Phase retrieval by using transport-of-intensity equation and differential interference contrast microscopy

We present a variational reconstruction algorithm for the phase-retrieval problem by using the differential interference contrast microscopy. Principally, we rely on the transport-of-intensity equation that specifies the sought phase as the solution of a partial differential equation. Our approach is based on an iterative reconstruction algorithm involving the total variation regularisation which is efficiently solved via the alternating direction method of multipliers. We illustrate the applicability of the method via real data experiments. To the best of our knowledge, this work demonstrates the performance of such an iterative algorithm on real data for the first time.