Modulation transfer function ($M(\nu )$)

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.