Propagation based phase retrieval of simulated intensity measurements using artificial neural networks.

Determining the phase of a wave from intensity measurements has many applications in fields such as electron microscopy, visible light optics, and medical imaging. Propagation based phase retrieval, where the phase is obtained from defocused images, has shown significant promise. There are, however, limitations in the accuracy of the retrieved phase arising from such methods. Sources of error include shot noise, image misalignment, and diffraction artifacts. We explore the use of artificial neural networks (ANNs) to improve the accuracy of propagation based phase retrieval algorithms applied to simulated intensity measurements. We employ a phase retrieval algorithm based on the transport-of-intensity equation to obtain the phase from simulated micrographs of procedurally generated specimens. We then train an ANN with pairs of retrieved and exact phases, and use the trained ANN to process a test set of retrieved phase maps. The total error in the phase is significantly reduced using this method. We also discuss a variety of potential extensions to this work.