Algorithmic image reconstruction using iterative phase retrieval schema

X-ray diffraction is potentially a strong candidate for biological imaging since it can in principle reconstruct thick samples at resolutions close to the diffraction limit of the radiation. Due to the non-crystalline nature of such samples, one seeks a phasing method other than that of traditional crystallography; such a method exists in the use of an iterative algorithm based on oversampling [1]. One of the tasks faced by an iterative method is to know when the iteration has given a faithful reconstruction. Past algorithms of this type [1,2,3] have employed the basic Fienup iterative schema [4]. In this paper we report on the use of a newer iterative schema due to Elser [5]; our computer simulations on real and complex test objects using Elser's schema show that his reconstruction-error function is a reliable measurement of the reconstruction. We also report that a magnitude-based histogram constraint can dramatically speed up the convergence of the reconstruction process.