Two Reconstruction Methods for Microwave Imaging of Buried

IEEE TRANSACTIONS ON COMPUTERS, VOL. c-24, NO. 4, APRIL 1975

Two Reconstruction Methods for Microwave Imaging

of Buried Dielectric Anomalies

ON-CHING YUE, MEMBER, IEEE, E.L. ROPE, AND G. TRICOLES, MEMBER, IEEE

Abstract-Microwave imaging of anomalies, such as voids or dis-continuities, in optically opaque regions is described. Images were

reconstructed with two techniques. The experimental techniqueutilized laser light for reconstructions from detour phase hologramsthat encoded data measured in the region of Fresnel diffraction.Examples of images are presented for smooth and rough interfaces.The numerical reconstruction technique was based on the angularspectrum technique, and an approximate propagator was derived todescribe propagation through two, homogeneous dielectric layers toone anomaly. Image quality was acceptable for either reconstructionmethod, but the optically reconstructed images are rather smallbecause scale reduction is limited in practice.

Index Terms-Holography, image formation, microwaves.

I. INTRODUCTION

ADIO WAVES have long been utilized to investigateinaccessible inhomogeneities inside or on the bound-

aries of dielectric regions. Analyses of reflected andscattered waves yield information about the compositionand configuration of the ionosphere and troposphere as

well as subterranean layers and the Earth's surface [1],[2]. More recently, imaging with radio waves has supple-mented analyses of wave propagation. The first imagingapplication appears to have been a terrestrial holographicsystem to image ionospheric layers [3], [4]. Maps of largeareas are formed by synthetic aperture radars [5].

This paper describes microwave imaging of anomalies,such* as voids or discontinuities, in optically opaque

regions. The anomalies were located within a solid di-electric region, so they were inaccessible, but they were

at relatively short distances from an interface with air.The images were formed from phase and intensity measure-ments made with external apparatus.The application emphasized involves imaging anomalies

in soil; for example, to locate defects in a roadbed or ingeophysical investigations. However, images can also beformed for nondestructive setting of laminations in manu-factured plastic parts such as radomes, which have twointerfaces with air. The anomalies were essentially voids,local regions with dielectric constant below that of thesurrounding regions. The anomalies were flat, a few wave-

lengths wide, and a fraction of a wavelength thick. Theywere located in a dielectric region, approximately a half-space, separated from air by a single, flat interface.

Manuscript received July 15, 1974; revised October 25, 1974.The authors are with the Electronics Division, General Dynamics,

San Diego, Calif. 92138.

Images are presented for smooth and slightly rough bound-aries. Boundary curvature was omitted, but imaging forcurved boundaries seems plausible. The anomalies weused were sheets of low dielectric constant material, suchas foam plastic, buried in soil.

This paper describes two reconstruction techniques forproducing images from measured microwave data. Onetechnique is experimental, and the other is numerical. Inthe experimental technique, reconstruction is obtainedwith laser light from detour phase holograms that arescale-reduced representations of the measured phase andintensity. The numerical technique is based on the an-gular spectrum concept; it utilizes Fourier transforms ofthe measured data and an approximate propagator func-tion. The computational method is useful because theobjects span only a few wavelengths and are near the re-ceiving apparatus. At larger, Fraunhofer distances theangular spectrum method requires a greater number ofsamples to avoid aliasing. The computational methodeliminates wavelength scaling, required in reconstructingwith laser light, and it can operate in nearly real time.Moreover, it permits subtracting the background reflec-tion from the interface. Although the production of opticalholograms is slow, the optical method can in prinoiplehandle large amounts of data.Both reconstruction methods have produced acceptable

images; however, the methods differ in convenience, andimage quality differs although we have not exhaustivelycompared image quality. The optical images are smallbecause of partial scaling. Surface roughness improvedimages formed with either method, apparently diffusingthe reflection from the air-soil interface. Both reconstruc-tion techniques utilized measured values of phase and in-tensity. The measurements were made by scanning oneantenna, that both transmitted and received, over anarea. An array of antennas would have accelerated dataacquisition, but a single scanned antenna was utilized toreduce equipment costs.

II. MICROWAVE APPARATUS ANDPROCEDURES

The microwave apparatus used is shown in Fig. 1. Itutilized one antenna for both transmission and reception.The antenna was connected to a continuous wave signalgenerator through a Hewlett-Packard reflection trans-mission unit, which separated the interface reflection andthe wave directly from the generator. Frequency was 2.5

381

IEEE TRANSACTIONS ON COMPUTERS, APRIL 1975

x

I_-SlIGNALGENERATOR

REFLECTION NETOTRANSMISSION ANALYZER

ANTENNA

I-zp

PROBING PATHS

SOIL

Fig. 1. Microwave apparatus.

