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Fast decimation-in-frequency direct binary search algorithms for synthesis of computer-generated holograms

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Abstract

Fast decimation-in-frequency direct binary search (DBS) algorithms for the computation of binary computer-generated holograms (CGH’s) are developed. The algorithms use the geometry of the image plane and the decimation-in-frequency property to design a fast method of scanning the hologram with the DBS method. In this way the computational complexity of the method is substantially reduced. For complex-amplitude-based error, the asymptotic computational complexity for an L-point CGH is reduced by a factor of O[(L/log2L)1/2]. For intensity-based error, the asymptotic computational complexity for an L-point CGH is reduced by a factor of O[(L log2L)1/4]. When the probability of accepting an inversion is small, an acceleration technique is also used to reduce further the time complexity.

© 1994 Optical Society of America

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