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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