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雅虎邮箱地址 :  [email protected] 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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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)

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


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.


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



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


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


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




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)


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

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


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 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