Improved Saunders method for the analysis of lateral shearing interferograms

Abstract

An interferogram obtained by use of ordinary interferometers, such as Fizeau and Twyman-Green interferometers, will show a contour map of the wave front under test. A lateral-shearing interferogram, however, will show a contour map of the difference between the wave front under test and a sheared wave front, that is, a contour map of the derivative of the wave front under test. Therefore one can reconstruct the shape of the wave front under test by analyzing that difference. Many methods for reconstructing a wave front have been proposed. The Saunders method reconstructs a wave front; rapidly however the wave-front data are reconstructed only at intervals of the amount of shear along the direction of the shear. Therefore the method has low spatial resolution. A method for reconstructing a wave front that is based on the Saunders method and has high spatial resolution is proposed. The method analyzes the differences that are produced by shearing of the wave front under test in many directions. This method requires a large number of interferograms for reconstructing the wave front. Here the method is described, and its validity is confirmed by simulation.

Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry

“…For achieving high spatial resolution reconstruction, some methods were presented in the literature [15][16][17][18][19]. A method based on discrete Fourier transformation was proposed by Elster and Weingärtner [15][16][17].…”

“…Based on the similar principle, an improved Saunders method was proposed by Yin [18], which requires two measurements with different shear amount at orthogonal shear directions. Another improved Saunders method was proposed by Nomura, et al [19]. In this method a large number of measurements in many directions are needed for reconstructing a two-dimensional wavefront.…”