Linear-time algorithm for phase-sensitive holography

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 N-x and N-y are the image dimensions. This gives a combined performance of order 0((NxNy2)-N-2). 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 x 1024-pixel test images, this gave us a approximate to 50,000x 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((NxNy2)-N-2) with the naive algorithm being O[(NxNy)!]. (C) 2020 Society of Photo-Optical Instrumentation Engineers (SPIE)