
340 OPTICS FOR ENGINEERS
All pupil functions are converted to coordinates of spatial frequency, f
x
, f
y
, before they are
multiplied to generate the ATF. In addition to the simplicity and insight that Fourier analy-
sis provides, formulating the problem in this particular way has computational advantages
as well. While different authors and computer programmers dene the Fourier transform in
slightly different ways, e.g., using different constants, all maintain the relationship between
the transform variable pairs ( f
x
, f
y
), and (x, y) on which Fourier analysis is based. Every
convention is self-consistent in that the inverse Fourier transform of the ...