= Modulation transfer function
{title2=$M(\nu)$}
The <modulation transfer function> is the magnitude of the normalized <optical transfer function> in a linear, shift-invariant <incoherent imaging> model. It describes how strongly the system transfers sinusoidal <image contrast> at each <spatial frequency>, while discarding the transfer function's <phase>.
For an input $I(x)=I_0[1+m\cos(2\pi\nu x)]$ and a unit-integral <point spread function>, the output modulation magnitude is $mM(\nu)$. Fine alternating bars contain higher <spatial frequencies>, so their diminishing visibility illustrates loss of transferred modulation. Measuring <image contrast> across a calibrated pattern tests this response, but detector sampling, noise and nonlinear image processing can alter the result. A transfer magnitude alone does not locate image features or specify their <phase> shifts.
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