FFT wavefront reconstruction algorithm with periodical extension for lateral shearing interferometry

Abstract

A new FFT wavefront reconstruction algorithm is proposed in this work, which can retrieve the test wavefront without spectrum leakage error. Since only part of the test wavefront interferes with its copy wavefront in the lateral shearing interferometer, the sizes of the sheared wavefronts are usually smaller than the test wavefront. To solve the issues introduced by the incompatible sizes of the sheared wavefronts, we used the measured information in the sheared wavefronts to compensate the missing parts based on the periodicity of the Fast Fourier Transform. This procedure can be applied under an arbitrary shear amount. Since no estimation is required during the extension, the accuracy of the reconstructed wavefront can be improved. We also provide an algorithm to estimate the lost information due to the illposed problem of reconstructing wavefront from the sheared interferometric data base on the proposed algorithm. The detail of the FFT processing and the sheared wavefront extension algorithm is given in this work. Some test is performed to evaluate the performance of the proposed algorithm. The test result shows that this algorithm is capable of reconstructing the test wavefront without introduces extra error. The estimation of the lost information based on our algorithm is convenient to be applied in the frequency. When the shear ratio is less than 25%, the estimation can always give a better result. The accuracy of the reconstructed wavefront is improved by up to 14.3% after estimation.