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.

中文翻译：

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通过区域相位微分检索高散射介质的复杂传输矩阵

准确测量散射介质（SM）的复传输矩阵（CTM）对于反散射光学成像、光疗和光学神经网络的应用具有至关重要的意义。非干涉测量方法利用相位检索算法，可以从穿过 SM 的多个探测场形成的散斑图案中稳健地提取 CTM。然而，在采用幅度型空间光调制器进行探测场调制的情况下，缺乏相位控制经常导致收敛到局部最优，从而损害测量精度。在这里，我们提出了一种基于区域相位分化（RPD）的高精度 CTM 检索（CTMR）方法。它将一系列附加相位掩模合并到探测场中，对相位检索算法施加先验约束。通过区分不同相位掩模产生的散斑图案的方差，RPD-CTMR 可以有效地将算法引导至非常接近 SM 的 CTM 的解决方案。我们构建了数字微镜器件调制 RPD-CTMR 的原型。通过精确测量扩散板的CTM，我们实现了抗散射聚焦的峰背景比提高了3.6倍，同时抗散射图像传输的误码率降低了24倍我们提出的方法旨在促进散射光场的精确调制，从而促进包括高分辨率显微镜、生物医学光学成像和光通信在内的各个领域的进步。