Spectral Method for Multiplexed Phase Retrieval and Application in Optical Imaging in Complex Media

We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple incoherent sources are sampled jointly, and one would like to recover their individual contributions. We show that a recent spectral method developed for phase retrieval can be generalized to this setting, and that its performance follows a phase transition behavior. We apply this new technique to light focusing at depth in a complex medium. Experimentally, although we only have access to the sum of the intensities on multiple targets, we are able to separately focus on each one, thus opening potential applications in deep fluorescence imaging and light delivery.