Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

Miao, Jianwei; Sayre, D.; Chapman, Henry N.

doi:10.1364/josaa.15.001662

Cited by 623 publications

(535 citation statements)

References 18 publications

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“…172 µm (Pilatus, Dectris) relaxes oversampling requirements. In simple terms, oversampling limits the ratio between beamsize and eld of view (FOV) in the sample plane per single di raction pattern [195]. According to the small angle approximation the FOV per single di raction pattern depends on the wavelength λ, the distance between sample and detector X and the pixel size of the detector D, i.e.…”

Section: Results: Ptychographic Imaging Of Nanowiresmentioning

confidence: 99%

“…Based on a counting argument of the number of measured data points (equations to solve) and unknown variables, Miao and colleagues de ned the so-called oversampling ratio' σ [195]:…”

Section: Coherent DI Ractive Imagingmentioning

confidence: 99%

“…The oversampling of the magnitude of the Fourier transform of the object needs to be > 2 for a 1d object but > √ 2 in each direction for a 2d object and > 2 1/3 in each direction for a 3d object [195].…”

Section: Coherent DI Ractive Imagingmentioning

confidence: 99%

“…In his Bachelor thesis other approaches to the re-scaling problem of the STCS data were analysed [310]. [195] by e ectively absorbing tails of the KB beam [98]. In the standard mode of ptychography the sample is scanned along a rectangular grid of points in a plane of the KB focus and the resulting di raction patterns are collected by the photon counting pixel detector (pixel size 172 µm × 172 µm) PILATUS 300K (DETCRIS) placed about 5.1 m behind the focal plane.…”

Section: Thank Matthias Hahn For Helping Me With the Sem-edx Analysismentioning

confidence: 99%

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Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

Wilke

2015

Göttingen Series in X-Ray Physics

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Section: Results: Ptychographic Imaging Of Nanowiresmentioning

confidence: 99%

“…Based on a counting argument of the number of measured data points (equations to solve) and unknown variables, Miao and colleagues de ned the so-called oversampling ratio' σ [195]:…”

Section: Coherent DI Ractive Imagingmentioning

confidence: 99%

Section: Coherent DI Ractive Imagingmentioning

confidence: 99%

Section: Thank Matthias Hahn For Helping Me With the Sem-edx Analysismentioning

confidence: 99%

See 2 more Smart Citations

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

Wilke

2015

Göttingen Series in X-Ray Physics

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“…The numerical aperture of the detector is 0.25. [ 22,46,48,49,51,52]. In this case the Shrinkwrap [48] algorithm was used because it required very little a priori knowledge of the same structure other than a well-defined upper bound on the area or volume of the "imaged field" that can be occupied by the sample.…”

Section: Multilayer Mirrormentioning

confidence: 99%

Time-resolved imaging using x-ray free electron lasers

Barty

2010

J. Phys. B: At. Mol. Opt. Phys.

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The ultra-intense, ultra-short X-ray pulses provided by X-ray Free Electron Laser (XFEL) sources are ideally suited to time resolved studies of structural dynamics with spatial resolution from nanometre to atomic length scales and temporal resolution of 10 fs or less. Using coherent X-ray diffraction as a diagnostic, XFELs enable the capturing of X-ray snapshots of previously unmeasurable transient phenomena, and the study of ultrafast processes such as sample damage on the timescales which they occur. With enough photons in a single pulse to enable single-shot measurements, and short enough pulses to freeze atomic motion, researchers now have a new window into the time evolution ultrafast phenomena that are intrinsically not cyclic in nature. In this review paper we recap some of the key time-resolved imaging experiments performed at FLASH and look ahead to a new generation of experiments at higher resolution using a new generation of new XFEL sources that are only just becoming available.

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Perspectives on Single Molecule Diffraction Using the X-Ray Free Electron Laser

Webster

Hilgenfeld²

2002

Single Mol.

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A free electron laser capable of operating at the short wavelengths and high energies characteristic of hard X-rays, could be a potentially powerful new tool for the determination of the structures of single biological macromolecules, subcellular organelles, or whole cells at high resolution. Current methods using relatively low-intensity, incoherent X-ray sources depend upon the high signal gain achieved by the coherent scattering of a large number of identical molecules from a crystalline sample. The prerequisite crystallization of biological macromolecules is a major bottleneck in this process and the discrete nature of the Fourier transforms of crystalline materials also complicates the process of the reconstruction of the original molecular structure from its corresponding diffraction pattern.The ability to record detailed diffraction patterns from single molecules would eliminate the need for crystalline samples. Furthermore, the continuous molecular transforms of single molecules can be sampled finely enough to enable the unrecorded phase information to be retrieved from the set of structural amplitudes without recourse to the additional, a priori structural information that is generally required for phase assignment using sets of diffraction amplitudes from crystalline samples.Currently, diffraction experiments with single biological macromolecules or other non-crystalline material are hampered by the significant radiation damage to the samples that occurs as a result of the very large radiation doses that are required. Model calculations indicate that this problem may be solved by using the ultra-short (< 100 fs) pulses of hard X-radiation that a new generation of X-ray free electron lasers should be capable of producing. In anticipation that the current, rapid development of this technology will make this potential a reality in the near future, the theoretical foundations of this new methodology are already being laid.

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Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

Cited by 623 publications

References 18 publications

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

Time-resolved imaging using x-ray free electron lasers

Perspectives on Single Molecule Diffraction Using the X-Ray Free Electron Laser

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