Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging

TL;DR

This paper introduces a novel Fourier-domain constraint for phase retrieval in coherent diffraction imaging, enabling faster and more reliable convergence in reconstructing atomic-resolution images from diffraction patterns.

Contribution

The authors propose a new Fourier-domain constraint based on holography principles, improving the speed and reliability of phase retrieval in CDI.

Findings

Enables initial low-resolution reconstruction in the first iteration.

Achieves faster convergence compared to traditional methods.

Provides high-resolution images after iterative refinement.

Abstract

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process.