Phase object retrieval through scattering medium

Optical imaging through a scattering medium has been an interesting and important research topic, especially in the field of biomedical imaging. However, it is still a challenging task due to strong scattering. This paper proposes to recover the phase object behind the scattering medium from one single-shot speckle intensity image using calibrated transmission matrices (TMs). We construct the forward model as a non-linear mapping, since the intensity image loses the phase information, and then a generalized phase retrieval algorithm is employed to recover the hidden object. Moreover, we show that a phase object can be reconstructed with a small portion of the speckle image captured by the camera. The simulation is performed to demonstrate our scheme and test its performance. Finally, a real experiment is set up, we measure the TMs from the scattering medium, and then use it to reconstruct the hidden object. We show that a phase object of size 32 x 32 is retrieved from 150 x 150 speckle grains, which is only 1/50 of the speckles area. We believe our proposed method can benefit the community of imaging through the scattering medium.