In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF
camera systems. They are at the level of final examination problems that have been made solvable by a student or
professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits,
four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between
phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
A smart camera is studied that combines the blurring logarithmic asphere lens and maximum entropy processing to extend the depth of field 10 times over that of a conventional lens and to provide near diffraction-limited performance. For this camera, a circularly symmetric logarithmic lens with radially varying focus length provides an image with distance invariant blur; a newly developed digital deconvolution technique, the accelerated maximum entropy processing, is thereafter applied to recover the sharp image providing an extended depth of field. Three types of logarithmic aspheres are described together with the effect of aperture apodizations. We show that the central obscuration of the aperture improves the overall performance of the smart camera, especially the near distance performance. The performance of the maximum entropy processing is greatly improved by introducing a new metric parameter into the algorithm. In the presentation, I will demonstrate the novel maximum entropy algorithm that has been devised, and also demonstrate the lens manufacturing technique of magnetorheological finisher that we used.
Transmission functions are derived for a novel logarithmic aspheric lens that provides an extended depth-of-field when used in an integrated digital processing system. Diffraction-theory equations valid in the non-paraxial case are presented together with a comparative study of two designs. This lens can be used either singly or in conjunction with a standard photographic lens. A tenfold increase in the depth-of-field has been obtained.
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