GHz. The reflected field was directed to a network ana-lyzer, which measured the phase and intensity of the re-flected field. The antenna was a pyramidal horn withaperture 3/4 by 1 wavelength. This antenna was selectedto minimize reradiation of the field reflected by the object.In addition, the antenna was tuned in a free space environ-ment to reduce the reflections of the transmitted wave atits aperture because these reflections interfere with andobscure the field scattered by the object.The apparatus of Fig. 1 was supported by a motor

driven carriage to scan the aperture over a set of parallelpaths, as in Fig. 2. The paths were spaced by 0.2 wave-length. The antenna aperture was within two wavelengthsof the interface; the object was within two free spacewavelengths of the interface. Because of these small sepa-rations and because the objects were approximately 22wavelengths on a side, the measurements were made in theregion of Fresnel diffraction. Fig. 2 shows an anomaly sym-metric about a diagonal. Because of this symmetry weassumed the data were also symmetric in most measure-ments and moved the antenna only over the paths in-dicated by solid lines. Measurements verified symmetry ofthe data. We have also imaged rectangular anomalies withtheir edges parallel or perpendicular to the probing pathsbut omit these for brevity.

III. MICROWAVE DETOUR PHASEHOLOGRAPHY

Detour phase holograms were first developed for opticaldata processing [(], [7]. They are usually computergenerated, plotted, and then scale-reduced for reconstruc-tion with laser light. Because detour phase holograms canhave binary optical transmittance, they are convenient forencoding measured microawve data obtained by photo-graphing an oscilloscope display. References [8] and [9]gave some of our early experimental results, obtained witha fixed transmitting and a scanning receive antenna.Originally detour phase holograms were I4aunhofer holo-grams. They were filters, placed in the front focal plane Fof a lens in a setup like that in Fig. 3. Fraunhofer diffrac-tion patterns were produced in the back focal plane of thelens. The aim in synthesizing a hologram filter was to finda filter mask with a predetermined diffraction pattern.This task was equivalent to finding a Fraunhofer diffrac-tion pattern that would give a predetermined image.

_F__g_. 2. Prbn paths.

A AlI. al H IMAGE

OBJECT \JF( v v

i'a 'i' t f -- f f 1

Fig. 3. Optical setup for filtering or reconstruction. A source is inthe 0 plane.

Hologram synthesis is an inverse scattering problem be-cause it starts with a desired or known field and the scat-terer or hologram is sought.

This section describes detour phase holograms thatencode measured, microwave data and produce imageswhen illuminated with laser light. The microwave fielddiffracted by an object is known, from measurement, andthe object is sought. This is also an inverse scatteringproblem, but it differs from hologram synthesis. The taskin experimental microwave holography is to start withmeasured field data and then find a hologram that pro-duces an image of the diffracting object. In the first workon binary masks Lohmann and Brown [6] also sought ahologram, but they started with the image.The theory of Fraunhofer detour phase holograms

utilizes Fourier transforms. Let u (y) be the desired imagein the image plane at z = 4f of the optical system in Fig.3. Let the hologram transmittance be F(vy5,i) wherepy = yf/Xf, vz = /Xf, f is focal length of the lenses and yfand zf are spatial coordinates in the hologram plane. Fromscalar diffraction theory, u and F are Fourier transformpairs;

F (v8ey = f u(y,z) exp i[-2Xr (yy + vzz) dy dz.

F(vyvz) is represented as a hologram by dividing thehologram plane into square cells, labeled by specific valuesof v, and vz. Reference [6] gives several methods for en-coding F into each cell, but one of them is most suitable forour measuring apparatus. Each cell is opaque except in arectangular region with unit transmittance as shown inFig. 4. Let the phase and amplitude of F be a (vy,,u') andA (Py,P,), respectively, and let AP' be the cell width in thevy, or vz direction. For this format, [6] showed for Fraun-hofer diffraction that phase can be represented by alateral displacement pAQ of the rectangular region as shownin Fig. 4 such that

.P--------------X

'hzN -.--.-- -. ---.-- ------ -a. r3"V

382

-

7l

YUE et al.: MICROWAVE IMAGING

| --- . ~KyFig. 4. Transmittance of a cell in a hologram plane; Ky is 2py,

and K, is 2w,.

a = -2irpN (1)

where N is an integer. The amplitude is encoded such that

A = (AP/lryo) sin (iryOwAv) (2)

where yo is a traverse coordinate of an object point, orimage point for unit magnification.

