Modulation Transfer Function (MTF) is an important method of describing the performance of an optical system. A consequence of applying Fourier theory to image forming optical systems, MTF describes the contrast in the image of a spatial frequency presented in the scene being viewed.

Spatial frequency is measured in cycles per mm in focal image space, and in cycles per milliradian or other angular unit in afocal spaces. "Cycles" is the correct term for sinusoidal MTF response. The term "line pairs" is often used, but strictly speaking line pairs only applies to bar, as opposed to sinusoidal targets. ZEMAX can compute MTF for both bar and sinusoidal targets.



The bitmap image analysis window above shows 'good' image quality¹ in the section showing the three boys: but how good is good? The contrast ratio in the various line images provides quantitative data on the quality of the image formed. MTF describes the transfer of modulation from the object to the image as a function of spatial frequency and is commonly used to specify lens performance, and as optimization and tolerancing targets during lens design.



The MTF plot for this lens, above, shows the contrast ratio for any spatial frequency up to the maximum that the lens can support. In this case, we choose to limit the spatial frequencies shown to a maximum of 100 cycles/mm.  Also shown for reference is the diffraction limited performance of an aberration-free lens of the same f/#. Once you are familiar with MTF plots, you can assess image quality at a glance.

[1] Note that the apparent image quality is reduced by screen resolution and the compression of the image. The original image as produced by ZEMAX is of photographic quality. See How to Produce Photo-Realistic Output Images for full details.