Direct phasing in femtosecond nanocrystallography. I. Diffraction characteristics

X-ray free-electron lasers solve a number of difficulties in protein crystallography by providing intense but ultra-short pulses of X-rays, allowing collection of useful diffraction data from nanocrystals. Whereas the diffraction from large crystals corresponds only to samples of the Fourier amplitude of the molecular transform at the Bragg peaks, diffraction from very small crystals allows measurement of the diffraction amplitudes between the Bragg samples. Although highly attenuated, these additional samples offer the possibility of iterative phase retrieval without the use of ancillary experimental data [Spenceet al.(2011).Opt. Express,19, 2866–2873]. This first of a series of two papers examines in detail the characteristics of diffraction patterns from collections of nanocrystals, estimation of the molecular transform and the noise characteristics of the measurements. The second paper [Chenet al.(2014).Acta Cryst.A70, 154–161] examines iterative phase-retrieval methods for reconstructing molecular structures in the presence of the variable noise levels in such data.

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Direct phasing in femtosecond nanocrystallography. II. Phase retrieval

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273313032725 ◽

2014 ◽

Vol 70 (2) ◽

pp. 154-161 ◽

Cited By ~ 9

Author(s):

Joe P. J. Chen ◽

John C. H. Spence ◽

Rick P. Millane

Keyword(s):

Free Electron Laser ◽

Phase Retrieval ◽

Laser Diffraction ◽

Selection Strategy ◽

Noise Levels ◽

Acta Cryst ◽

X Ray ◽

Retrieval Algorithms ◽

Simulation Results ◽

Diffraction Patterns

X-ray free-electron laser diffraction patterns from protein nanocrystals provide information on the diffracted amplitudes between the Bragg reflections, offering the possibility of direct phase retrieval without the use of ancillary experimental diffraction data [Spenceet al.(2011).Opt. Express,19, 2866–2873]. The estimated continuous transform is highly noisy however [Chenet al.(2014).Acta Cryst.A70, 143–153]. This second of a series of two papers describes a data-selection strategy to ameliorate the effects of the high noise levels and the subsequent use of iterative phase-retrieval algorithms to reconstruct the electron density. Simulation results show that employing such a strategy increases the noise levels that can be tolerated.

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A novel crystal-analyzer phase retrieval algorithm and its noise property

Journal of Synchrotron Radiation ◽

10.1107/s1600577515003616 ◽

2015 ◽

Vol 22 (3) ◽

pp. 786-795 ◽

Cited By ~ 5

Author(s):

Yuan Bao ◽

Yan Wang ◽

Panyun Li ◽

Zhao Wu ◽

Qigang Shao ◽

...

Keyword(s):

Phase Retrieval ◽

Signal To Noise Ratio ◽

Transfer Characteristic ◽

Photon Flux ◽

Retrieval Algorithm ◽

X Rays ◽

Contrast Imaging ◽

Signal To Noise ◽

Noise Characteristics ◽

Signal Response

A description of the rocking curve in diffraction enhanced imaging (DEI) is presented in terms of the angular signal response function and a simple multi-information retrieval algorithm based on the cosine function fitting. A comprehensive analysis of noise properties of DEI is also given considering the noise transfer characteristic of the X-ray source. The validation has been performed with synchrotron radiation experimental data and Monte Carlo simulations based on theGeant4toolkit combined with the refractive process of X-rays, which show good agreement with each other. Moreover, results indicate that the signal-to-noise ratios of the refraction and scattering images are about one order of magnitude better than that of the absorption image at the edges of low-Zsamples. The noise penalty is drastically reduced with the increasing photon flux and visibility. Finally, this work demonstrates that the analytical method can build an interesting connection between DEI and GDPCI (grating-based differential phase contrast imaging) and is widely suitable for a variety of measurement noise in the angular signal response imaging prototype. The analysis significantly contributes to the understanding of noise characteristics of DEI images and may allow improvements to the signal-to-noise ratio in biomedical and material science imaging.

