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雅虎邮箱地址 : PW:zjuopt. 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.

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Docu ioi@yahoo com cn pw zjuopt



Basic framework of optical system
basic framework of Optical System

Docu ioi yahoo pw zjuopt

Optical system

Imperfection of optical system

Ideal point object → optical system → diffused patch of light


  • Aberration

  • Diffraction limitation

  • Imperfection of the medium

  • ( air disturbance, anisotropy of the medium)

Docu ioi yahoo pw zjuopt

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
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

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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.

Docu ioi yahoo pw zjuopt

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

Docu ioi yahoo pw zjuopt


microdensitometric scanning.  Other reduction ranges, contrasts and materials are available.

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2. Contrast Modulation

A definition for repetitive periodic object or image:

a series of dark bars on bright background

highest contrast:

no contrast:

barely visible contrast:

2 1 contrast1
2-1 Contrast

3.Non-repetitive contrast

example--dark letterson 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

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4.Normalized ModulationM

For objects of repetitive sinusoidal light distribution ( in most cases)

The mean:

The variation around the mean:

2 2 transfer function
2-2 Transfer Function

1.Transfer factor—Modulation transfer factor T

The transfer factor is a function of spatial frequency R



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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 function1
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)

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Point Spread Function

Point Spread Function as a function of the visual angle

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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

2 2 transfer function2
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:

O. T. F. describes the degration of an image, at different space frequencies

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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.

Docu ioi yahoo pw zjuopt

Modulation Transfer Function

Variation of the Modulation transfer function of the human eye model with wavelength

2 2 transfer function3
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
2-3The experiment of MTF

1—light source


3—lens under test

4—rotating drum


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.

MTFtotal=MTFlens1MTFlens2…… MTFfilm


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


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