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

Abstract

We numerically and experimentally demonstrate an iterative method to simultaneously reconstruct two unknown interfering wavefronts. A three-dimensional interference pattern is analyzed and then Zernike polynomials and the stochastic parallel gradient descent algorithm are used to expand and calculate wavefronts.

Phase reconstruction of two interfering fields using a lenslet array and an optimization method

“…The method of minimizing the cost function is the SPGD algorithm which has been successfully used in phase reconstruction [10,21] and phase distortion correction [14,15,26,27] for its high convergence speed. The phase difference distribution Δfat the reconstruction plane is derived using the phase shifting technique.…”

“…The shear must be small enough. For overcoming theses limitations, several techniques have already been proposed to simultaneously reconstruct the unknown phases of two interfering fields without the need for a reference field or duplicating the unknown field [5][6][7][8][9][10][11].…”

“…Importantly, the fields do not have to be identical replicas of each other. In addition, the reconstruction of the two interfering fields has applications in retracing the fields and determining their origins; simultaneously testing the quality of two surfaces of an optical component from which the interfering fields are reflected or transmitted; and finding the optical parameters of an element, such as the thickness, radii of curvature, and refractive index of a lens [5,[10][11][12]. So the method opens new possibilities for holography, wavefront sensing, and metrology.…”

“…An effective way for reconstructing the unknown phases of two interfering fields is the use of an optimization technique [9][10][11]. Such techniques require the phase difference distributions between the two interfering fields at two planes and an optimization algorithm, such as simulated annealing [13] and stochastic parallel gradient descent (SPGD) [14,15].…”

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].…”