Generalizing the Gerchberg–Saxton algorithm for retrieving complex optical transmission matrices
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.
基金项目：National Key Research and Development Program of China
Daixuan Wu：Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
Jiawei Luo：Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
Liang Lu：Information Materials and Intelligent Sensing Laboratory of Anhui Province, Key Laboratory of Opto-Electronic Information Acquisition and Manipulation of Ministry of Education, Anhui University, Hefei 230601, China
Fan Li：Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China
Yuecheng Shen：Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China；e-mail: email@example.com
Zhaohui Li：Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou 510275, China；Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China；e-mail: firstname.lastname@example.org
备注：National Key Research and Development Program of China
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Guoqiang Huang, Daixuan Wu, Jiawei Luo, Liang Lu, Fan Li, Yuecheng Shen, and Zhaohui Li, "Generalizing the Gerchberg–Saxton algorithm for retrieving complex optical transmission matrices," Photonics Research 9(1), 34-42 (2021)