In this section the theory of detour phase holograms isextended to include measured data and to describe Fresneldiffraction, which occurs when the distance to the objectis appreciably less than D2/X, where D is a dimensi'oncharacterizing the object. The theory relates the measuredphase to the aperture displacement in a hologram cell, asin Fig. 4. The theory also determines the positions of theimages formed in the reconstruction by locating maximaof diffracted intensity.

Phase and Displacement RelationshipIn the reconstruction step suppose that the hologram is

illuminated with a coherent plane wave, wavelength X'.Let the transmittance of the hologram be zero except inrectangles of width 2a where it is unity. The apertures arecentered at points x,, = no- + a,, along an x-axis. The cellwidth o" is a sampling interval and'n enumerates a cell.The displacements 8,n encode phase. The optical trans-mittance of the hologram on the plane Zh iS

t = E rect [(rnxh - nu - 6,) /2a] (3)

where rect (t/2a) has unit value for < a and is zeroelsewhere, and m is the scale of the hologram from itsoriginal microwave dimensions to its size for optical recon-struction. Images are formed by a lens of focal length fbehind the hologram. On the basis of scalar diffractiontheory to the quadratic approximation [10], it has beenshown [11] that the lens forms an image at zp with ampli-tude

up = CE E exp {i(ir/X') t,2m-2

+ 2rnM-1u sin O} >X sin cf2 (4)

where r,,no" + 8,n, sinef2 = f2-1 sin f2,f2 (a/X'mo") T27n- +u sin 0, and

E = exp {I (ir X') [(z - z1) + u + u2o"-']} sin 20.

In deriving (4) three integrals arise. These are over theobject and lens planes and the image plane of the hologram.The integrals were done by standard techniques such as the

focusing condition and large' argument expansions ofFresnel integrals.Now consider how the hologram represents the micro-

wave data. The field Uh in the hologram plane z = Zh iSmeasured by a probe antenna with a small aperturecentered at points Xh = na. By applying the Fresnelsampling theorem [12] to scalar diffraction integrals overthe hologram, lens, and hologram image planes it can beshown [11] that

up= 2cam-'CE exp [i(2-x/X')c2"2/vn2] X E () (5)

where

1 ( ) = a-n exp (i(%) exp (ik'n2o"2/vm2)n

sinc (2k'nc2/vm2)

and Uh has been written as an,,e04'i to locate measured phaseand amplitude at the appropriate cell.By equating the expressions of the image field as given

in (4) and (5), we obtain for each term that

exp i[En + 27r no) 2(X'm2p) -1]= exp it (7r/Xv) [r2m-2 + 27m-lu sin O] . (6)

Equation (8) leads to relationships between 4)n and bn.Suppose first that 4,n is zero for all n; that is, no object ispresent. Clearly An is zero. We then obtain grating ordersfrom the binary hologram when each term in (4) hasequal phase modulo 27r where N is an integer. From (6)for reasonably small holograms with n less than about ten,grating orders occur for

sin 0 N= NX'u/v(o-/m). (7)

Equation (7) predicts the locations of grating orders,bright intensity spots, when the '1,, are zero. When anobject is present, the grating is modulated and images areformed. Although approximately derived, (7) gives thepositions of images in the image plane.

Proceeding further, suppose the i,, are sufficiently smallrelative to o-. This condition may restrict the classes ofobjects that can be imaged, but in 'some cases relativelysmall phase changes may occur. From (6),

an = [XI'pm2((/7r) - 2mno"u sin 0

+ (no) 2] (2mu sin 0+ no)-'. (8)

For the holograms of interest n < 10, so that by omittingthe term no-/mu sin 0, small relative to unity, and with(7), we obtain

Dn = 27rb,,u (X'mI')-1 sin 0+ n (227rN).

Near the grating maxima we omit n(2-rN), so that

4',, = (2r/X') (u/v)'ml8, sin 0.

(9)

(10)

Equation (10) has structure quite similar to the detourphase formula given by Lohmann and Brown [6]. Thefactor mn- is a trivial difference, but the factor (u/v) ismore significant. It arises because a lens is utilized in the

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reconstruction. The lens is necessary because the micro-wave data were measured for Fresnel diffraction.

