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We present a general analytic approach to spatially resolve the nano-scale lattice distortion field of strained and defected compact crystals with Bragg coherent x-ray diffraction imaging (BCDI). Our approach relies on fitting a differentiable forward model simultaneously to multiple BCDI datasets corresponding to independent Bragg reflections from the same single crystal. It is designed to be faithful to heterogeneities that potentially manifest as phase discontinuities in the coherently diffracted wave, such as lattice dislocations in an imperfect crystal. We retain fidelity to such small features in the reconstruction process through a Fourier transform -based resampling algorithm designed to largely avoid the point spread tendencies of commonly employed interpolation methods. The reconstruction model defined in this manner brings BCDI reconstruction into the scope of explicit optimization driven by automatic differentiation. With results from simulations and experimental diffraction data, we demonstrate significant improvement in the final image quality compared to conventional phase retrieval, enabled by explicitly coupling multiple BCDI datasets into the reconstruction loss function., 30 pages, 23 figures

Nanoscale heterogeneity (including size, shape, strain, and defects) significantly impacts material properties and how they function. Bragg coherent x-ray imaging methods have emerged as a powerful tool to investigate, in three-dimensional detail, the local material response to external stimuli in reactive environments, thereby enabling explorations of the structure-defect-function relationship at the nanoscale. Although progress has been made in understanding this relationship, coherent imaging of extended samples is relatively slow (typically requiring many minutes) due to the experimental constraints required to solve the phase problem. Here, we develop Bragg coherent modulation imaging (BCMI), which uses a modulator to solve the phase problem thereby enabling fast, local imaging of an extended sample. Because a known modulator is essential to the technique, we first demonstrate experimentally that an unknown modulator structure can be recovered by using the exit wave diversity that exists in a standard Bragg coherent diffraction imaging (BCDI) experiment. We then show with simulations that a known modulator constraint is sufficient to solve the phase problem and enable a single view of an extended sample that is sensitive to defects and dislocations. Our results pave the way for BCMI investigations of strain and defect dynamics in complex extended crystals with temporal resolution limited by the exposure time of a single diffraction pattern.

Bragg coherent x-ray diffractive imaging is a powerful technique for investigating dynamic nanoscale processes in nanoparticles immersed in reactive, realistic environments. Its temporal resolution is limited, however, by the oversampling requirements of 3D phase retrieval. Here we show that incorporating the entire measurement time series, which is typically a continuous physical process, into phase retrieval allows the oversampling requirement at each time step to be reduced leading to a subsequent improvement in the temporal resolution by a factor of 2 to 20 times. The increased time resolution will allow imaging of faster dynamics and of radiation dose sensitive samples. This approach, which we call "chrono CDI", may find use in improving time resolution in other imaging techniques.

This supplemental material gives additional detail on Experimental Methods and Hard X-ray FEL Source Characteristics, Calculation of Maximum Speckle Contrast, Extracting Contrast of Weak Speckle Patterns, Estimated Temperature Increase from X-ray Absorption, Split-Pulse XPCS Feasibility, and Sample Disturbance During Single Pulses., Comment: This is the supplemental material for arXiv:1207.2458 by the same authors entitled: "High Contrast X-ray Speckle from Atomic-Scale Order in Liquids and Glasses"