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Aspects of direct phasing in femtosecond nanocrystallography

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2013.0498 ◽

2014 ◽

Vol 369 (1647) ◽

pp. 20130498 ◽

Cited By ~ 13

Author(s):

Rick P. Millane ◽

Joe P. J. Chen

Keyword(s):

Free Electron Laser ◽

Phase Retrieval ◽

Laser Diffraction ◽

Intensity Data ◽

Noise Levels ◽

Signal To Noise ◽

X Ray ◽

Unit Cells ◽

Diffraction Patterns ◽

Selection Of

X-ray free-electron laser diffraction patterns from protein nanocrystals provide information on the diffracted amplitudes between the Bragg reflections, offering the possibility of direct phase retrieval without the use of ancillary experimental data. Proposals for implementing direct phase retrieval are reviewed. These approaches are limited by the signal-to-noise levels in the data and the presence of different and incomplete unit cells in the nanocrystals. The effects of low signal to noise can be ameliorated by appropriate selection of the intensity data samples that are used. The effects of incomplete unit cells may be small in some cases, and a unique solution is likely if there are four or fewer molecular orientations in the unit cell.

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Shape transform phasing of edgy nanocrystals

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s205327331900113x ◽

2019 ◽

Vol 75 (2) ◽

pp. 239-259 ◽

Cited By ~ 2

Author(s):

J. P. J. Chen ◽

J. J. Donatelli ◽

K. E. Schmidt ◽

R. A. Kirian

Keyword(s):

Phase Retrieval ◽

Crystal Surface ◽

Simulated Data ◽

Partial Coherence ◽

Retrieval Algorithm ◽

X Rays ◽

Additional Information ◽

Interference Signals ◽

Diffraction Patterns ◽

Phase Retrieval Algorithm

Diffraction patterns from small protein crystals illuminated by highly coherent X-rays often contain measurable interference signals between Bragg peaks. This coherent `shape transform' signal introduces enough additional information to allow the molecular densities to be determined from the diffracted intensities directly, without prior information or resolution restrictions. However, the various correlations amongst molecular occupancies/vacancies at the crystal surface result in a subtle yet critical problem in shape transform phasing whereby the sublattices of symmetry-related molecules exhibit a form of partial coherence amongst lattice sites when an average is taken over many crystal patterns. Here an iterative phase retrieval algorithm is developed which is capable of treating this problem; it is demonstrated on simulated data.

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Dynamic nanoimaging of extended objects via hard X-ray multiple-shot coherent diffraction with projection illumination optics

Communications Physics ◽

10.1038/s42005-021-00539-x ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Yuki Takayama ◽

Keizo Fukuda ◽

Motoki Kawashima ◽

Yuki Aoi ◽

Daiki Shigematsu ◽

...

Keyword(s):

Phase Retrieval ◽

Frame Rate ◽

Retrieval Algorithm ◽

X Rays ◽

Full Field ◽

X Ray ◽

Cell Functions ◽

Multiple Shot ◽

Spatio Temporal ◽

Diffraction Patterns

AbstractThe quest for understanding the structural mechanisms of material properties and biological cell functions has led to the active development of coherent diffraction imaging (CDI) and its variants in the hard X-ray regime. Herein, we propose multiple-shot CDI, a full-field CDI technique dedicated to the visualisation of local nanostructural dynamics in extended objects at a spatio-temporal resolution beyond that of current instrumentation limitations. Multiple-shot CDI reconstructs a “movie” of local dynamics from time-evolving diffraction patterns, which is compatible with a robust scanning variant, ptychography. We developed projection illumination optics to produce a probe with a well-defined illumination area and a phase retrieval algorithm, establishing a spatio-temporal smoothness constraint for the reliable reconstruction of dynamic images. The numerical simulations and proof-of-concept experiment using synchrotron hard X-rays demonstrated the capability of visualising a dynamic nanostructured object at a frame rate of 10 Hz or higher.

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Lensless Reflection Imaging of Obliquely Illuminated Objects I: Choosing a Domain for Phase Retrieval and Ptychography

Symmetry ◽

10.3390/sym13081439 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1439

Author(s):

Igor A. Artyukov ◽

Nikolay L. Popov ◽

Alexander V. Vinogradov

Keyword(s):