Equation (10) helps us to understand the images formedby optical reconstruction. These images are usually small,and in initial experiments they often have low quality.The focusing condition that was used to derive (10)locates the image plane after u is determined by Meier'stheory of image properties [13]. Equation (10) locates theimages in photographs of reconstructions. A reconstructionoften gives several images in its image plane because thehologram is a discrete, nonsinusoidal grating. The imagesare distributed about a bright central order of light thatcoincides with the direction of the illuminating beam.Images appear on each side of the central order. Higherorders may appear as bright spots beside or above therecognizeable images. The images correspond to low valuesof N such as 1 or 2 in (7) ; higher values such as 2 or 3 givespots rather than images. This multiplicity of imagesoccurs in the reconstructions that are presented in thesection on experimental examples.

Encoded Measured Data

A Network Analyzer measures the intensity S and thephase 4 of the reflected field. To represent the field weassume that S is proportional to the electric intensityS = nEE * /2, where E is the total or diffracted field.For this form of S we assume that the electrical andmagnetic fields are related by the intrinsic impedance.This assumption is accurate in the antenna's farfield butis approximate in the near-field. Measurements show thatthe field received by the antenna at each position can bedescribed by a specular ray so the assumption seems valid.The network analyzer generates one output voltage thatis the logarithm of the intensity of the reflected field. Thisfact helps separate the front surface reflection whichobscures the object. To see this, consider the total fieldE = Eo + E, where Eo is the field scattered by the objectand E is the field reflected at the interface. Let the in-tensity be I = IE + E8 2, so that the observed voltageis

VI = logI = log (IE8 12 + EO2 + EoE,* + Eo*E,).(11)

In the experiments, the voltage VIH supplied to theoscilloscope is normalized by adjusting the networkanalyzer to give zero voltage when the antenna is far fromthe object. This normalization helps separate Eo from E,.Consequently, the voltage forming the hologram is

VrH = 10g (I) - log I8 12.If EO is sufficiently smaller than E8 , then a seriesexpansion of the logarithm in (11) gives

VIH I= E0Iexp [i((0(-o I8)]

+ exp[-i(4)o- ))]} E 8 1-1. (12)

If E8 is uniform and 4'o - (D is small, then

VIH = c Eo (13)

where c is a proportionality constant. The quantity VIIH in(13) is applied to an amplifier, which produces a voltageto control the heights of the rectangles formed by theoscilloscope beam, as described in the next section.To see how measured phase is encoded, consider the

measured electric fie'ld

E = IE exp (i4)) = Eo exp (i)o)

+ E8 exp (i4b.). (14)

The output voltage for the phase channel of the networkanalyzer is adjusted to zero when the probe is far from theobject. Because the amplitude voltage is set to unit value,E8 = 1 in this region. Therefore if E8 varies slightly,

[E Iexp (isb) = 1 + Eo exp (i4)o). (15)

When 4) is small, which in our work was usually the case,we can expand the exponential functions, and equate theirimaginary parts to obtain

I [E = Eo sin Do. (14)Equation (16) states that the encoding of 4) should benonlinear to effect the encoding of (D. However, if theamplitude variation is small, or E/Eo is approximatelyconstant, and if (Do is small then

bo = E/EO 4). (17)

With these restrictions the encoding of 4) encodes 4)o.Recall 4) is observable; and we seek (Do.The ratio E/Eo is approximately constant except at

the edges, which affect a small part of the hologram.However, the sine function in (16) requires more care.When 4)o is small, the approximation of (17) is valid.Other ranges are not a problem, however, because thevariation of Eo is small. For example consider 3-r/4 <4bo < 5Xr/4. To separate the variable part of 4) considerb0 = 4)o' + r. Equation (16) gives 4) Eo =-l Eo sin4)0. If (DO is small, then Eo = -I Eo 4)o. To encode 4)owe merely reverse the displacements in setting up thehologram formation experiment. If 4)0 is in the range suchthat (Do' is small when 4bo = (Do' + 7r/2, then 4)o' = cos-1(4 E I / Eo 1), so that nonlinear encoding of 4) would berequired.

