Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed, and those calculated from a present guess of the object. Efficient minimization methods require analytical calculation of the derivatives of the error metric, which is not always straightforward. This limits our ability to explore variations of basic imaging approaches. In this paper, we propose to substitute analytical derivative expressions with the automatic differentiation method, whereby we can achieve object reconstruction by specifying only the physics-based experimental forward model. We demonstrate the generality of the proposed method through straightforward object reconstruction for a variety of complex ptychographic experimental models.

This two‐part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real‐space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post‐processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real‐space distortions in the phase‐retrieved object, along with the necessary post‐retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase‐retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X‐ray science community with a set of generalized BCDI shear‐correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

The factors limiting the performance of alternative polycrystalline solar cells as compared with their single-crystal counterparts are not fully understood, but are thought to originate from structural and chemical heterogeneities at various length scales. Here, it is demonstrated that multimodal focused nanobeam X-ray microscopy can be used to reveal multiple aspects of the problem in a single measurement by mapping chemical makeup, lattice structure and charge collection efficiency simultaneously in a working solar cell. This approach was applied to micrometre-sized individual grains in a Cu(In,Ga)Se2 polycrystalline film packaged in a working device. It was found that, near grain boundaries, collection efficiency is increased, and that in these regions the lattice parameter of the material is expanded. These observations are discussed in terms of possible physical models and future experiments.

X‐ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub‐micrometre‐scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non‐orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non‐orthogonal real‐ and Fourier‐space frames, and to transform the 3D sample image into an orthogonal frame as a post‐processing step for result analysis. In this article, which is a direct follow‐up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non‐evenly sampled data along the direction of sample rotation (i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase‐retrieval Fourier transformation than the strategy presented in Part I. Two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear‐free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

The grain structure of an Al-0.3 wt%Mn alloy deformed to 1% strain was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). 14 equally spaced HEDM layers were acquired and their exact location within the DCT volume was determined using a generic algorithm minimizing a function of the local disorientations between the two data sets. The microstructures were then compared in terms of the mean crystal orientations and shapes of the grains. The comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1 and that HEDM and DCT grain boundaries are on average 4 mm apart from each other. The results are important for studies targeting the determination of grain volume. For the case of a polycrystal with an average grain size of about 100 mm, a relative deviation of about 10% was found between the two techniques.

Strain within grains and at grain boundaries in polycrystalline thin-film absorber layers limits the overall performance due to higher defect concentrations and band fluctuations. However, the nanoscale strain distribution in operational devices is not easily accessible using standard methods. X-ray nanodiffraction offers the unique possibility to evaluate the strain or lattice spacing at nanoscale resolution. Furthermore, the combination of nanodiffraction with additional techniques in the framework of multi-modal scanning X-ray microscopy enables the direct correlation of the strain with material and device parameters such as the elemental distribution or local performance. This approach was applied for the investigation of the strain distribution in CdTe grains in fully operational photovoltaic solar cells. It was found that the lattice spacing in the (111) direction remains fairly constant in the grain cores but systematically decreases at the grain boundaries. The lower strain at grain boundaries is accompanied by an increase of the total tilt. These observations are both compatible with the inhomogeneous incorporation of smaller atoms into the lattice, and local stress induced by neighboring grains.

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Bragg coherent diffraction imaging (BCDI) is a powerful technique to explore the local strain state and morphology of microscale crystals. The method can potentially reach nanometer-scale spatial resolution thanks to the advances in synchrotron design that dramatically increase coherent flux. However, there are experimental bottlenecks that may limit the image reconstruction quality from future high signal-to-noise ratio measurements. In this work we show that angular uncertainty of the sample orientation with respect to a fixed incoming beam is one example of such a factor, and we present a method to mitigate the resulting artifacts. On the basis of an alternative formulation of the forward problem, we design a phase retrieval algorithm which enables the simultaneous reconstruction of the object and determination of the exact angular position corresponding to each diffraction pattern in the data set. We have tested the algorithm performance on simulated data for different degrees of angular uncertainty and signal-to-noise ratio.