Reconstructing the phase distribution of two Interfering wavefronts by analysis of their nonlocalized fringes with an iterative method

Abstract

This paper presents a technique for reconstructing two interfering wavefronts by analyzing their 3D interference field pattern. The method is based on the numerical inverse problem and will present a robust algorithm for reconstructing of wavefronts. Several simulations are done to validate the proposed method.

Experimental verification of reconstruction of two interfering wavefronts using the transport of intensity equation

“…In this case, there is no need to have a known reference wavefront or it may be used to test validity of the reference wavefront. For reconstructing two unknown interfering wavefronts, four methods have already been proposed [6][7][8][9].…”

Reconstruction of two interfering wavefronts using Zernike polynomials and stochastic parallel gradient descent algorithm

“…For reconstructing two unknown interfering wavefronts, two methods have already been proposed [6,7] in which it is assumed that the angle between two wavefronts is small enough to satisfy the paraxial approximation. In these methods, the phase difference distributions (PDDs) are determined from the recorded interference intensity patterns at two observation planes perpendicular to the average propagation direction of wavefronts.…”

“…In these methods, the phase difference distributions (PDDs) are determined from the recorded interference intensity patterns at two observation planes perpendicular to the average propagation direction of wavefronts. Then, the phase distributions are derived with an analytical method in [6] and an iterative method in [7]. These methods have some limitations.…”

“…Moreover, this technique fails wherever the phase difference gradient becomes zero, and its accuracy is very sensitive to the distance between two observation planes. The latter [7] is a simpler method, but it takes too much time even for simple wavefronts such as spherical ones. In this Letter, we introduce a fast and accurate method for reconstructing two unknown interfering wavefronts based on Zernike polynomials [8].…”

“…The effectiveness of this wavefront propagator has been demonstrated in [7]. To numerically investigate the wavefront reconstruction capability of the proposed method, we simulated two wavefronts with the typical arbitrary phase distributions.…”