Diffractive optical element for Zernike decomposition

A Zernike polynomial can be used to describe not only the phase of a wavefront, but also its entire complex amplitude. For the latter case, a diffractive optical element (DOE) is proposed to decompose the incident wavefront into a set of diffraction orders with their amplitudes proportional to the coefficients of the Zernike polynomial. A 25-channel Zernike decomposer is designed by means of an iterative method, and its operation simulated. When the amplitude distribution of the incident wavefront is known, its shape can be uniquely determined from the intensity measured on the output plane of the DOE. An exemplary algorithm for the phase retrieval is also presented. Such a DOE can be very useful in the rapid analysis of wavefronts.