Phase-visibility modulating interferometry by binary non-quadrature amplitude modulation with neutral density filters

• Phase retrieval from interferograms with inhomogeneous variations of phases and visibilities.
• NQAM achieved in two beams of a three-beam Mach–Zehnder interferometer.
• Amplitude modulation of two reference beams with neutral density filters.

An alternative method for phase retrieval based on spatial and binary non-quadrature amplitude modulation (NQAM) is presented. This proposal is based on the superposition of a probe beam with a reference beam modulated in phase and amplitude (PAM) by NQAM, which is implemented by two neutral density filters (NDF) in a three-beam Mach–Zehnder interferometer (MZI). The principal advantage of this proposal lies in an analytical relationship between the variations of phase and visibility in an interferogram with the variations in the amplitudes of the reference beams used to implement NQAM; thus, the interferograms can be normalized and their introduced phase variations can be known from the measured intensities. Consequently it is possible to successfully retrieve the object phase. It is worthy to note that this method is capable of accepting that the phase and visibility variations in the interferograms could be spatial functions.