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.