Probabilistic Phase Shaping Guided Wavefront Control of Complex Media with Information-Limited Intensity Measurements

Recent developments in wavefront shaping for complex media bring new possibilities to a variety of applications, including optical imaging, optical manipulation, and optical communications. In these applications, retrieving transmission matrices is critically important to the synthesization of arbitrary optical fields inside or through complex media. According to the information theory, 2N measurements contain sufficient information to determine N elements of the transmission matrix that include both amplitude and phase, suggesting a sampling ratio of & gamma;=2$\gamma = 2$. While holographic approaches are sensitive to environmental disturbance, nonholographic phase-retrieval methods take more intensity measurements to fight against nonlinearity. Untill today, a non-holographic phase-retrieval method that can effectively retrieve the transmission matrix with information-limited intensity measurements, i.e., & gamma;=2$\gamma = 2$, was still absent. In this work, this blank is filled by developing a probing strategy, termed probabilistic phase shaping (PPS) guided amplitude flow (AF). Retrieval of the transmission matrix of a multimode fiber (MMF) is experimentally demonstrated using the PPS-AF method over (& gamma;=3.5$\gamma = 3.5$) and with (& gamma;=2$\gamma = 2$) information limit. Using the retrieved transmission matrix, wavefront control including projecting single optical foci and synthesizing English letters is demonstrated successfully. This work is an important step toward efficient wavefront control of complex media, showing great prospects for a wide range of applications.