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Below is a tutorial on modulation transfer functions (MTF) and how to measure the MTF of an optical system. 


The modular transfer function (MTF) is a measure of contrast versus spatial frequency.  Full contrast, 100%, is a pattern of a given spatial frequency or line pair.  The MTF plot is typically normalized at 1 or 100% contrast (vertical axis), while the horizontal axis is the dependent variable spatial frequency normally in units of lines/mm.  The figure below gives an illustration of how the image degrades with decreasing contrast

Figure 1: Image of degrading line pairs with decreasing contrast.


The next figure shows a MTF chart for a typical system.

Figure 2: This is a MTF plot showing the MTF for each field angle (0°, 20°, -20°).




The MTF figure shows a fairly straight black line (top line), which represents a diffraction limited or ideal design MTF performance.  Due to diffraction, from light scraping on the lens limiting aperture, there is limited contrast performance that is resolvable - as is observed, the maximum/best resolvable contrast for 200 lines per mm is 30%, and the real contrast gives only ~5% contrast for 200 lines per mm.



A good criterion for excellent optical performance for different camera applications is given:

1.        Motion picture camera lenses - 50% MTF at 50 lpm.

2.        35-mm camera lenses - 20% MTF at 30 lpm over the whole field (FOV).

3.        35-mm camera lens on axis - 50% MTF at 30 lpm.

4.        Additional aberration criterion for common camera lenses:

a.        Distortion <2%.

b.        Optical Path Difference (OPD) < 2 waves.

c.        Ray Fan < 50µm.

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