Non-convex optimization for retrieving the complex transmission matrix of a multimode fiber

Measuring the complex transmission matrix (TM) is highly desired for light focusing and image transmission through complex media such as biological tissue and multimode fiber (MMF), which allows full modulation of incident light field. Instead of using holography-based methods, here we utilize advanced phase retrieval algorithms to retrieve the complex TM of MMF from speckle intensity data. A non-convex optimization method, reweighted amplitude flow (RAF), has been adopted for TM retrieval, which shows superior performance and fast computation speed. The comparisons with previous approaches are implemented numerically regarding different sampling ratios and input sizes. We further modified RAF to boost its TM retrieval performance in noisy environment, achieving experimental results of high-quality focusing through MMF and image transmission with high fidelity. These, collectively, validate the accuracy of the proposed TM retrieval method.