Phase-retrieval algorithms for nonnegative and finite-extent objects

Abstract

We propose new phase-retrieval algorithms that utilize the nonnegativity and the finite extent of objects. The squared error in the Fourier domain is minimized with an improved conjugate-gradient method that uses the Kuhn–Tucker theorem to estimate the nonnegative object. The squared error outside the finite support of the object is minimized to estimate the phase of the Fourier transform of the object. This phase-estimation method is combined with the improved conjugate-gradient method. The effectiveness of these phase-retrieval algorithms is clearly shown through computer simulations.