Complex transmission matrix retrieval for a highly scattering medium via regional phase differentiation

Abstract

Accurately measuring the complex transmission matrix (CTM) of the scattering medium (SM) holds critical significance for applications in anti-scattering optical imaging, phototherapy, and optical neural networks. Non-interferometric approaches, utilizing phase retrieval algorithms, can robustly extract the CTM from the speckle patterns formed by multiple probing fields traversing the SM. However, in cases where an amplitude-type spatial light modulator is employed for probing field modulation, the absence of phase control frequently results in the convergence towards a local optimum, undermining the measurement accuracy. Here, we propose a high-accuracy CTM retrieval (CTMR) approach based on regional phase differentiation (RPD). It incorporates a sequence of additional phase masks into the probing fields, imposing a priori constraints on the phase retrieval algorithms. By distinguishing the variance of speckle patterns produced by different phase masks, the RPD-CTMR can effectively direct the algorithm towards a solution that closely approximates the CTM of the SM. We built a prototype of a digital micromirror device modulated RPD-CTMR. By accurately measuring the CTM of diffusers, we achieved an enhancement in the peak-to-background ratio of anti-scattering focusing by a factor of 3.6, alongside a reduction in the bit error rate of anti-scattering image transmission by a factor of 24. Our proposed approach aims to facilitate precise modulation of scattered optical fields, thereby fostering advancements in diverse fields including high-resolution microscopy, biomedical optical imaging, and optical communications.