Speckle spatial correlations aiding optical transmission matrix retrieval: the smoothed Gerchberg–Saxton single-iteration algorithm

The estimation of the transmission matrix of a disordered medium is a challenging problem in disordered photonics. Usually, its reconstruction relies on a complex inversion that aims at connecting a fully controlled input to the deterministic interference of the light field scrambled by the device. At the moment, iterative phase retrieval protocols provide the fastest reconstructing frameworks, converging in a few tens of iterations. Exploiting the knowledge of speckle correlations, we construct a new phase retrieval algorithm that reduces the computational cost to a single iteration. Besides being faster, our method is practical because it accepts fewer measurements than state-of-the-art protocols. Thanks to reducing computation time by one order of magnitude, our result can be a step forward toward real-time optical imaging that exploits disordered devices.