF1CATION
S Dys - . REQUIREMENT
INFORMATION ----►--- QUANTITATIVE CONTROL FLOW PATH
• -1).-• -a SWITCH CONTROLQAN UTITATIVE}CONTROL ērQVAL1TATIVE
oB?ECT PLANE
FILTER FOURIER PLANE
IMAGE PLANE
O
0
0
0
SUBSECTION -$ MAGNIFICATION
VV
0
EVALUATION (HUMAN)
5 15 < 30 *
600 200 >100 t
F(42.2) 6 CCTV Performance: Object/Image Plane (f=25mm f/1.4 TV Lens)
i•.AGNIFICATION (Television Screen/Optical Bench)
FIELD SIZE (Optical Bench) mm
FIELD AREA (Percentage of 55mm x 55mm ERTS Frame)
RESOLUTION (Optical Bench) c/mm
RESOLUTION ('Ground') metres (Using 55mm x 55mm ERTS Frame)
x 5 x 15 x 30
Eo x 60 27 x 20 <13 x 10
160% 1 ū% < 4/
(* Over reduced field size; picture distortion caused by using TV lens at conjugates unsuited to its design makes Zone 2 of TV screen image unusable)
(t Resolution governed by input frame - not by TV system) All figures quoted are estimates for Main Bench extrapolated from Pilot Bench experimental measurements
FiG(..2)7 CCTV Performance: Fourier Plane Display (f=25r?m f/1.4 TV Lens;
Mt1GNIF IC ATION (Television Screen/Optical Bench) x 5 x 15 x 150 t
FIELD LIMIT c/mm 90 30 3 (Fourier plane spatial frequency at edge of TV field)
RESOLUTION (Optical Bench) c/mm 5 15 <150 *
RESOLUTION ('Fourier') c/mm 0.6 0.2 >0.02 (Spatial frequency discrimination)
Cr Using enlarger lens for primary magnification of x 10) (* Resolution losses due to TV lens - see FI_i(2.2)6 footnote) All figures quoted are estimates for Main :,ench extrapolated from Pilot Tench experimental rneasur.nents
FIG (2 2) g SoNAR IMAGE OF SEA3EP OFF HARTLAND POINT, PEVON _ (DIFFRACTION PATTER 4 5 BLOW ARE TAKEN FROM THE ErvCi2Li-EP RQ F/l)
FIG5(2.2)%I0 —0'
DIRECT PHo-coo-R1kPHY
oF pIFFRACTIo NJ PATTERN
Al- Two EXPosORE LEJELS
FIGs(2-2) 11) 12 —I•
PuoTOrr2APt-t7 of DIFF{1 CTDN
PAITERN oN CCTV rioNCTb2
RT -NJo Co ,J72P-sT sETrinf~S
• l•-•;. 1-717-1..,
.1
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! I .__1. L 17_-:•17-- .. L. __I . , I...•• i . - .
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• I , , I 1 .1 , - : : I .'
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; • • e
.... i • ; I •7 j- . • -4-
micRoDENSIToteIETER TRACES OF A STEP- WE DG-E PHOTOGRAPHEDD DIRECTLY frIcr-C2-2.)13] ) AND VIA A CCTV SYSTEM frl &5.(2.2) ne, 15, . rtf VERTICAL SCALE REPRESENTS DENSITY IN AR51711ART UNITS
• • ; • ! ;; . ! _
2-
• • • I .. ,...i. : _ i . I._ . • . . , i
__EIG,42.2.1:15 .r-1-7- -:- --- •-'• -I. 1. 1 . • ' ; ! • 1 ; ; 1 _,._1.. i. _..... - --F.:-
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, . . .
, . • ; ; ; i I ! f-o-,„,„,„....4
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--71-71---f-- --;-- -;-- -4.-- -'• -- --'-t-- -----1-1. -
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.; _I 1 _ . _- _':_.:1. ..I .. I-_-.7.- :_._. ...'L!. • . . . • - i-r-"T- 7-- ,
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n6_0_3)1 Di FFscV J pA-r-rcnl of 0/L-1 rr r ats‘ o (6- OrED) so Weta SEA-Oki it'.
