Phase map retrieval in digital holography: avoiding the under-sampling effect by a lateral shear approach

Abstract

In Digital Holography (DH) the numerical reconstruction of the whole wavefront refracted or reflected by a sample object allows one to extract the wrapped phase map mod, 2π. In fact, since the hologram is coded numerically as a digitized image, both the wavefront amplitude and phase can be reconstructed simultaneously to provide amplitude and phase contrast imaging. The resolution in the image plane is the reconstruction pixel size that depends on wavelength, reconstruction distance and the size of the CCD recording area. Efforts to improve the resolution of DH reconstructions have been accomplished, following various strategies: increasing of the hologram aperture by moving the camera in different positions or even by using synthetic aperture approaches, using a diffraction grating to record digital holograms with a wider solid angle in the object beam, or using multiple sources and/or multiple acquisitions. Although all of these methods allow one to increase the spatial resolution, one more complication exists concerning the loss of resolution that occurs in the usual DH reconstruction approaches. It can occur that the reconstructed wrapped phase map in the image plane is undersampled because of the limited pixel size which limits the spatial bandwidth of the reconstructed image. In such a case the phase distribution cannot be retrieved correctly by the usual unwrapping procedures. We show that the use of the digital Lateral-Shearing Interferometry (LSI) approach in DH provides the correct reconstruction of the phase map in the image plane, even in extreme cases where the phase profile changes very rapidly. We demonstrate the effectiveness of the method in a particular case where the profile of a highly curved silicon micro-electromechanical system membrane has to be reconstructed.