A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry

Abstract

An improved partial differential equation algorithm with high validity and accuracy has been proposed to reconstruct a wavefront from its phase differences in lateral shearing interferometry. The algorithm is based on a complete point to point mapping relationship between the wavefront phase and its differences via a least squares principle. A special set of linear equations which relates the phase of the wavefront under test to its bi-direction difference data is derived initially, and then by solving the set of equations the wavefront phase is determined. As the coefficient matrix of the set of equations is sparse and symmetric, it is transformed to a new small matrix to reduce the memory and numerical calculation needs in the solving process. Since the matrix is a positive-definite matrix, the Choleski factorization is adopted to solve the set of equations conveniently. The advantages of the algorithm such as reduction of computer memory needs, high reconstruction accuracy and efficiency are analyzed and discussed. The error propagation analysis and testing shows a good noise suppression ability.