Strolls with my Dog

Musings about Photography and the Science behind it

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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 P 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 uv space to a fast fourier transform routine and, presto, it produces MxN numbers that represent the amplitude of the PSF on the xy sensing plane, as shown below for the pupil function of a perfect lens with a circular aperture and MxN = 1024×1024.

Figure 1. 1a Left: Array of numbers representing a circular aperture (zeros for black and ones for white).  1b Right: Array of numbers representing the PSF of image 1a (contrast slightly boosted).

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

Figure 2. A slice through the center of the PSFshown in figure 1b.

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

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Musings about Photography