Phase retrieval in Digital Holographic Microscopy using a Gerchberg-Saxton algorithm

Fourier interferometry (FI) is a robust and simple method for reconstruction of phase modulated objects. Its main advantage is that it only requires the recording of one interference pattern, avoiding the problems caused by mechanical vibrations in the optical setup. Unfortunately, the conventional FI method can be employed in digital holography (DH) only for samples with reduced frequency bandwidth, because of the low spatial resolution of available electronic image recording devices (CCDs). We report two methods that partially overcome this bandwidth limitation of the FI technique implemented in DH. The first of these methods consists in a modified version of the conventional FI approach where, instead of processing the Fourier transform of the hologram, we calculate its Fresnel back propagation to the object plane. Although this modified FI approach provides appropriate reconstruction of objects with increased bandwidth, the local SNR tends to be low at thin phase modulated features of the object. In order to increase this SNR we employ the sample reconstructed with the modified FI method as the input in a Gerchberg-Saxton (GS) iterative method. In this GS procedure, the constraints are the modules of the fields at the object and at the hologram planes. This iterative method, implemented by numerical simulations, provides highly accurate phase corrections with fast convergence.