# 27. What is "MTF".

## Description

This article is from the
Photographic Lenses FAQ, by David Jacobson with numerous
contributions by others.

# 27. What is "MTF".

MTF is an abbreviation for Modulation Transfer Function. It is
the normalized spatial frequency response of film or an optical
system. The spatial frequency is usually measured in cycles per
millimeter. For an ideal lens and ignoring diffraction, the MTF would
be a constant 1 at all spatial frequencies. For all practical lenses
lenses, the MTF starts out near 1 and falls off at increasing
frequencies. MTFs vary with the aperture, the distance the image
region is from the center, the direction of the pattern (along a
radius or 90 degrees to that), the wavelength of the light, and the
subject distance.

Even for an ideal lens, diffraction effects fundamentally force the
MTF be be zero at spatial frequencies beyond 1/(lambda*N) cycles per
mm, where lambda is the wavelength of the light. For lambda = 555nm,
the peak of the eye's response, this is very close to 1800/N cycles
per mm.

The MTF of a system is the product of the properly scaled MTFs of each
of its components, as long as there are not two consecutive
non-diffusing components. (Thus with proper scaling you can multiply
camera lens MTF by film MTF by enlarger lens MTF by paper MTF, but
usually not a telescope objective MTF by an eyepiece MTF. There are
also some other obscure conditions under which MTFs can be
multiplied.)

Note that although MTF is usually thought of as the spatial frequency
response function and is plotted with spatial frequency as the
abscissa, some manufacturers (e.g. Canon) publish plots of the MTF at
specific spatial frequencies with distance from the center of the
image as the abscissa.

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