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Chapter 2 System Evaluation
Optical System
basic framework of Optical System
Types of Optical System
Reading/writing system
Image system
Image system
Illumination system
Special optical system
International optical standards & associations
Optical design flow diagram
Optical design products
Double zoom lenses
Ghost image analysis
Opto-mechanical design
Optical detection
Optical testing
Imperfection of optical system
Ideal point object → optical system → diffused patch of light
Reason? 1.Aberration
2.Diffraction limitation
3.Imperfection of the medium
( air disturbance, anisotropy of the medium)
Optical system
Resolution(Resolving power): The ability to distinguish the closely spaced lines or points
Transfer function:
Measure of performance of a system
Measure of transfer ability of a system
Let us predict theoretically, confirm or disprove experimentally
can be also to evaluate peripheral components, include: lens, photographic film, CCD, atmosphere, eyes etc.
Means of evaluation:
2-1 Contrast
1.Object targetMust take into account the
contrast
High contrast: a deep black object on a pure white background
Low contrast: a gray object in a fog
test chart
MICROCOPY TEST TARGET
Data: Conforms to NIST/NBS 1010A, & ANSI/ISO test chart #2; frequency shown in cycles per mm and changes by an average of 12.2% per step; image overall 38mm x 45mm
Notes:
Read direct resolution; ideal for evaluation of Optical / Mechanical Systems where reduction and low resolution is of interest.
Data: Designed to MIL-STD-150A; frequency changes by 6 √2 progression; image overall 71mm x 58mm; also available in custom sizes and contrasts. Ideally suited for Imaging materials, Visual resolution or Optical systems.
USAF 1951 TEST TARGET
Data: Layout and features are the same as provided in the traditional USAF 1951 Test Target (T-20) meeting all requirements specified in MIL-STD-150A. The following improvements have been made:
USAF 1951 TEST TARGET - w/ Improved Labeling
- The chart has direct frequency labeling in c/mm eliminating the need for cross reference documentation of frequencies.- Numeric labeling is enhanced, based on OCR-A extended font for maximum recognition.
Data:
All bars and spaces are the same as provided in the traditional USAF 1951 Test Target chart T-20, meeting all requirements as specified in MIL-STD-150A. The following are improvements:
USAF 1951 TEST TARGET - w/ Improved Labeling and Features
- The chart has DIRECT frequency labeling in C/MM. - Numeric labeling is enhanced and based on OCR-A extended font. - Bars are laid out in two straight columns, for easier scanning. - Smaller elements have finder squares next to them to aid in determining their locations
Data: Alphanumeric configuration with frequency range 1-18 cycles/mm in 25 groups. Overall image area of 50 x 50mm is divided into 4 quadrants. Available in custom sizes and contrasts.
RIT ALPHANUMERIC CHART
Notes:
Especially useful in Optical / Visual evaluation or where cross consistency among users is important.
Data:
The NBS-1952 Resolution Test Chart is described in the NBS circular 533, 1953 in the section titled Method of Determining the Resolution Power of Photographic Lenses. The design features of this target reduce edge effects, minimize spurious resolution and permit single pass scanning.
NBS-1952 RESOLUTION TEST CHART
Notes:
The NBS method of using this chart to test lenses involves placing the chart at a distance from the lens equal to 26 times the focal length of the lens, resulting in a 25x reduction. The reduction effective frequency is 12 to 80 cycles per mm.
Data:
Frequency range in c/mm (20:1). Other frequencies are available on request.
Notes:
Each bar and space is progressively smaller in a log manner. Peaked groups every 10 bars. Ideally suited for
SAYCE TARGET
microdensitometric scanning. Other reduction ranges, contrasts and materials are available.
Data: Wedge shaped segments with 45 equal bar and space widths over a 360 circumference (8 degrees per cycle or 4 degrees per spoke). Image size is 50mm in diameter.
STAR SECTOR TARGET
Notes:
An ideal target for detecting Optical Astigmatism, Focus Errors and other aberrations. Can easily be incorporated into complete target arrays.
