Wave Front Reconstruction from Off-Axis Holograms Using Four-Quarter Phase Shifting Method

In this paper a method for digitally recording four quarter-reference-wave holograms (by CCD) in a Mach-Zehnder interferometer setup, and reconstructing the object wave-front by numerical method is presented. The terms of direct transmission, auto-correlation and conjugate wave in the four waves reconstruction are cancelled out and only one original object wave is left after overlapping. Reconstructed digital holograms are obtained by computing the Fresnel-Kirchhoff integral. Since the phase distribution of the wave field can be computed from the digital hologram, one can measure micrometric displacements and deformations of the reflecting object as well as small changes in refractive index field of the transmission object. In order to calibrate a specially designed device necessary for phase shifting purpose, we introduce a second Mach-Zehnder interferometer inside the main imaging interferometer. With this second interferometer we can directly observe displacement of a sector of circular interferometric fringes without the presence of the (reflecting or transmitting) object. By simultaneously transferring the images from the second interferometer to the computer and recording the holograms we measure, using image processing, fringe displacement in pixel units. Since the mirror on the phase shifting device is shared between two interferometers, the measured optical path difference is automatically applied in the main interferometer and thus the errors in shifting are substantially reduced.