Open AccessUse of numerical orthogonal transformation for the Zernike analysis of lateral shearing interferograms
Author(s) -
Fengzhao Dai,
Feng Tang,
Xiangzhao Wang,
Peng Feng,
Osami Sasaki
Publication year - 2012
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.20.001530
Subject(s) - zernike polynomials , wavefront , shearing interferometer , shearing (physics) , optics , apodization , numerical analysis , transformation matrix , orthogonal functions , mathematics , physics , mathematical analysis , interferometry , classical mechanics , kinematics , astronomical interferometer , thermodynamics
A numerical orthogonal transformation method for reconstructing a wavefront by use of Zernike polynomials in lateral shearing interferometry is proposed. The difference fronts data in two perpendicular directions are fitted to numerical orthonormal polynomials instead of Zernike polynomials, and then the orthonormal coefficients are used to evaluate the Zernike coefficients of the original wavefront by use of a numerical shear matrix. Due to the fact that the dimensions of the shear matrix are finite, the high-order terms of the original wavefront above a certain order have to be neglected. One of advantages of the proposed method is that the impact of the neglected high-order terms on the outcomes of the lower-order terms can be decreased, which leads to a more accurate reconstruction result. Another advantage is that the proposed method can be applied to reconstruct a wavefront on an aperture of arbitrary shape from its difference fronts. Theoretical analysis and numerical simulations shows that the proposed method is correct and its reconstruction error is obviously smaller than that of Rimmer-Wyant method.