雅虎邮箱地址 : firstname.lastname@example.org 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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Imperfection of optical system
Ideal point object → optical system → diffused patch of light
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
- 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.
- 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.
A definition for repetitive periodic object or image:
a series of dark bars on bright background
barely visible 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
For objects of repetitive sinusoidal light distribution ( in most cases)
The variation around the mean:
1.Transfer factor—Modulation transfer factor T
The transfer factor is a function of 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
Example3: Line width=interval width=1mm → R=0.5 mm-1
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 as a function of the visual angle
the Integral form
the derivation form:
The modulation transfer function:
the Fourier transfer of the spread function of that lens
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
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.
Variation of the Modulation transfer function of the human eye model with wavelength
Both T(R) and(R) are the function of spatial frequency:
Ideal perfect lens:
T(R ) = 1, and(R) = 0
At all spatial frequency
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
3—lens under test
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.
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.
R=1, T=0.8, → M’=0.8 0.43=0.34
R=10, T=0.7, → M’=0.7 0.43=0.3 OK to be seen
R=100, T=0.2, → M’=0.2 0.43=0.086 cannot be seen