6Q20.10 - Abbe's Theory of Imaging - Optical Fourier Transform

Code Number:
6Q20.10
Demo Title:
Abbe's Theory of Imaging - Optical Fourier Transform

Disclaimer

Procedure:

Get the "Unit" slide from the Electron Diffraction - Optical Simulation demo (6D20.58).  The bottom left hand pattern of small characters is the one to use.  This will give a crystal diffraction pattern when a laser beam is pointed though the slide.  Place an 18 mm lens from the Michelson Interferometer (6D40.10) demo in front of the slide and observe that the diffraction pattern is now transformed to the real image of the optical crystal showing the original "L" shaped characters.  Basically you see the diffraction pattern consisting of the body factor convolved with the form factor.  When you insert the lens you see it Fourier transfrom, the real image of the Optical Crystal.

References:
  • Jack Higbie, "Abbe's Sine Theorem from a Thermodynamic and Fourier Transform Argument", AJP, Vol. 49, #8, Aug. 1981, p. 788.
  • Bernard M. Jaffe, "Geometrical Optics Derivation of the Fourier Transform Property of a Lens", AJP, Vol. 48, #2, Feb. 1980, p. 157.
  • D. G. Sargood, "On Abbe's Theory of Imaging: A Simple Lecture Room Demonstration", AJP, Vol. 46, #2, Feb. 1978, p. 185.
  • Dieter B. Ast, "Optical Simulation of the Origin of Contrast in the Electron Microscope", AJP, Vol. 39, #10, Oct. 1971, p. 1164.
  • Anthony Gerrard, "An Elementary Theoretical Approach to the Abbe Theory of Optical Image Formation", AJP, Vol. 31, #9, Sept. 1963, p. 723.

Disclaimer: These demonstrations are provided only for illustrative use by persons affiliated with The University of Iowa and only under the direction of a trained instructor or physicist.  The University of Iowa is not responsible for demonstrations performed by those using their own equipment or who choose to use this reference material for their own purpose.  The demonstrations included here are within the public domain and can be found in materials contained in libraries, bookstores, and through electronic sources.  Performing all or any portion of any of these demonstrations, with or without revisions not depicted here entails inherent risks.  These risks include, without limitation, bodily injury (and possibly death), including risks to health that may be temporary or permanent and that may exacerbate a pre-existing medical condition; and property loss or damage.  Anyone performing any part of these demonstrations, even with revisions, knowingly and voluntarily assumes all risks associated with them.