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 ) ! ] .

中文翻译：

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相敏全息的线性时间算法

摘要。诸如直接搜索 (DS) 和模拟退火之类的全息搜索算法允许以较长的执行时间为代价生成高质量的全息图。这是由于 O ( NxNy ) 的单次迭代计算成本和 O ( NxNy ) 阶所需的迭代次数，其中 Nx 和 Ny 是图像尺寸。这给出了 O(Nx2Ny2) 阶的组合性能。我们使用一种技术将相敏计算机生成的全息图的迭代成本降低到 O ( 1 ) ，从而给出 O ( NxNy ) 的最终算法性能。我们通过重新制定均方误差 (MSE) 度量来实现这一点，以允许从衍射场计算它，而不需要前向变换步骤。对于 1024 × 1024 像素的测试图像，这给了我们 ≈50，000 × 与传统 DS 相比的加速，几乎没有额外的复杂性。当应用于相位调制或幅度调制设备时，所提出的算法在 O ( NxNy ) 时间内收敛于全局最小 MSE。相比之下，大多数现有算法不能保证获得全局最小值。那些这样做的，具有至少 O(Nx2Ny2) 的计算复杂度，而朴素的算法是 O [ ( NxNy ) ！]。