Evaluation of partial coherence correction in X-ray ptychography

Abstract

Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography both heavily rely on the high degree of spatial coherence of the X-ray illumination for sufficient experimental data quality for reconstruction convergence. Nevertheless, the majority of the available synchrotron undulator sources have a limited degree of partial coherence, leading to reduced data quality and a lower speckle contrast in the coherent diffraction patterns. It is still an open question whether experimentalists should compromise the coherence properties of an X-ray source in exchange for a higher flux density at a sample, especially when some materials of scientific interest are relatively weak scatterers. A previous study has suggested that in CDI, the best strategy for the study of strong phase objects is to maintain a high degree of coherence of the illuminating X-rays because of the broadening of solution space resulting from the strong phase structures. In this article, we demonstrate the first systematic analysis of the effectiveness of partial coherence correction in ptychography as a function of the coherence properties, degree of complexity of illumination (degree of phase diversity of the probe) and sample phase complexity. We have also performed analysis of how well ptychographic algorithms refine X-ray probe and complex coherence functions when those variables are unknown at the start of reconstructions, for noise-free simulated data, in the case of both real-valued and highly-complex objects. K. Robinson, "Shearing interferometer for quantifying the coherence of hard x-ray beams," Phys. Rev. Lett. 94, 164801 (2005). 30.

Partially coherent ptychography by gradient decomposition of the probe

“…It was solved by the alternating projection algorithm in [5], when κ is a Gaussian kernel function with free horizontal and vertical coherence length parameters. Burdet et al [2] applied the above model to ptychographic imaging and proposed the Douglas-Rachford algorithm with a known Gaussian kernel function. A more general description of a partially coherent wave field illuminating a specimen in a ptychography experiment was considered in [27], where the authors employed an orthogonal decomposition of the mutual coherence function [30] to describe partially coherent measurement as follows:…”

“…Other existing studies focus mostly on (2), which only addressed blurring coherent intensities at the detector. In practice, the blur is dominated by the source dimensions and by the translation of the probe with respect to the image during an exposure [7,21].…”

Multi-Modal Ptychography: Recent Developments and Applications

“…Previously, researchers adopted RL deconvolution to accommodate spatial partial coherence into CDI [5,6] and ptychographic [11] iterative algorithms, and their mathematical formulations have been described in details in Ref [5,6,11]. To further develop the mathematical concept of partial coherence that suits ptychography, a different version of representation of partial coherence of electromagnetic waves has been suggested [7,9], which adopts the theorem that transverse and longitudinal partially coherent X-rays can be generally formulated equivalently by introduction of superposition states of multiple modes in both spatial and wavelength (spectra) regimes.…”

Transverse Coherence Limited Coherent Diffraction Imaging using a Molybdenum Soft X-ray Laser Pumped at Moderate Pump Energies

“…This constraint can be resolved if the SXRL is used in conjunction with ptychography 47, 48 or if isolated objects are imaged that are smaller than 1.5 micron, which is also suggested by high fringe contrast obtained from the SXRL for sufficiently small slit spacing (Fig. 2a).…”