The document defines contrast and the modulation transfer function (MTF). It states that MTF is a measurement of the image contrast divided by the object contrast and represents the ability of an optical system to transfer the contrast of an object to its image. The document provides an example MTF graph showing this ratio at different frequencies, with an ideal lens having a MTF of 1.0.

1. Definition of Contrast

9. Fourier Analysis
• Square wave = Sum of sine waves
• Square wave = Fundamental sine wave +
harmonics
• Fundamental sine wave is a wave with the
same frequency as the square wave
• Third harmonic is a sine wave with 3 times the
square wave
• Fifth harmonic is a sine wave with 5 times the
frequency of the square wave

12. Modulation Transfer Function
• Object Contrast-> Lens -> Image contrast
• MTF = Image Contrast/ Object Contrast
• MTF = 1.0 for an ideal lens (or system)
MTF is determined by frequency to obtain a
graph.

13. Modulation Transfer Function (MTF)
Frequency Object Contrast Image Contrast MTF
2 10 8 0.80
5 9 7.5 0.83
8 8.7 6.3 0.72
10 7.5 5.2 0.69
15 6.3 3.8 0.60
18 5.2 2.1 0.40
25 4.2 1.5 0.36
30 4 0.9 0.23
40 4 0.7 0.18
50 3.8 0.4 0.11
60 3.6 0.33 0.09
MTF
0.90
0.80
0.70
0.60
0.50
0.40 MTF
0.30
0.20
0.10
0.00
2 5 8 10 15 18 25 30 40 50 60

15. Contrast Sensitivity Function(CSF)

38. Mach bands