In the last article we saw that the Point Spread Function and the Modulation Transfer Function of a lens could be easily obtained numerically by applying Discrete Fourier Transforms to its generalized exit pupil function twice in sequence.^{[1]}

Obtaining the 2D DFTs is easy: simply feed MxN numbers representing the two dimensional complex image of the pupil function in its space to a fast fourier transform routine and, presto, it produces MxN numbers that represent the amplitude of the PSF on the sensing plane, as shown below for the pupil function of a perfect lens with a circular aperture and MxN = 1024×1024.

Simple *and* fast. Wonderful. Below is a slice through the center, row 513, zoomed in. Hmm…. What are the physical units on the axes of displayed data produced by the DFT?

Less easy – and the subject of this article as seen from a photographic perspective.