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

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 arbitrary shapes. It is shown that, for wavefront slope data, modal reconstruction with Fourier series using an iterative algorithm 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.