Definition of Contrast

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

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.

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

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

2 5 8 10 15 18 25 30 40 50 60

MTF

MTF

Contrast Sensitivity Function(CSF)

Mach bands