Iterative diffraction pattern retrieval from a single focal construct geometry image

Understanding the crystal structure of materials under extreme conditions of pressure and temperature has been revolutionized by major advances in laser‐driven dynamic compression and in situ X‐ray diffraction (XRD) technology. Instead of the well known Debye–Scherrer configuration, the focal construct geometry (FCG) was introduced to produce high‐intensity diffraction data from laser‐based in situ XRD experiments without increasing the amount of laser energy, but the resulting reflections suffered from profoundly asymmetrical broadening, leading to inaccuracy in determination of the crystal structure. Inspired by fast‐neutron energy spectrum measurements, proposed here is an iterative retrieval method for recovering diffraction data from a single FCG image. This iterative algorithm restores both the peak shape and relative intensity with rapid convergence and requires no prior knowledge about the expected diffraction pattern, allowing the FCG to increase the in situ XRD intensity while simultaneously preserving the angular resolution. The feasibility and validity of the method are shown by successful recovery of the diffraction pattern from both a single simulated FCG image and a single laser‐based nanosecond XRD measurement. A general iterative algorithm is proposed, to recover the X‐ray diffraction data from a single focal construct geometry image, allowing the focal construct geometry to increase the diffraction intensity while simultaneously preserving the angular resolution.