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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
Optical system
Reason?
1.Aberration
2.Diffraction limitation
3.Imperfection of the medium
( air disturbance, anisotropy of the
medium)
Means of evaluation:
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.
2-1 Contrast
1.Object target
Must 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.
USAF 1951 TEST TARGET
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 - w/ Improved Labeling
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:
- 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.
USAF 1951 TEST TARGET - w/ Improved
Labeling and Features
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:
- 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
RIT ALPHANUMERIC CHART
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.
Note Especially useful in Optical
s: / Visual evaluation or where
cross consistency among
users is important.
NBS-1952 RESOLUTION TEST CHART
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.
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.
SAYCE TARGET
Data Frequency range in c/mm (20:1). Other frequencies are available
: on request.
Note Each bar and space is progressively smaller in a log manner.
s: Peaked groups every 10 bars. Ideally suited for
microdensitometric
scanning. Other reduction
ranges, contrasts and
materials are available.
STAR SECTOR TARGET
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.
Note An ideal target for
s: 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 ??
2. Contrast Modulation 
A definition for repetitive periodic object or
image:
Lmax  Lmin

Lmax  Lmin
Lmin  0
  100%
a series of dark bars on bright background
highest contrast:
Lmin  Lmax
 0
no contrast:
  20%
barely visible contrast:
2-1 Contrast
3.Non-repetitive contrast
example --dark letters on a gray background
LB  LO
LO
C
 1
LB
LB
LB—amount of light from background
LO-- amount of light from object
 Object darker than background, C positive
 Object brighter than background, C negative
4. Normalized Modulation M
For objects of repetitive sinusoidal light distribution ( in
most cases)
The mean:
a  ( Lmax  Lmin ) / 2  Lmin
The variation around the mean: b  Lmax  a
M
Lmax  Lmin (a  b)  ( a  b) b


Lmax  Lmin (a  b)  ( a  b) a
2-2 Transfer Function
object
image
1.Transfer factor—Modulation transfer factor T
T
M image
M object
The transfer factor is a function of spatial frequency R
T ( R)  f ( R)  MTF
spatial frequency R:
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
2-2 Transfer Function
2.Spread Function
A point(pixel) → optical system → diffuse patch of light
point spread function S(y,z)
A line → optical system → line spread function S(z)
S ( z) 



S ( y, z )dy
Point Spread Function
Point Spread Function as a function of the visual angle
The light distribution on image:
E( z) 
the Integral form
the derivation form:



I ( z ) S ( z )dz
dE ( z )
 I ( z)S ( z)
dz
The modulation transfer function:

MTF   S ( z)e2iRzdz

the Fourier transfer of the spread function of that lens
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:
OTF  MTF  e
OTF 
i ( R )
Fourier transform of light distributi on in image
Fourier transform of light distributi on in object
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 source
2—slit
3—lens under test
4—rotating drum
5—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
signal of object
R
signal of image
MTFtotal=MTFlens1MTFlens2…… 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
52
 43%
contrast:  
52
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
Home work: Question 1, 2, 3, 4, 5