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From: perry@netcom.com (Perry West)
Subject: Re: Aperture Function / Diffraction Pattern relationship
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Date: Sun, 18 Jun 1995 14:45:28 GMT
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D.Kampmann-Hudson ESE PG (dmh@sys.uea.ac.uk) wrote:
: Is the Fourier Transform relationship between the Aperture function of
: a lens and the Fraunhofer diffraction pattern which it produces just a
: mathematical coincidence or is there some sound, real, physical
: principle which relates them? In other words, how is the diffraction
<snip>

Light passing through an aperture creates a diffraction pattern.  Check 
any reasonable textbook on optics for the details.

: The reason I ask this is that I find it slightly puzzling since both
: the aperture function and the diffraction pattern surely exist in the
: space domain and not in the frequency domain. The Fourier transform
: relationship almost seems to point to the fact that the Aperture
: function is in the space domain and the diffraction pattern exists in
: the frequency domain! This is not true.

Spatial functions can be described by a distribution of spatial 
frequencies.  When I studied electronics, we were taught that frequency 
was event per unit time (de/dt).  I don't remember being taught that this 
was temporal frequency.  Spatial frequency is event per unit distance 
(de/dx).  I guess if I had taken more mechanical engineering courses I 
would have learned this.  Consult any good book on image processing that 
covers fourier transforms of images.

For optics, I use Matt Young's book, Lasers and Optics (on something 
close to this), publised by Elsiver.

For image processing I would use any number of books, say Rosenfeld and 
Kak, Digitial Image Processing.