FI c. C2.3) 2 PI c ri o / PPrrr A of se rA-rt SEA-Q EJ' 4GL 1A1 Ala
>TI ME
VIDEO SIGNAL LEVEL A
pROCESSEV VIDEO SI AL
WINDOW
I
2
3 4
LEVEL
1
F1&(2.3)3 VIDEO PROCESSOR INTENS ITY-SLICING'
VIDEO SIGNAL LEVEL
PEAK WHITE
A A (TV SCREEN IMAGE INTENSITY)
UNPROCESSED VI CEO SI(rNAL
4
RANGE 1
WINDOW RANGE 2. RANGE 3 RANGE 4..
LEVEL BASE
aLACK >71 ME
r
`TV SCREEN IMAGE Po•S I TION) 1
Et&C2.3)6 UNPRocESSED
pIFFRA(TION PATTERN
F1 C-4 2 -3)6- sg.TcN rt& of G-4 4-Nlo c/MIY6.f PKAA
4110t
11
FIG- (2 3)7 INTcrvsrn'-sucEp
piFFRAC IoN PRTTc,RN
"PA 444,v F1G(2.3) $ RELIEF MODE
PIFFRACT1oN PriTTERN
LANDSRT 21R-cz oF (nfAnlo CANYo'.I / 42L
FiCr(2.3) 9 coNsYOug MopE
PiFFRAcrioN PATTERN
4
Ak g#41.1%
vsogi 401_,o.v 2o Km
11111111
CAL_ DIFFRAcrloN PaTTERNs r2o r1 L A Np s AT T H R{rE)
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AUTO/CEO S-CORRE .ANON PLANE U TI1ERMOPL.ASPIC IiOLCM. i:F':TI :G UNIT K SAMPLING CONTROL UNIT V1,V2 ANALOGUE VIDEO-PR3C-SSi.iiG UNITS
L1, L2 P0UK1:R--TRANS RM LENSES THERMOPLASTIC HOLOGRAM CUA FG NG UNIT
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L I FIRST Fot)14ER TRAKI)FoiM L.1 N5
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COI.UMAT02 L REFEREKCE BEAM n, 2¢o2S
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C CaLL1MPrToa
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FIG(3.2)10 Specification for Fourier-Transform Lenses
Transform Lens for Spatial Filtering Project for Department of Industry
Equivalent Focal Length: About 700mm, not critical.
Back Focal Length: Greater than 200mm.
Conjugates: Corrections as below for two sets of conjugates:- (a) image at infinity (object imagery) (b) object at infinity (transform imagery) Thus the design is probably symmetrical since both object and transform fields will be of equal sizes with 700mm equivalent focal length.
Object Format: 55mm x 55mm - applies to conjugates (a).
Object Field Angle: 10.058 radians (13.3°) - also for conjugates (a).
Transform Field: About 80mm diameter, depending on the exact value of the equivalent focal length.
Aperture: The aperture stop for conjugates (a) is at the transform plane, i.e. it is telecentric; the field stop for conjugates (a) is the aperture stop for conjugates (b); individual components must be large enough to ensure no vignetting of pencils for conjugates (a) at maximum field angle.
Wavelength Range: The system is to operate in monochromatic light, ultimately 0.488 microns wavelength. It would be useful if the design were also correct at 0.33 microns apart from changes in equivalent focal length and back focal length.
Aberrations: The system should be diffraction limited for both sets of conjugates for spherical aberration, coma, astigmatism and field curvature;distortion is not important for either conjugate. Coma is strictly not important for conjugates (a), since the complete optical system comprises two lenses with magnification -1 overall. However, if each lens is symmetrical, the correction of coma for conjugates (b) will ensure it is corrected for conjugates (a). If it is not possible to comply with diffraction limit correction for both conjugates, the lens could be made asymmetrical and the strict correction aimed at only for conjugates (a); however, we should very much prefer to have an aberration-free transform plane also.
. i
AIR SPACE AIR SPACE
2 1
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In the table below, bra~keted figures refer to optimisation using catalogue glasses; Plain figures refer to optimisation using melt glasses, made test plates and measured element thicknesses.
