28 August 2020 Linear-time algorithm for phase-sensitive holography
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Abstract

Holographic search algorithms such as direct search (DS) and simulated annealing allow high-quality holograms to be generated at the expense of long execution times. This is due to single iteration computational costs of O  (  NxNy  )   and number of required iterations of order O  (  NxNy  )  , where Nx and Ny are the image dimensions. This gives a combined performance of order O(Nx2Ny2). We use a technique to reduce the iteration cost down to O  (  1  )   for phase-sensitive computer-generated holograms, giving a final algorithmic performance of O  (  NxNy  )  . We do this by reformulating the mean-squared error (MSE) metric to allow it to be calculated from the diffraction field rather than requiring a forward transform step. For a 1024  ×  1024-pixel test images, this gave us a ≈50,000  ×   speed-up when compared with traditional DS with little additional complexity. When applied to phase-modulating or amplitude-modulating devices, the proposed algorithm converges on a global minimum MSE in O  (  NxNy  )   time. By comparison, most extant algorithms do not guarantee that a global minimum is obtained. Those that do, have a computational complexity of at least O(Nx2Ny2) with the naive algorithm being O  [    (  NxNy  )    !    ]  .

© 2020 Society of Photo-Optical Instrumentation Engineers (SPIE) 0091-3286/2020/$28.00 © 2020 SPIE
Peter J. Christopher, Ralf Mouthaan, Miguel El Guendy, and Timothy D. Wilkinson "Linear-time algorithm for phase-sensitive holography," Optical Engineering 59(8), 085104 (28 August 2020). https://doi.org/10.1117/1.OE.59.8.085104
Received: 6 July 2020; Accepted: 13 August 2020; Published: 28 August 2020
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CITATIONS
Cited by 3 scholarly publications.
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KEYWORDS
Holograms

Holography

Spatial light modulators

Diffraction

Fourier transforms

Modulation

Detection and tracking algorithms

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