Inverse Problem ◽

Phase Retrieval ◽

Extreme Ultraviolet ◽

X Rays ◽

Reflection Mode ◽

Optical Elements ◽

Diffraction Integral ◽

Diffraction Patterns ◽

Set Up ◽

Object Material

Ptychography is a lensless imaging technology that is validated from hard X-rays to terahertz spectral range. It is most attractive for extreme ultraviolet (EUV) and X-rays as optical elements are expensive and often not available. Typically, the set up involves coherently illuminated object that directs the scattered radiation normally to detector which is parallel to the object plane. Computer processing of diffraction patterns obtained when scanning the object gives the image, more precisely, the distribution of intensity and phase on its surface. However, this scheme is inefficient for EUV and X-rays due to poor reflectivity and low penetration in all materials. Reflection mode ptychography solves the problem if illumination angles do not exceed the critical angle of object material. Changing the geometry of experiment changes physical and mathematical model of image formation. Including: diffraction integral describing beam propagation from object to detector, inverse problem, optimization of object illumination angle, position and orientation of detector, choosing size and grid of coordinate and frequency computer domains. This paper considers the wavefield scattered to detector by obliquely illuminated object and determines a domain for processing of obtained scans. Solution of inverse problem with phase retrieval and resulting numerical images will be presented in the next paper.

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Examination of Rabbit Fc Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100445 ◽

1968 ◽

Vol 26 ◽

pp. 140-141

Author(s):

J. P. Robinson ◽

P. G. Lenhert

Keyword(s):

Molecular Weight ◽

Flat Plate ◽

Phosphate Buffer ◽

Asymmetric Unit ◽

X Ray Diffraction ◽

X Ray ◽

Neutral Ph ◽

Small Crystals ◽

Carbon Coated ◽

Diffraction Patterns

Crystallographic studies of rabbit Fc using X-ray diffraction patterns were recently reported. The unit cell constants were reported to be a = 69. 2 A°, b = 73. 1 A°, c = 60. 6 A°, B = 104° 30', space group P21, monoclinic, volume of asymmetric unit V = 148, 000 A°3. The molecular weight of the fragment was determined to be 55, 000 ± 2000 which is in agreement with earlier determinations by other methods.Fc crystals were formed in water or dilute phosphate buffer at neutral pH. The resulting crystal was a flat plate as previously described. Preparations of small crystals were negatively stained by mixing the suspension with equal volumes of 2% silicotungstate at neutral pH. A drop of the mixture was placed on a carbon coated grid and allowed to stand for a few minutes. The excess liquid was removed and the grid was immediately put in the microscope.

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Structural studies of small amorphous volumes by electron diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173741 ◽

1990 ◽

Vol 48 (4) ◽

pp. 122-123

Author(s):

Pierre Moine

Keyword(s):

Electron Diffraction ◽

Born Approximation ◽

Structural Information ◽

Fundamental Relation ◽

X Rays ◽

Structural Studies ◽

Diffraction Experiment ◽

Transmission Electron ◽

Amorphous Structures ◽

Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

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Morphological and synchrotron X-ray microdiffraction studies of large columnar CVD diamond crystallites

Journal of Applied Crystallography ◽

10.1107/s0021889899006652 ◽

1999 ◽

Vol 32 (5) ◽

pp. 924-933 ◽

Cited By ~ 2

Author(s):

A. R. Lang ◽

A. P. W. Makepeace ◽

J. E. Butler

Keyword(s):

Vapour Deposition ◽

Chemical Vapour ◽

Coarse Grained ◽

X Rays ◽

Small Cross Section ◽

X Ray ◽

Chemical Vapour Deposition Diamond ◽

Core Column ◽

Diffraction Patterns ◽

Goniometric Measurements

Optical microscopic and goniometric measurements were combined with microradiography, diffraction-pattern analysis and topography to study a 2 mm thick [001]-texture CVD (chemical vapour deposition) diamond film that had developed a coarse-grained structure composed of separate columnar crystallites. Individual columns were capped by large (001) facets, with widths up to 0.5 mm, and which were smooth but not flat, whereas the column sides were morphologically irregular. The refractive deviation of X-rays transmitted through the crystallites was exploited for delineating facet edges, thereby facilitating the controlled positioning of small-cross-section X-ray beams used for recording diffraction patterns from selected volumes in two representative crystallites. Their structure consisted of a [001]-axial core column surrounded by columns in twin orientation with respect to the core. The diamond volume directly below the (001) facets was free from low-angle boundaries, and no dislocation outcrops on the facets were detected. Significant elastic deformation of this volume was only present close to the facet periphery, where misorientations reached a few milliradians. Lattice imperfection was high in the twins, with ∼1° misorientations.

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