Phase‐Only Approximate Message Passing for Reference‐Free Transmission Matrix Retrieval in Multimode Fibers

ABSTRACT Multimode fibers (MMFs) support high optical throughput within ultra‐compact waveguides, holding great promise for minimally invasive imaging, optical manipulation, and optical communication. However, modal coupling during propagation generates random speckle fields, and accurate transmission matrix (TM) measurement typically relies on interferometric setups that are sensitive to environmental disturbances. Existing reference‐free phase retrieval methods often exhibit limitations in spatially continuous TM recovery and deliver unbalanced overall performance under limited intensity measurements. This work develops a phase‐only approximate message passing (PO‐AMP) framework for robust reference‐free MMF TM retrieval. A customized preprocessing pipeline adapts continuous phase‐only probes to a statistical message‐passing model, supporting stable complex TM reconstruction with Onsager‐corrected iterations. Simulations validate its superiority in sampling efficiency, noise immunity, and convergence. Experiments reveal more complete TM recovery under limited measurements, reconstructing a full 1024 16 384 TM within a practical runtime of 17.22 s at a sampling rate . Multi‐point focusing and far‐field scanning imaging further confirm its higher focusing uniformity and better image continuity. Overall, PO‐AMP delivers a well‐balanced reference‐free TM retrieval strategy combining low‐measurement recovery, noise robustness, practical runtime, and spatial recovery completeness, making it promising for diverse MMF‐based wavefront control applications.