Deep Learning for Phase Retrieval in Lensless Imaging

Abstract

The phase problem refers to the loss of phase information during an imaging process. For imaging methods that utilize the Fourier transform, such as coherent diffraction imaging, the solution of the phase problem is necessary. The phase distribution provides information about an object’s shape and the thickness of transparent objects. The phase problem is ill-posed and thus cannot be solved analytically. Phase retrieval refers to the algorithmic solution of the phase problem. Classic phase retrieval methods are some form of constrained optimization, where the phase is estimated from an amplitude image. In this work, the phase is estimated statistically using a deep neural network. The advantage is that the network does not need to know any constraints or priors about the problem, it should learn them innately. The difference to previous approaches is that the network is used purely for phase retrieval, and optical backpropagation is done algorithmically using the angular spectrum method. The network used is a U-net model. It has been enhanced with dilated convolution, residual connections and a dense structure. It is trained with both simulated and experimentally captured amplitude images. The experimental images are modulated using a spatial light modulator. The results are evaluated quantitatively using absolute error, normalized root-mean-square error and the structural similarity index measure. The results show that the network has learned a generalizable solution to the phase problem. Separating the optical backpropagation from the network provides favourable visual quality compared to previous approaches. It is notable that the network trained on simulated images could also generalize to experimental images. The limitations were mainly in the experiment set-up used, and especially the phase modulation capability of the spatial light modulator.