
Modulation transfer function
The modulation transfer function (MTF) describes the contrast reduction introduced by the imaging system. If the object has a sinusoidal modulation of intensity with size M as defined in the figure below, and the resulting image has a modulation of intensity with size M', then the MTF is defined as the ratio M'/M. The MTF is a function of the spatial frequency of the sinusoidal pattern. The MTF is always less than one.

The modulation transfer function (MTF) is the real part of the complex-valued optical transfer function (OTF) that describes the transfer of spatial information from the object plane to the image plane.
The OTF is the Fourier transform of the point spread function (PSF).
The OTF is defined by a pair of functions Gx and Gy that describe the effect of the lens on x-structure and y-structure, respectively. The formulas for these functions are

where f is the spatial frequency (usually expressed in cycles per mm on the image plane) and (x,y) is the image coordinate.
Geometrical OTF
In the geometrical approximation the OTF is calculated for a discrete set of rays at the image surface by the sums

For an axially symmetric system the OTF is real-valued on the system axis, but off axis it can have an imaginary part, corresponding to a shift of the sinoisoidal pattern.