Impact and mitigation of angular uncertainties in Bragg coherent x-ray diffraction imaging

Calvo-Almazán, Irene; Allain, Marc; Maddali, Siddharth; Chamard, Virginie; Hruszkewycz, S. O.

doi:10.1038/s41598-019-42797-4

Cited by 10 publications

(12 citation statements)

References 26 publications

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“…We note that Equations (38) and (40) can be used as flexible building blocks by which to design new phase retrieval reconstruction algorithms, as has been recently shown (Hruszkewycz et al, 2017;Hill et al, 2018;Calvo-Almazán et al, 2019). As an aid to interested readers, an example of matlab code for such an algorithm is provided in Appendix B in which the projection/back-projection strategy is implemented for the BCDI-ER phase-retrieval algorithm.…”

Section: Numerical Evaluation With Digital Fourier Transformsmentioning

confidence: 79%

“…However, if we consider the case when the RC is regularly sampled, then the regularity of the mesh along k 3 allows one to sidestep the slice-by-slice approach and simply obtain all the slices with a single, much faster, 3D DFT:Ψ = DFT(ψ). As a result, the projection/backprojection strategy described here will be appealing in situations, for example wheñ q 3 is unevenly-sampled, as was demonstrated in (Calvo-Almazán et al, 2019).…”

Section: Numerical Evaluation With Digital Fourier Transformsmentioning

confidence: 88%

“…Solutions to these, and other related problems, all hinge on a phase-retrieval description of the sample on an orthogonal real space reference frame onto which other experimental constraints and models map naturally. A recent example, wherein such a strategy was utilized to determine the angular uncertainty of each measurement step in a rocking curve during the course of image reconstruction with phase retrieval (Calvo-Almazán et al, 2019), shows the potential of such a construction. We anticipate that further advances of this nature could be possible, provided that formalisms for experimental-geometry-aware Fourier transformations are developed and provided to the community.…”

Section: Introductionmentioning

confidence: 99%

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General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

Li¹,

Maddali²,

Pateras³

et al. 2020

J Appl Cryst

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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.

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Section: Numerical Evaluation With Digital Fourier Transformsmentioning

confidence: 79%

Section: Numerical Evaluation With Digital Fourier Transformsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

Li¹,

Maddali²,

Pateras³

et al. 2020

J Appl Cryst

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show abstract

“…Because of this angular sensitivity, any uncontrolled rotations due to local heating or to radiation pressure [17,18] make controlled BCDI experiments of small particles very difficult. An approach to deal with small deviations from nominal rocking angles has been developed [19]. The method which re-formulates the phase retrieval problem is limited to small deviations from an ideal reciprocal space sampling pattern, and therefore optimized to deal with slow drifts and instrumental errors.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional coherent Bragg imaging of rotating nanoparticles

Björling,

Marçal,

Solla-Gullón

et al. 2020

Preprint

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Bragg Coherent Diffraction Imaging (BCDI) is a powerful strain imaging tool, often limited by beam-induced sample instability for small particles and high power densities. Here, we devise and validate an adapted diffraction volume assembly algorithm, capable of recovering three-dimensional datasets from particles undergoing uncontrolled and unknown rotations. We apply the method to gold nanoparticles which rotate under the influence of a focused coherent X-ray beam, retrieving their three-dimensional shapes and strain fields. The results show that the sample instability problem can be overcome, enabling the use of fourth generation synchrotron sources for BCDI to their full potential.

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“…This latter capability is demonstrated for the cases of even as well as uneven signal sampling in Fourier space, greatly increasing the scope of applicability of 3D phase retrieval. An entirely new class of BCDI experiments potentially stand to benefit from this enhanced reconstruction capability, for instance measurements on dynamically varying samples or BCDI in the presence of unstable or vibrating components(Calvo-Almazán et al, 2019). As we shall see in Part II, such reconstructions can be achieved with minimal computational overhead through the modified 3D Fourier transform.…”

mentioning

confidence: 99%

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

Maddali¹,

Li²,

Pateras³

et al. 2020

J Appl Cryst

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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.

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Impact and mitigation of angular uncertainties in Bragg coherent x-ray diffraction imaging

Cited by 10 publications

References 26 publications

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

Three-dimensional coherent Bragg imaging of rotating nanoparticles

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

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