Wavefront Reconstruction from Slope Data Within Pupils of Arbitrary Shapes Using Iterative Fourier Transform

Abstract: This letter presents a new modal technique that reconstructs a wavefront using iterative Fourier transforms and converts the Fourier coefficients as needed to and from the coefficients of the orthonormal basis set over pupils of arbi-trary shapes. It is shown that, for wavefront slope data, modal reconstruction with Fourier series using an iterative algo-rithm is faster and more accurate than when an orthonormal basis set is used. Elliptical, annular, hexagonal, and irregular pupils are considered as practical examples to illustrate the results