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

2020 ◽  
Vol 53 (2) ◽  
pp. 404-418 ◽  
Author(s):  
P. Li ◽  
S. Maddali ◽  
A. Pateras ◽  
I. Calvo-Almazan ◽  
S.O. Hruszkewycz ◽  
...  
Keyword(s):  
Phase Retrieval ◽  
Bragg Diffraction ◽  
Fourier Space ◽  
Sampled Data ◽  
Bragg Structure ◽  
Angular Rotation ◽  
Data Set ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging ◽  
Orthogonal Frame

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.

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

2020 ◽  
Vol 53 (2) ◽  
pp. 393-403 ◽  
Author(s):  
S. Maddali ◽  
P. Li ◽  
A. Pateras ◽  
D. Timbie ◽  
N. Delegan ◽  
...  
Keyword(s):  
Phase Retrieval ◽  
Geometric Theory ◽  
Correction Method ◽  
Real Space ◽  
Bragg Diffraction ◽  
Retrieval Algorithm ◽  
Spatially Resolved ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging ◽  
Shear Distortion

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.

scholarly journals Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rujia Li ◽  
Liangcai Cao
Keyword(s):  
Phase Retrieval ◽  
Dynamic Range ◽  
A Priori ◽  
Measured Intensity ◽  
Physical Constraints ◽  
Coherent Diffraction Imaging ◽  
Effective Dynamic ◽  
Ill Posed ◽  
Retrieval Problem ◽  
Diffraction Imaging

AbstractPhase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

scholarly journals Phase retrieval for Bragg coherent diffraction imaging at high x-ray energies

2019 ◽  
Vol 99 (5) ◽  
Author(s):  
S. Maddali ◽  
M. Allain ◽  
W. Cha ◽  
R. Harder ◽  
J.-S. Park ◽  
...  
Keyword(s):  
Phase Retrieval ◽  
X Ray ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging

scholarly journals The Nanodiffraction beamline ID01/ESRF: a microscope for imaging strain and structure

2019 ◽  
Vol 26 (2) ◽  
pp. 571-584 ◽  
Author(s):  
Steven J. Leake ◽  
Gilbert A. Chahine ◽  
Hamid Djazouli ◽  
Tao Zhou ◽  
Carsten Richter ◽  
...  
Keyword(s):  
Spatial Resolution ◽  
Imaging Techniques ◽  
Bragg Diffraction ◽  
Scanning Probe ◽  
Objective Lens ◽  
Full Field ◽  
User Community ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging ◽  
Focused Beams

The ID01 beamline has been built to combine Bragg diffraction with imaging techniques to produce a strain and mosaicity microscope for materials in their native or operando state. A scanning probe with nano-focused beams, objective-lens-based full-field microscopy and coherent diffraction imaging provide a suite of tools which deliver micrometre to few nanometre spatial resolution combined with 10−5 strain and 10−3 tilt sensitivity. A detailed description of the beamline from source to sample is provided and serves as a reference for the user community. The anticipated impact of the impending upgrade to the ESRF – Extremely Brilliant Source is also discussed.

scholarly journals Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities

2013 ◽  
Vol 46 (2) ◽  
pp. 312-318 ◽  
Author(s):  
Jose A. Rodriguez ◽  
Rui Xu ◽  
Chien-Chun Chen ◽  
Yunfei Zou ◽  
Jianwei Miao
Keyword(s):  
Phase Retrieval ◽  
High Harmonic ◽  
Solution Space ◽  
Real Space ◽  
X Ray ◽  
Coherent Diffraction Imaging ◽  
Wide Range ◽  
Diffraction Imaging ◽  
Correlation Information ◽  
Noise Robust

Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free-electron lasers, high harmonic generation, soft X-ray lasers and electrons. Despite recent rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities is presented. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stages of the iterative process (i.e.a smoothness constraint), OSS finds a balance between the hybrid input–output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER–HIO and noise robust (NR)–HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. It is expected that OSS will find application in the rapidly growing CDI field, as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed. TheMATLAB(The MathWorks Inc., Natick, MA, USA) source code of the OSS algorithm is freely available from http://www.physics.ucla.edu/research/imaging.

scholarly journals Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging

2011 ◽  
Vol 19 (20) ◽  
pp. 19330 ◽  
Author(s):  
Tatiana Latychevskaia ◽  
Jean-Nicolas Longchamp ◽  
Hans-Werner Fink
Keyword(s):  
Phase Retrieval ◽  
Fourier Domain ◽  
Fast Phase ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging

scholarly journals Coherent Diffraction Imaging in Transmission Electron Microscopy for Atomic Resolution Quantitative Studies of the Matter

Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2323
Author(s):  
Elvio Carlino ◽  
Francesco Scattarella ◽  
Liberato Caro ◽  
Cinzia Giannini ◽  
Dritan Siliqi ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Phase Retrieval ◽  
Atomic Resolution ◽  
Significant Information ◽  
Heavy Atoms ◽  
Coherent Diffraction Imaging ◽  
Transmission Electron ◽  
Diffraction Imaging ◽  
Set Up

The paper focuses on the development of electron coherent diffraction imaging in transmission electron microscopy, made in the, approximately, last ten years in our collaborative research group, to study the properties of materials at atomic resolution, overcoming the limitations due to the aberrations of the electron lenses and obtaining atomic resolution images, in which the distribution of the maxima is directly related to the specimen atomic potentials projected onto the microscope image detector. Here, it is shown how augmented coherent diffraction imaging makes it possible to achieve quantitative atomic resolution maps of the specimen atomic species, even in the presence of low atomic number atoms within a crystal matrix containing heavy atoms. This aim is achieved by: (i) tailoring the experimental set-up, (ii) improving the experimental data by properly treating parasitic diffused intensities to maximize the measure of the significant information, (iii) developing efficient methods to merge the information acquired in both direct and reciprocal spaces, (iv) treating the dynamical diffused intensities to accurately measure the specimen projected potentials, (v) improving the phase retrieval algorithms to better explore the space of solutions. Finally, some of the future perspectives of coherent diffraction imaging in a transmission electron microscope are given.

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