Surface Radius of Spacing mm Thickness mm Edge mm Glass Refractive InC.=x Humber Curvature mm Diameter Type !1el t/(Catalogue)
1 +162·2o8(+162·0CO) 19·2550(19·4978) 104 ·0CO EaLF4 1·58731(1·53711) 2 -1 68 · ~01 ( - 16~ · 71 1 ) 0·6237( 0 ·7370) 3 -1 66 ·7q;:;J _ .-::;;; . l•;c;~ 7 •1000( 6·6341) 102·000 S72 1·66209(1·66123) 4 +2522 · c63( + 2~-- 3 · ·J9i3 1~1·9803(110·6561) ') +1~~ · ub~( ~ 1?c; · ?~~\
6 +91 • ~97( +Y 1 · ~~~) 15·2400(17·0061) 80·000 BK1 1•51558(1•515t6)
7 - .) 1 . -:;::)C. ( - '-i • • -; 'l 130·4233(132·113u) 8 -17'5· 4,:: -.:.( - 17c; . 7'"''7':
15·2680(17·0061) 80·000 BK1 1·51558(1·515E6) _9 -25_2::> • ~G6( - 2c;: • ': 0 ·~
112·2271(110·6561) 10 + 166 · 7~2( ~ 1~6 · ~2))
7·1500( 6·6341) 102·0CO SF2 1·66209(1·66123) 11 + 16~ · LIJ!l -4 1 f-)~ · 'I ' 1 '1
0·5E05( 0·7370) 12 -162 ·298( -1 62 ·9CO) 19·2950(19·4978) 104·000 BaLF4 1·58731(1·58711)
Front Conjugate 181·65~m from Surface 1 Back Conjugate 205·60mm from Surface 12 Object Field Dianeter: 80mm Wavelength: 488nm Transform Field Diameter: 62mm Equivalent Focal Length: 700•00mm Object Field Angle: ±0•044 radians
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.. F1G-(? 2) /6 ATING- PLATFORM ASSEMBLY - NOTES The p'.iri.ose of this assembly is to provide a platform which will
sulpert a heavy lens and its mounting (about 50 kg weight), and is
capable of intermittent rotation about a distant bearing. The wheels on
which the platform is to be supported. will run on the surface of a cast-
iron table-top, to which the base of the bearing will be secured.. The
following description of the design accompanies. Figs(3.2)17,18, which
illustrate the method of construction..
Part :1 is the bearing base fixed plate, upon which rests part B,
the bearin.; base movable plate. It is desirable to have provision for
making occasional adjustments to the position of the axis of the bearing.
To acheivn this, the fixed plate is to support four horizontal translation
.,crews, which act on the sides of the movable plate. Between adjustments,
tt:!. movable plate can be clamped to the fixed plate by means of four bolts
e• ,:i)pcd with large diameter washers, running through large diameter clear
ho7.:s in tae movable plate and tapped into the fixed plate.
In plan, both thses plates are of an H-shape; this is dictated by the
fact that, when finally attatched to the table, they will occupy a confined,
~:nac:• between other parts of apparatus..
Part C is the bearing pin assembly, consisting of a pin, upper and
bushes, a ball-race bearing (supplied with these drawings), and a
loekin; nut.. To make provision for the possibility of future modifications.
to our apparatus, it is desirable that the bearing pin be detatchable from
the surrounding assembly.. In consequence, the pin should be a sliding fit
through the ball-race and both bushes, and should locate in the socket of
the bearing base movable plate (part B), in which it can be secured by a
::ircugh-bolt.
The lower bush rests on top of the socket, and the inner race of the
ball-race bearing is clamped between the two bushes by the locking nut
mounted on the threaded section of the bearing pin.
The outer race of the ball-race bearing is located between the
upper and lower parts of part D, the bearing head, and should be a
press fit into the recess of the lower part.
Part D is connected via part E, a connecting arm and spacer, to
part F, the platform; part F is provided with clear holes for the
attatchment of the lens mounting, 'and is supported by two wheel units,
part (3.
The design arranges for the points of contact between the wheels.
and the table-top to be directly beneath the centre of gravity of the
combined. lens/lens mounting/platform massa It is desired that the top
surface of the platform be about 1" above the table-top, so the wheel-
units have been designed to be bolted to the top surface and to project
through slots out in the platform; the sides of these slots are not
intended to act as guideways to the wheel units, whose location is
fixed by the positions of the securing bolt-holes; the units are angled,
such that the wheels run along the circumference of a circle centred at
the bearing axis..
Each unit consists of a ball-race bearing (supplied with these drawings)
whose outer race rests on the table-top, and whose inner race is a press
fit on a spindle, that/ is secured by a split-gin or grub-screw in the forks
of the unit.
Each of the parts A-l3 is the subject of a separate dimensioned
drawing shown as Figs(3.2)19a-g..
COMPLETED ASSEMBLY DRAW! NG
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