论文标题
相敏感全息图的线性时间算法
Linear time algorithm for phase sensitive holography
论文作者
论文摘要
全息搜索算法（例如直接搜索和模拟退火）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（n_x n_y）$的单个迭代计算成本以及订单$ o（n_x n_y）$的必需迭代数，其中$ n_x $和$ n_y $是图像尺寸。这给出了订单$ O（n_x^2 n_y^2）$的组合性能。在本文中，我们使用一种新颖的技术将迭代的成本降低至$ O（1）$，用于相关计算机生成的全息图，提供最终的算法性能为$ O（n_x n_y）$。我们通过重新设计于点误差度量来实现此操作，以便从衍射场计算出来，而不是需要前向变换步骤。与传统的直接搜索相比，$ 1024 \ times 1024 $ PIXEL测试图像，这给了我们$ \ 50,000 \ times $加速。当应用于相位调节或振幅调节设备时，提出的算法会在$ O（n_x n_y）$时间的全局最小平方误差上收敛。相比之下，大多数现存的算法不能保证获得全局最小值，而那些确实具有至少$ o的计算复杂性（n_x^2 n_y^2）$，而天真算法为$ o（（n_xn_y）！）$。
Holographic search algorithms such as direct search 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 $O(N_x N_y)$ and number of required iterations of order $O(N_x N_y)$, where $N_x$ and $N_y$ are the image dimensions. This gives a combined performance of order $O(N_x^2 N_y^2)$. In this paper we use a novel technique to reduce the iteration cost down to $O(1)$ for phase-sensitive computer generated holograms giving a final algorithmic performance of $O(N_x N_y)$. We do this by reformulating the mean-squared error metric to allow it to be calculated from the diffraction field rather than requiring a forward transform step. For a $1024\times 1024$ pixel test images this gave us a $\approx 50,000\times$ speed-up when compared with traditional direct search with little additional complexity. When applied to phase-modulating or amplitude-modulating devices the proposed algorithm converges on a global minimum mean squared error in $O(N_x N_y)$ time. By comparison, most extant algorithms do not guarantee a global minimum is obtained and those that do have a computational complexity of at least $O(N_x^2 N_y^2)$ with the naive algorithm being $O((N_xN_y)!)$.
