Extension of nonnegative constraints to difference-map algorithm on both real and imaginary parts of real space in phase retrieval

Abstract

The difference-map (DM) algorithm is an iterative method to retrieve the image of an object from its diffraction pattern. Our study proposes the use of nonnegative constraints, reducing the number of unknown variables by half, on both the real and imaginary parts of the object space to reconstruct the image of a complex-valued object in the iterative process of the DM algorithm. The feasibility of the algorithm in biological cell applications was demonstrated using both simulations and optical laser coherent diffraction experiments. The results show that a more accurate image of the object can be retrieved using a loose support by nonnegative constraints than by the same support alone. The comparison indicates that the DM algorithm is superior to the hybrid input–output algorithm in the presence of nonnegative constraints. Therefore, during the execution of a DM algorithm, a loose support allows for more accurate reconstruction than a tight support, which can hardly be found in most cases because of the noise blurring of the retrieved image, and considerable reduction in the reconstruction errors.