The Gerchberg–Saxton (GS) algorithm, which retrieves phase information from the measured intensities on two related planes (the source plane and the target plane), has been widely adopted in a variety of applications when holographic methods are challenging to be implemented. In this work, we showed that the GS algorithm can be generalized to retrieve the unknown propagating function that connects these two planes. As a proof-of-concept, we employed the generalized GS (GGS) algorithm to retrieve the optical transmission matrix (TM) of a complex medium through the measured intensity distributions on the target plane. Numerical studies indicate that the GGS algorithm can efficiently retrieve the optical TM while maintaining accuracy. With the same training data set, the computational time cost by the GGS algorithm is orders of magnitude less than that consumed by other non-holographic methods reported in the literature. Besides numerical investigations, we also experimentally demonstrated retrieving the optical TMs of a stack of ground glasses and a 1-m-long multimode fiber using the GGS algorithm. The accuracy of the retrieved TM was evaluated by synthesizing high-quality single foci and multiple foci on the target plane through these complex media. These results indicate that the GGS algorithm can handle a large TM with high efficiency, showing great promise in a variety of applications in optics.

中文翻译：

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通用Gerchberg-Saxton算法检索复杂的光传输矩阵

Gerchberg-Saxton（GS）算法可从两个相关平面（源平面和目标平面）上测得的强度中检索相位信息，当全息方法难以实现时，该算法已广泛用于各种应用中。在这项工作中，我们证明了可以将GS算法推广到检索连接这两个平面的未知传播函数。作为概念验证，我们使用广义GS（GGS）算法通过目标平面上测得的强度分布来检索复杂介质的光传输矩阵（TM）。数值研究表明，GGS算法可以在保持精度的同时有效地检索光学TM。使用相同的训练数据集，GGS算法的计算时间成本比文献中报道的其他非全息方法所消耗的时间少几个数量级。除了数值研究之外，我们还实验性地证明了使用GGS算法检索一堆毛玻璃和1米长的多模光纤的光学TM。通过在这些复杂介质上在目标平面上合成高质量的单个病灶和多个病灶，可以评估检索到的TM的准确性。这些结果表明，GGS算法可以高效地处理大型TM，在光学的各种应用中显示出巨大的希望。我们还通过实验证明了使用GGS算法检索一堆毛玻璃和1米长的多模光纤的光学TM。通过在这些复杂介质上在目标平面上合成高质量的单个病灶和多个病灶，可以评估检索到的TM的准确性。这些结果表明，GGS算法可以高效地处理大型TM，在光学的各种应用中显示出巨大的希望。我们还通过实验证明了使用GGS算法检索一堆毛玻璃和1米长的多模光纤的光学TM。通过在这些复杂介质上在目标平面上合成高质量的单个病灶和多个病灶，可以评估检索到的TM的准确性。这些结果表明，GGS算法可以高效地处理大型TM，在光学的各种应用中显示出巨大的希望。