Experimental Examples

Holograms were generated with the apparatus in Fig. 5and photographed with an oscilloscope camera. We usedPolaroid film that developed rapidly but was nonlinear.The antenna was scanned by a motor driven carriage. Aservomechanism connected to the antenna drive motorgenerated a voltage that moved the electron beam in the xdirection while the antenna scanned a line of constant x.The beam was moved along y for each scan line. The oscil-loscope beam was vertically broadened by a small audiovoltage. The beam was periodically blanked by a pulsedvoltage applied to the intensity control of the oscilloscope;a cam, connected to the antenna driven motor, periodically

384


Fig. 6. Images for dielectric slab oriented as in Fig. 2; for smoothsurface. The images are in the central horizontal row, and a pairappears on each side of the central zero order. The dots, in thehighest and lowest rows, are higher orders.

DC VOLTAGESOURCE

Fig. 5. Apparatus for forming detour phase holograms.

actuated a switch. When no voltages were applied from thenetwork analyzer, the arrangement produced a uniformgrating consisting of rows of small, bright rectangles.However, when the antenna passed over an anomaly non-zero voltages were generated by the network analyzer.The phase voltage was applied to the x-axis of the oscil-loscope to displace each rectangle. The amplitude voltagewas applied to the y-axis to control the height of therectangles. The oscilloscope face was photographed with anopen shutter while the antenna scanned a set of parallellines. The resulting photograph is a modulated gratingwhich when scale-reduced is a hologram transparency.Each rectangle became a small aperture within a cell, as inFig. 2.Holograms and images were formed for a dielectric

foam slab of dielectric constant 1.05, thickness 0.32X,width 2.2X and length 2.5X, where X is the free-space wave-length. The orientation was diagonal as in Fig. 2. Theantenna was 0.85X above the soil and the top of theanomaly was 0.64N below the surface. A hologram was firstformed for smooth soil, and another was formed after thesurface was roughened with 1 cm deep, randomly orientedgrooves. Images were reconstructed from 1/885 scaleholograms with 632.8 nm laser light in a setup like that inzFig. 3 except that lenses had unequal focal lengths andspacings were not multiples of f.

Fig. 6 shows images for smooth soil, and Fig. 7 showsimages for rough soil. Each figure has a pair of images oneach side of the zero order. The best image is the first-order image on the right of each figure. Apparently therough surface acts as a diffuser, reducing the reflectionfrom the interface. The relative intensities of the ordersdepend on the aperture width in each cell [11].

IV. COMPUTATIONAL RECONSTRUCTIONIn this section we describe numerical wavefront recon-

struction which has some advantages over optical tech-niques, e.g., flexibility, nearly real time capability, accuratescaling, and the subtraction of background reflections. Amathematical model of our system is developed in the firstpart, and an image forming algorithm is designed. Thealgorithm was used to process holograms from our imagingsystem and some results are presented in the second part ofthis section. In our experiments we measured the field

U~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Fig. 7. Images for dielectric slab with orientation as in Fig. 2; for

roughened surface.

near an anomaly with an antenna that also transmitted,forming a hologram as the antenna scanned an area abovethe soil surface. This system is different from conventionalmicrowave holographic systems, that have a fixed trans-mitting antenna working in a homogeneous medium.

Mathematical Model

We first extend Snell's law to nonplane waves by super-position and show that the spectrum is continuous at theboundary. Let there be two homogeneous isotropic mediawith refractive indices n and m, with corresponding wave-lengths X and X at the frequency of interest (nX = mq),separated by a plane boundary at z = 0. If a plane waveis propagated across the boundary (from medium n tomedium )n) with direction cosines of incidence and trans-mission given by (a,3,'y) and (co,wU) and since the direc-tions of the two waves and the normal of the boundary(the z-axis in this case) are coplanar, Snell's law yields

a =w (3 A(- = - and - = -.X -1 X 71

(18)

Since a plane wave with direction cosines (a,fl,y) andwavelength X has a field distribution at z = 0 of

h(x,y,0) = expj27rLax++y1from (18) we can see that the field distribution is con-tinuous at the boundary. Based on the principle of super-position and assuming that there is no reflection, the fieldanywhere inside the second medium can be computed fromthe spectrum at the boundary. Consequently, for the back-ward propagation problem of determining h (x,y,-.a) fromh(x,y,b) with both a and b positive we can write

H(f,g,-a) = H(f,g,b)P(f,g,-b,-q)P(f,g,-a,X)where H is the spectrum of h and P(f,g,z,X) = exp (j2irz)* (X-2 - f2 g2)1/2Next we derive a mathematical model of our system for

a single medium in terms of angular spectrum and suggest

385


RECEIVER (xo, yo, Z0)i U

T-RSTRx

TRANSMITTER Nx, Y., -Zo)

Fig. 8. Equivalent stationary synthetic aperture system.

an approximate solution to the inverse scattering problem.To make the analysis easier to comprehend, we shall use aneguivalent object transmittance -y (x,y) (instead of a re-flecting object) located at z = 0 and have the transmitterand receiver at (xo,yo, -zo) and (xo,yo,zo), respectively.The equivalent system is shown in Fig. 8. Moreover, weassume the transmitter to be a point source and the re-ceiver to be omnidirectional. Then the spectrum at z =-Zo is

byf2 + 92 = X-2, it can be seen that Q(f,g,z,X) is zero out-side R (2/X). Moreover we observe that

d IF1r/d [P(f,g,z,X) {f2 + g2 - } = P(f,g,z,x).

