Non-quadrature amplitude modulation: a novel interferometric method for phase retrieval

Abstract

Phase-shifting interferometry (PSI) is a well-known technique used to calculate the phase of a resulting wavefront. This wavefront is commonly originated from the superposition of a known reference wavefront with a distorted wavefront, resulting in an interference pattern. In order to extract information about the resulting wavefront (which can be related to surfaces thicknesses, surface roughness, optical power, material homogeneity, temperature, index of refraction, just to mention a few), a set of interference patterns are generally changed in a known phase-step to form a resoluble system of equations. In PSI the contrast, visibility and phase variations of the resulting interference patterns are considered homogeneous and spatially constant, respectively. These conditions are hard to obtain experimentally, even though a carefully calibrated phase shifter and/or optical elements of high quality are used to carry out the experimental setup. In this manuscript, we present a novel and alternative method for phase extraction named phase-visibility modulating interferometry (PVMI), which introduces spatial variations of phase and visibility in the interferogram. The phase is computed from the measured intensities, and thus the interferograms can be normalized and their phase variations can be also known. The spatial variations are introduced by modulating in phase and amplitude a reference beam by non-quadrature amplitude modulation (NQAM), achieved by the sum of two beams out of phase within the range (0, 2Pi) and by the modulation of their amplitudes. NQAM is produced in this proposal by using dark sheets as amplitude filters, neutral density filters and the diffraction orders of a grating, which considerably reduce the expenses generated when using common phase shifter devices such as piezoelectric transducers; besides that the amplitude filters need no calibration. In PVMI the spatial variations of phase and visibility do not represent any problem, however the phase difference between the reference beams has to remain temporally constant, which represent an experimental problem. For this reason, in order to overcome this inconvenient PVMI also has been implemented in a single shot. A theoretical analysis and experimental results will be shown for each implementation. The viability of these proposed experimental setups allows them to be easily replicated and used for researching purposes or for teaching special topics in optics for undergraduate or graduate studies in the field of physics.