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Re: More on Basic Fourier Optics

For kits and details about optical transforms and diffraction patterns, take
a look at the optical transform kit, DNA Optical Transform kit, and other
materials available from the Institute for Chemical Education at the
following site:

Lawrence D. Woolf; General Atomics; 3550 General Atomics Court, San Diego,
CA 92121; Phone:858-455-4475; FAX:858-455-4268

-----Original Message-----
From: brian whatcott
Sent: Friday, June 22, 2001 12:32 PM
Subject: More on Basic Fourier Optics

The optical method of generating a 2D Fourier transform of the
spatial information in a slide is ridiculously easy.
It goes like this:

On an optical bench set out a laser of a few milliwatts and a
beam expander in order to illuminate a 35 mm slide.
Set out a converging lens of convenient focal length, say
15cm, at one focal length behind the slide.
Then one focal length behind the lens, set out a white card.

The card displays a fourier transform of the spatial frequencies
present in the slide.
Consider a small hole as the image to analyze.
Its FT is a large circle of light, with two visible haloes of
reduced intensity surrounding it.
If we consider a slice through this original image, it is a square
shouldered pulse in shape, so it is no surprise that examination
of the FT at the transform plane shows a zero frequency component
at the center, surrounded by third and fifth spatial harmonics
in all radial directions. These are the haloes that I mentioned.

If we place a second similar converging lens at a focal length behind
this transform plane, we see the original image once more at a focal length
behind this second lens - the FT is symmetrical.