Since it can be shown that the inverse transform of thequantity inside the square brackets is exp (jkr)/r, itfollows that (19)

H(f,g,zo) = exp [-j2ir(fxo + gyo)](f ± g2 - X2 /

With r (f,g) the transform of y (x,y), the field measured at(xo,yo,zo) is given by

d exp (jkr)]dz r

and

1 d [exp (j2kr)]2 dz r2

h(xo,yo,zo) = ff r(a,b)_00

11 [l(f -a) 2 + (g -b)2 - /212dd

*exp [j2ir (axo + bYo) ] dadb

00

_ f rP(a,b)Q(a,b,zo,X)

*exp [j27r(axo + byo)] dadb. (19)

It should be noted that while H(f,g,zo) is a function of xoand yo, r (f,g) Q (f,g,zo,X) is independent of xo and yo and isthe spectrum of the hologram data measured in our system.Equation (19) suggests an obvious solution to the inverseproblem of computing y (x,y) from h (x,y,zo) but we haveto examine the new propagator Q (f,g,zo,X) more closely.If we write Q(f,g,z,X) as a convolution and restrict P(f,g,z,X) to the harmonic region R (1/X) which is a disc bounded

where q(x,y,z,X) and p(x,y,z,X) are the inverse transformof Q(f,g,z,X) and P(f,g,z,X)., respectively.

Equation (19) suggests that we compute r(f,g) bydividing the spectrum of the measured data by Q(f,g,zo,X).This procedure is similar to that used in the conventionalimaging system, where dividing by vanishingly smallvalues of the propagator P (f,g,zo,X) can be neatly avoidedby restricting f and g to R(1/X). However Q (f,g,zo,X) maybe very small even inside R (2/X), and the division opera-tion can greatly amplify the error in the estimation of thespectrum from the hologram. Comparison between p(x,y,z,X) and q(x,y,z,X) suggests a rough approximation of thelatter by 2p(x,y,z,X/2) whose spectrum has a harmonicregion of R (2/X) the same as Q(f,g,zo,X) . This approximatepropagator P(f,g,-z,X/2) can be modified to include theeffect of a second medium, yielding P(f,g,-z,,1,/2) XP (f,g, -z2,X2/2) where zi and Z2 are the propagation dis-tances in the two media and X1 and X2 are the correspondingwavelengths. The algorithm based on this was used to formthe images presented in this paper.

In the discussion so far, we have ignored the componentof the scattered field due to reflection from the soil surface.

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In general, this component is random with a nonstationarymean over the aperture and independent data acquisitionis necessary for estimating the varying mean surfacereturn at the hologram. If the nonstationarity is planar or

locally planar, the signal return from regions where theanomaly is assumed absent may provide sufficient infor-mation for estimating a plane or a set of planes. However,in the cases where we have done measurements this com-

ponent was fairly constant for surface roughness up to halfthe wavelength; roughness shall be defined as maximumpeak to valley vertical separation. This means that if weestimate and substract a constant surface reflected com-

ponent from the data, considerable image enhancement can

be expected. In our first attempt to compute images we

assume no a priori available information on the surfaceroughness and apply the algorithm described before di-rectly. But we also implemented the image enhancementtechnique of estimation and subtraction.

