Phase retrieval in crystallography and optics

TLDR

Phase retrieval, a longstanding challenge in x‑ray crystallography, has recently attracted interest in optics and imaging, and while crystallographic phase problems differ from other imaging contexts, they share common features. The paper outlines and contrasts the principles of phase retrieval in crystallography with those in general imaging. The authors present a comparative analysis of crystallographic phase‑retrieval principles versus general imaging techniques. Uniqueness results are discussed, emphasizing how phase‑retrieval algorithms and insights from one discipline can inform the other.

Abstract

Phase problems occur in many scientific disciplines, particularly those involving remote sensing using a wave field. Although there has been much interest in phase retrieval in optics and in imaging in general over the past decade, phase retrieval has a much longer history in x-ray crystallography, and a variety of powerful and practical techniques have been developed. The nature of crystallography means that crystallographic phase problems are distinct from those in other imaging contexts, but there are a number of commonalities. Here the principles of phase retrieval in crystallography are outlined and are compared and contrasted with phase retrieval in general imaging. Uniqueness results are discussed, but the emphasis is on phase-retrieval algorithms and areas in which results in one discipline have, and may, contribute to the other.