Influence of Electron Noise on Three-dimensional Image Reconstruction

Hegerl, R.; Hoppe, W.

doi:10.1515/zna-1976-1241

Cited by 140 publications

(77 citation statements)

References 2 publications

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“…2, 3, and 4, it appears clear that such dose reduction does not come at the cost of image quality. Namely, according to the dose-fractionation theorem (27), the total dose required to achieve statistical significance for each voxel of a computed 3D reconstruction (tomogram) is the same as that required to obtain a single 2D image (projection) of that isolated voxel at the same level of statistical significance. Thus, a statistically significant 3D image can be computed from statisti- Fig.…”

Section: Discussionmentioning

confidence: 99%

Low-dose, simple, and fast grating-based X-ray phase-contrast imaging

Zhu

Zhang²,

Wang³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

218

156

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Phase sensitive X-ray imaging methods can provide substantially increased contrast over conventional absorption-based imaging and therefore new and otherwise inaccessible information. The use of gratings as optical elements in hard X-ray phase imaging overcomes some of the problems that have impaired the wider use of phase contrast in X-ray radiography and tomography. So far, to separate the phase information from other contributions detected with a grating interferometer, a phase-stepping approach has been considered, which implies the acquisition of multiple radiographic projections. Here we present an innovative, highly sensitive X-ray tomographic phase-contrast imaging approach based on grating interferometry, which extracts the phase-contrast signal without the need of phase stepping. Compared to the existing phase-stepping approach, the main advantages of this new method dubbed "reverse projection" are not only the significantly reduced delivered dose, without the degradation of the image quality, but also the much higher efficiency. The new technique sets the prerequisites for future fast and low-dose phase-contrast imaging methods, fundamental for imaging biological specimens and in vivo studies.X-ray imaging | differential phase contrast | grating interferometer | tomography O ver the last few decades X-ray imaging has experienced a true revolution. The most striking advancement has been the production of coherent X-ray beams with their intrinsic capability of generating interference signals and, as a consequence, providing access to phase information within the investigated sample. This fact has been very stimulating for the X-ray-imaging community, which had been continually challenged by the frustrating question of how to increase the contrast in X-ray images without increasing the dose imparted to a specimen. It is well known that, different from conventional visible light, the refractive index in X-ray optics is very close to and smaller than unity. In first approximation, for a small and negligible anisotropy in the medium, the index of refraction characterizing the optical properties of a tissue can be expressed-including X-ray absorptionwith its complex form: n ¼ 1-δ-iβ where δ is the decrement of the real part of the refractive index, responsible for the phase shift, while the imaginary part β describes the absorption property of the tissue. In conventional absorption-based radiography, the X-ray phase shift information is usually not used for image reconstruction. However, at photon energies greater than 10 keV and for soft tissues (made up of low-Z elements), the phase shift term plays a more prominent role than the attenuation term because δ is typically three orders of magnitude larger than β (1). As a consequence, phase-contrast modalities can generate significantly greater image contrast compared to conventional, absorptionbased radiography. In fact, far from absorption edges, δ is inversely proportional to the square of the X-ray energy while β decreases as the fourth power of it. Conseq...

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Section: Discussionmentioning

confidence: 99%

Low-dose, simple, and fast grating-based X-ray phase-contrast imaging

Zhu

Zhang²,

Wang³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

218

156

View full text Add to dashboard Cite

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“…(1). We perform calculations only for two-dimensional images since the required fluence to achieve a particular contrast in a three-dimensional tomographic reconstruction is the same as for the two-dimensional image, according to the dose fractionation theorem [32]. We find that the required fluence Φ 0 depends on the width d of the feature and thickness L of the object in which it is embedded, as It is seen that the slope of the curve changes at photon energies greater than 30 keV as incoherent scattering becomes the dominant process for low-Z materials.…”

Section: Scattering-to-dose Optimizationmentioning

confidence: 99%

Dose efficient Compton X-ray microscopy

Villanueva-Pérez¹,

Bajt²,

Chapman³

2018

Optica

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X-ray imaging techniques have proven invaluable to study biological systems at high resolution due to the penetration power and short wavelength of this radiation. In practice, the resolution and sensitivity of current X-ray imaging techniques are not limited by the performance of optics or image-recovery methods but by radiation damage. We propose the use of Compton (inelastic) X-ray scattering for high-resolution cellular imaging and provide a study of a scanning microscope geometry that requires a dose to achieve a given resolution that is three orders of magnitude lower than for coherent (elastic) scattering. We find that the dose per imaging signal is minimized at a photon energy of 64 keV. This corresponds to a short enough wavelength (0.02 nm) to provide nanometer transverse resolution and micrometer depth of field for tomographic imaging of whole cells. The microscope could be implemented at future high-energy and high-brightness synchrotron-radiation facilities to provide images of unsectioned and unlabeled cells in their native conditions at enough detail to bridge the techniques of super-resolution optical microscopy and cryo-electron microscopy. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (110.7440) X-ray imaging; (340.7460) X-ray microscopy; (170.3880) Medical and biological imaging.

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“…Using diffraction patterns from different protein orientations independently would then increase tremendously the time required for data acquisition. However, if the correlation between various projections is taken into account for 3D reconstruction according to the dose fractionation theorem (Hegerl and Hoppe, 1976), the dose required for each projection in the 3D imaging will be reduced. The Hegerl -Hoppe theorem states that the full 3D reconstruction of an object requires the same total dose (distributed over many orientations) as the reconstruction of a single 2D projection at the same resolution.…”

Section: Scattering Simulationmentioning

confidence: 99%

Dose, exposure time and resolution in serial X-ray crystallography

Starodub

Rez

Hembree

et al. 2007

J Synchrotron Radiat

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The resolution of X-ray diffraction microscopy is limited by the maximum dose that can be delivered prior to sample damage. In the proposed Serial Crystallography method, the damage problem is addressed by distributing the total dose over many identical hydrated macromolecules running continuously in a single-file train across a continuous X-ray beam, and resolution is then limited only by the available molecular and X-ray fluxes and molecular alignment. Orientation of the diffracting molecules is achieved by laser alignment. We evaluate the incident X-ray fluence (energy/area) required to obtain a given resolution from (1) an analytical model, giving the count rate at the maximum scattering angle for a model protein, (2) explicit simulation of diffraction patterns for a GroEL-GroES protein complex, and (3) the frequency cut off of the transfer function following iterative solution of the phase problem, and reconstruction of an electron density map in the projection approximation. These calculations include counting shot noise and multiple starts of the phasing algorithm. The results indicate counting time and the number of proteins needed within the beam at any instant for a given resolution and X-ray flux. We confirm an inverse fourth power dependence of exposure time on resolution, with important implications for all coherent Xray imaging. We find that multiple single-file protein beams will be needed for subnanometer resolution on current third generation synchrotrons, but not on fourth generation designs, where reconstruction of secondary protein structure at a resolution of 7 Å should be possible with short (below 100 s) exposures.

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Influence of Electron Noise on Three-dimensional Image Reconstruction

Cited by 140 publications

References 2 publications

Low-dose, simple, and fast grating-based X-ray phase-contrast imaging

Low-dose, simple, and fast grating-based X-ray phase-contrast imaging

Dose efficient Compton X-ray microscopy

Dose, exposure time and resolution in serial X-ray crystallography

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