Experimental ResultsThe data used for computing images in this section were

all obtained -with a rectangular void in dry dirt orienteddiagonally with respect to the scanning direction. The voidis 2.2Xi by 2.5X1 and 0.64X1 below the surface, where X1 isthe wavelength in free space. 5.1X1 by 6.8X1 hologramsconsisting of 32 X 32 complex data matrices were formedby measuring 0.85X above the surface. To reduce dataacquisition time we only scanned half the aperture andreflected the data to fill the hologram. Images computed

frorn the data taken with rough and smooth soil surfacesare presented in Figs. 9 and 10. The algorithm used in thesecases was derived from P(f,g,zi,Xi/2)P(f,g,z2,X2/2) as

described in the first part of this section. The computedoutput is in the form of a matrix whose elements are

samples of the intensity distribution reconstructed as theobject plane. In order to present the images in a form thatresembles pictures, we quantize the range of intensityvariation into 13 levels and assign a 3 X 4 dot pattern toeach level to approximate different shades of gray. Forthe purpose of comparison the hologram and the image are

presented side by side in the figures. The size of theboundary of all holograms and images presented in thissection is the same; the scales for both directions are

approximately equal.The basic idea underlying all image enhancement tech-

niques is to suppress the unwanted (noise) part of theavailable information with respect to the desirable -(signal)portion by predetection filtering or nonlinear processing,the detector being the image forming algorithm in thiscase. Therefore, the first problem in the design of the ap-propriate predetection processing is deciding what con-

stitutes the signal and the noise, otherwise valuable infor-mation would be lost. Then comes the problem of noisecharacterization which may be deterministic or probabilis-tic.

In our imaging system the signal is the field scattered bythe void and the noise consists mainly of the surface re-

flection since the equipment noise-is insignificant. When

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387


HOLOGRAM IMAGEFig. 10. Intensity in hologram and image for smooth surface.

the air-to-soil interface is perfectly smooth, it acts like aplane mirror, which means the reflected field is constant aslong as the relative positions of the transmitter, the re-ceiver, and the soil surface are fixed. In our experiment wealso disturbed the surface causing the reflected field to beweaker but still fairly constant because the roughness wasless than half the wavelength. Consequently our noisecomponent is essentially deterministic and the requiredpredetection processing is simply a subtraction.The surface reflected components for each case were

estimated and subtracted from the original data. Themodified holograms were processed and the results areshown in Figs. 11 and 12. The improvement in imagequality was stunning. Another remarkable, though notunexpected, observation from these figures is that even theunprocessed holograms reveal much more informationabout the object.The similarity between this image enhancement tech-

nique and the processing of optical hologram is obvious,but one important difference is that while in the latter casethe appropriate reference wave is known a priori, we haveto estimate this component from our data. The estimationproblem in the cases we have considered was fairly easy tosolve, but under other conditions it may become morecomplicated. Nevertheless, considering the kind of im-provement in image quality possible it is definitely worth-while to investigate the estimation problem under moregeneral circumstances.

V. SUMMARYThis paper described two microwave methods for imag-

ing buried dielectric anomalies. Both methods utilize

measured values of phase and intensity, but reconstruc-tions are done experimentally with one method and com-putationally with the other. The experimental recon-structions were formed with laser light from scale-reduced,binary, detour-phase holograms that encode the measuredmicrowave data; the detour-phase theory extends Loh-mann and Brown's well-known theory for computer-generated, Fourier holograms to include experimental data,measured in the region of Fresnel diffraction. The compu-tational reconstructions were formed by evaluating analgorithm that is based on the angular spectrum conceptand that utilizes an approximate propagator.Data were measured by a coherent system that utilizes

the same antenna for transmission and for reception. Theobjects were flat low-density, plastic slabs, with widthsapproximately 3 free space wavelengths and thicknessesfrom X to 8 warvelength. The objects were within a wave-length of air-soil interface, as was the antenna. The an-tenna scanned a series of parallel paths to collect data overan area.Both methods gave acceptable images. The optical

reconstructions gave small images because the hologramswere reduced by less than the ratio of microwave and op-tical wavelengths. The computational reconstructionswere initially comparable in quality to the experimental;however, the computationally-formed images were greatlyenhanced by subtracting an estimate of the field that wasexperimentally determined in the region far from theanomaly. Surface roughness of height less than " wave,length improved images formed with either method;apparently, the roughness diffuses the reflection at the air-soil interface.

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YUE et al.: MICROWAVE IMAGING 389

IMAGE

Fig. 11. Intensity in hologram and image for rough surface withsurface reflection subtracted.

HOLOGRAM IMAGE

Fig. 12. Intensity in hologram and image for smooth surface withsurface reflection subtracted.

The computational.method has the advantage that itavoids partial scale reductions; moreover, a backgroundcan be readily subtracted. The computational method alsocan be instrumented for nearly real-time operation byutilizing an array of antennas and rapid analog to digitalconversion; however, for economy we utilized an existing

procedure (a single antenna, punched paper tape datarecording, digital conversion, and a scientific computer).

