Phase Retrieval Using Complex Speckle Illumination Patterns and Multiplexing

A method is proposed for reconstructing the phase of the optical response function of some object by illuminating the object with complex illumination patterns, and measur- ing the power and power spectral centroid position at the image plane for each pattern. The method is shown to work for complex speckle patterns as produced by a multi-mode waveguide. Alongside the continuous derivation of the method, a totally discrete analog is derived for use in numerical simulations. We also show that uniform random complex illumination patterns can be used instead of speckle patterns. The reconstructed optical response function differs from the ground truth by a factor of 10^−11 in simulation, from which we claim that the reconstruction is exact.