Continuous Recovery of Phase from Single Interferogram

Abstract: A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities, typically addressed through intricate algorithms. Our method bypasses the unfolding and unwrapping, instead formulating a first-order differential equation directly relating the phase to the interferogram. Integration of this equation enables continuous retrieval of phase along any straight path. Representing a new class of analytical tools for single-interferogram phase retrieval, this approach is derived from first principles and accommodates both Newton-type and Fizeau-type interferograms. Its performance is demonstrated on multiple idealized synthetic interferograms of increasing complexity, validating against the known seed phase.