REFERENCES[1] H. Bremmer, Terrestrial Radio Wave Propagation. New York:

Elsevier, 1949, pp. 1-8.[21 J. R. Wait, Ed., Electromagnetic Probing in Geophysis. Boul-

der, Colo.: Golem, 1971, pp. 77-130.

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[3] G. L. Rogers, "A new method of analyzing ionospheric move-ment records," Nature, vol. 177, pp. 613-614, 1956.

[4] , "Diffraction microscopy and the ionosphere," J. Atmos.Terr. Phys., vol. 10, pp. 332-337, 1957.

[5] R. 0. Harger, Synthetic Aperture Radar Systems: Theory andDesign. New York: Academic, pp. 1-14, 1970.

[6] B. B. Brown and A. W. Lohmann, "Complex spatial filteringwith binary masks," Appl. Opt., vol. 5, pp. 967-969, 1966.

[7] A. W. Lohmann and D. P. Paris, "Binary holograms, generatedby computer," Appl. Opt., vol. 6, pp. 1739-1743, 1967.

[8] E. L. Rope and G. Tricoles, "Microwave holography: diffusersand binary detour phase holography," in Applications of Holog-raphy, J. Vienot et al., Ed. Paris, France: Univ. Besancon, p.15-3, 1970.

[9] G. Tricoles and E. L. Rope, "Binary, detour phase holography,"in IEEE/G-MTT Microwave Symp. Dig., 1970, pp. 124-125,IEEE Catalog No. 70 C 10-MTT.

[10] J. W. Goodman, Introduction to Fourier Optics. New York:McGraw-Hill, 1968, pp. 59-61.

[11] G. Tricoles, "Some topics in microwave holography," Ph.D.dissertation, Univ. Calif., San Diego, 1970. (Available fromUniversity Microffims, Ann Arbor, Mich.)

[12] A. W. Lohmann, "Data economy in holography," J. Opt. Soc.Amer., vol. 59, p. 482 (abstract), 1969. (This paper derived aFresnel sampling theorem from the well-known Fourier samplingtheorem.)

[13] R. W. Meir, "Magnification and third-order aberrations inholography," J. Opt. Soc. Amer., vol. 55, p. 987, 1965.

[14] A. Banos, Dipole Radiation in the Presence of A ConductingHalf-Plane. New York: Pergamon, 1966, pp. 16-19.

On-Ching Yue (S'66-M'68) was born inMacao on April 9, 1947. He received theB.E.E. degree from Cooper Union, NewYork, in 1968, and the M.S.E.E. degree fromRochester Institute of Technology, Rochester,N. Y. in 1971, and is currently workingtoward the Ph.D. degree in informationscience at the University of California, SanDiego.

If* 0 S.: He joined General Dynamics/ElectronicsDivision, Rochester, N. Y. in 1968 and is a

Senior Engineer in the Research Department at GD/E San Diego,Calif. His current research interests are microwave holography,image enhancement, and linear processes.Mr. Yue is a member of Eta Kappa Nu, Tau Beta Pi, and Phi

Kappa Phi.

E. L. Rope was born in Clerinda, Iowa onAugus 22,19Re2a5He received an A.S. degree

W |W from Grossmont College, El Cajon, Calif., in1963.

After service in the U. S. Army, he joinedGeneral Dynamics in 1956. He has mostrecently performed experimental research inmicrowave holography and he has also de-veloped microwave antennas and radomes.He holds five patents and has publishedseveral papers.

G. Tricoles (M'58) was born in San Fran-cisco, Calif. on October 18, 1931. He receivedthe B.A. in Physics from the University ofCalifornia, Los Angeles in 1955, the M.S. inapplied mathematics from San Diego StateCollege in 1958, M.S. in physics from theUniversity of California, San Diego in 1962,and Ph.D. in applied physics from the Uni-versity of California, San Diego in 1971.He was employed at General Dynamics,

San Diego from 1955 to 1959, at Smyth Re-search Associates from 1959 to 1961, and since then has been at theElectronics Division of General Dynamics. His main technical workhas been in the analysis and development of radomes, on wavepropagation, and on microwave holography. He holds six patents,has published several technical papers, and is the author of a chapterin Radome Engineering Handbook, edited by J. D. Walton.

Dr. Tricoles is a member of the Optical Society of America andU. S. Commission VI of U.R.S.I. He is also a member of the IEEEStandards Subcommittee on Antenna Measurements.

Documents

Two Reconstruction Methods for Microwave Imaging of Buried