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

Code Number:
6Q20.10
Demo Title:
Abbe's Theory of Imaging - Optical Fourier Transform
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.
  • Anthony Gerrard, "An Elementary Theoretical Approach to the Abbe Theory of Optical Image Formation", AJP, Vol. 31, #9, Sept. 1963, p. 723.

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