# Phase Retrieval

## Abstract

Phase retrieval implies extraction of the phase of a complex function f(x) from its modulus. There is no general solution to this problem, unless additional constraints on f(x) are given. Examples of such constraints are analyticity, knowledge of the modulus of the Fourier transform of f(x), and compact support of its transform (which means that f(x) is bandlimited). The third constraint is useful in optics, because only the modulus of f(x) can be measured by an optical detector and because f(x) is usually The third constraint is useful in optics, because only the modulus of f(x) can be measured by an optical detector and because f (x) is usually bandlimited by the input aperture of the optics (the pupil). In this talk we show the basic math of phase retrieval, show some of the methods to extract the phase, and show a real-life example of the phase retrieval method, namely the identification of the phase aberration in the Hubble Space Telescope.