Do you trust your vision ??
Do you still trust your vision ??
A definition for repetitive periodic object or image:
a series of dark bars on bright background
highest contrast:
no contrast:
barely visible contrast:
minmax
minmax
LL
LL
%1000min L
0maxmin LL
%20
2. Contrast Modulation
2-1 Contrast
3.Non-repetitive contrast
example --dark letters on a gray background
LB—amount of light from background
LO-- amount of light from object Object darker than background, C positive Object brighter than background, C negative
B
O
B
OB
L
L
L
LLC
1
For objects of repetitive sinusoidal light distribution ( in most cases)
The mean:
The variation around the mean:
4. Normalized Modulation M
minminmax 2/)( LLLa
aLb max
a
b
baba
baba
LL
LLM
)()(
)()(
minmax
minmax
2-2 Transfer Function
1.Transfer factor—Modulation transfer factor T
The transfer factor is a function of spatial frequency R
object
image
M
MT
MTFRfRT )()(
imageobject
the number of lines, or other detail, within a given length. Unit: 1p/mm or mm-1
Example1: R=4.0mm-1 → 4 pairs of black(lines) and white(intervals) in 1mm;
Example2: R=100 mm -1 →100 pairs in 1mm
→line width=1/200mm
Example3: Line width=interval width=1mm → R=0.5 mm-1
spatial frequency R:
2-2 Transfer Function
2.Spread FunctionA point(pixel) → optical system → diffuse patch of light
point spread function S(y,z)
A line → optical system → line spread function S(z)
dyzySzS ),()(
Point Spread Function
Point Spread Function as a function of the visual angle
The light distribution on image:
the Integral form
the derivation form: The modulation transfer function:
the Fourier transfer of the spread function of that lens
dzzSzIzE )()()(
)()()(
zSzIdz
zdE
dzezSMTF iRz2)(
2-2 Transfer Function
3.Phase transfer & OTF position incorrect (caused by coma, distortion)
→ dislocation of the image points
→ dislodged with respect to the ideal position
Phase shift: (spatial phase)
is a function of spatial frequency
= f ( R )
Optical transfer function: )(RieMTFOTF
objectinondistributilightoftransformFourier
imageinondistributilightoftransformFourierOTF
O. T. F. describes the degration of an image, at different space frequencies
Optical Transfer Function (OTF)The OTF is a complex function that measures the loss in contrast in the image of a sinusoidal target, as well as any phase shifts. The MTF is the amplitude (i.e. MTF = |OTF|) and the Phase Transfer Function (PTF) is the phase portion of the OTF.
Modulation Transfer Function
Variation of the Modulation transfer function of the human eye model with wavelength
2-2 Transfer Function
Both T(R) and (R) are the function of spatial frequency:
Ideal perfect lens:
T(R ) = 1, and (R) = 0
At all spatial frequency
Practical lens: at low spatial frequency: R<10mm-1
T(R ) → 1, and (R) → 0
at high spatial frequency: R>100mm-1
T(R )↓→ 0, and (R) ↑ → 1
2-3The experiment of MTF
1—light source2—slit3—lens under test4—rotating drum5—photo-detector 6—reference grid
Before adding the lens, put the grid on the drum,
record the signal as object;After adding the lens, form image of slit on the drum,
record the signal as image.
I
R
signal of image
signal of object
MTFtotal=MTFlens1MTFlens2…… MTFfilm
Example
Photographs are taken from a high-altitude aircraft of a cruise ship, the MTF of a typical camera lens is that show in figure
ship brightness: 5 units, the ocean: 2 units
contrast:
chose the focal length for the image size.
Image 0.5mm
R=1, T=0.8, → M’=0.8 0.43=0.34
Image 0.05mm
R=10, T=0.7, → M’=0.7 0.43=0.3 OK to be seen
Image 0.005mm
R=100, T=0.2, → M’=0.2 0.43=0.086 cannot be seen
%4325
25
Home work: Question 1, 2, 3, 4, 5