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For an experiment in which a surface is scanned by a coherent beam and the scattered far field is measured, the correct mathematical tools are provided by the Gabor transform formalism. This work describes a method that uses this approach together with a parallel POCS algorithm, to reconstruct surface features. The method shows how to reconstruct a phase only object from amplitude-only data measured in a scanning experiment. An improvement of the method permits to recover frequencies lost due to the finite aperture of the optical setup.
Michael Friedmann
"Optical Gabor transform in surface reconstruction", Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27782H (1 September 1996); https://doi.org/10.1117/12.2298971
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Michael Friedmann, "Optical Gabor transform in surface reconstruction," Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27782H (1 September 1996); https://doi.org/10.1117/12.2298971