Equally sloped tomography with oversampling reconstruction

Miao, Jianwei; Förster, Friedrich; Levi, Ofer

doi:10.1103/physrevb.72.052103

Cited by 158 publications

(137 citation statements)

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“…In our reconstructions, we terminated the algorithm after ∼150 iterations when the error function became stabilized. Both numerical simulations and experimental results from cryoelectron microscopy have indicated that EST produces superior results relative to FBP and the algebraic reconstruction technique when there is a limited number of projections as well as the missing wedge problem (12,39,40). After the 3D image was obtained by EST, we verified the fidelity of the reconstruction by calculating 25 diffraction patterns from the reconstructed 3D image.…”

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confidence: 87%

“…In reciprocal space, the Fourier coefficients with both the magnitudes and phases, which are obtained from the reconstructed projections, are updated in each iteration, while the other Fourier coefficients remain unchanged. The convergence of EST is monitored by an error function, defined as the difference between the calculated Fourier coefficients and those obtained from the experimental data (39,40). In our reconstructions, we terminated the algorithm after ∼150 iterations when the error function became stabilized.…”

mentioning

confidence: 99%

“…To address this problem, the EST method, an iterative reconstruction method that aims to solve for a portion of the missing projection data, was employed for the tomographic reconstruction. The EST method is coupled with an acquisition scheme for which the projections are acquired at equal slope intervals, instead of equal angle intervals, which results in the elimination of interpolative inaccuracies in conventional tomographic methods (12,39,40). EST iterates back and forth between real and reciprocal space.…”

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confidence: 99%

“…Using this method, we aligned the 25 images to a common tilt axis (Materials and Methods). The 3D image reconstruction was computed by the equally sloped tomography (EST) method (39,40). Because only a limited number of projections was acquired due to concerns about radiation damage to the yeast spore cell, conventional tomographic reconstruction methods, such as filtered back projection (FBP), do not usually yield satisfactory results.…”

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confidence: 99%

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Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Jiang

Song

Chen

et al. 2010

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

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Microscopy has greatly advanced our understanding of biology. Although significant progress has recently been made in optical microscopy to break the diffraction-limit barrier, reliance of such techniques on fluorescent labeling technologies prohibits quantitative 3D imaging of the entire contents of cells. Cryoelectron microscopy can image pleomorphic structures at a resolution of 3-5 nm, but is only applicable to thin or sectioned specimens. Here, we report quantitative 3D imaging of a whole, unstained cell at a resolution of 50-60 nm by X-ray diffraction microscopy. We identified the 3D morphology and structure of cellular organelles including cell wall, vacuole, endoplasmic reticulum, mitochondria, granules, nucleus, and nucleolus inside a yeast spore cell. Furthermore, we observed a 3D structure protruding from the reconstructed yeast spore, suggesting the spore germination process. Using cryogenic technologies, a 3D resolution of 5-10 nm should be achievable by X-ray diffraction microscopy. This work hence paves a way for quantitative 3D imaging of a wide range of biological specimens at nanometer-scale resolutions that are too thick for electron microscopy.coherent diffractive imaging | equally sloped tomography | lensless imaging | iterative phase-retrieval algorithms | oversampling A pplication of the long penetration depth of X-rays to the imaging of large, unstained biological specimens has long been recognized as a possible solution to the thickness restrictions of electron microscopy. Indeed, using sizable protein crystals, X-ray crystallography is currently the primary methodology used for determining the 3D structure of protein molecules at near-atomic or atomic resolution. However, many biological specimens such as whole cells, cellular organelles, some viruses, and many important protein molecules are difficult or impossible to crystallize and hence their structures are not accessible by crystallography. Overcoming these limitations requires the employment of different techniques. One promising approach currently under rapid development is coherent diffraction microscopy (also termed coherent diffractive imaging or lensless imaging) in which the coherent diffraction pattern of a noncrystalline specimen or a nanocrystal is measured and then directly phased to obtain an image (1-28). The well-known phase problem is solved by using the oversampling method (29) in combination with the iterative algorithms (30-33). Since its first experimental demonstration in 1999 (1), coherent diffraction microscopy has been applied to imaging a wide range of materials science and biological specimens such as nanoparticles, nanocrystals, biomaterials, cells, cellular organelles, viruses by using synchrotron radiation (2-21), high harmonic generation (22-24), soft X-ray laser sources (23, 25), and free electron lasers (26-28). Until now, however, the radiation damage problem and the difficulty of acquiring high-quality 3D diffraction patterns from individual whole cells have prevented the successful high-resolution ...

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confidence: 87%

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confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Jiang

Song

Chen

et al. 2010

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

Self Cite

253

150

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“…4). Using these 27 projection images, we have reconstructed the 3D density map by performing equal-slope tomography (EST) 50 . All 27 projection images were aligned selfconsistently to the same rotation center by employing the center-of-mass alignment scheme 51 .…”

Section: Methodsmentioning

confidence: 99%

Macromolecular structures probed by combining single-shot free-electron laser diffraction with synchrotron coherent X-ray imaging

et al. 2014

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Nanostructures formed from biological macromolecular complexes utilizing the self-assembly properties of smaller building blocks such as DNA and RNA hold promise for many applications, including sensing and drug delivery. New tools are required for their structural characterization. Intense, femtosecond X-ray pulses from X-ray free-electron lasers enable single-shot imaging allowing for instantaneous views of nanostructures at ambient temperatures. When combined judiciously with synchrotron X-rays of a complimentary nature, suitable for observing steady-state features, it is possible to perform ab initio structural investigation. Here we demonstrate a successful combination of femtosecond X-ray single-shot diffraction with an X-ray free-electron laser and coherent diffraction imaging with synchrotron X-rays to provide an insight into the nanostructure formation of a biological macromolecular complex: RNA interference microsponges. This newly introduced multimodal analysis with coherent X-rays can be applied to unveil nano-scale structural motifs from functional nanomaterials or biological nanocomplexes, without requiring a priori knowledge.

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Electron Tomography: A Three‐Dimensional Analytic Tool for Hard and Soft Materials Research

et al. 2015

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Three-dimensional (3D) structural analysis is essential to understand the relationship between the structure and function of an object. Many analytical techniques, such as X-ray diffraction, neutron spectroscopy, and electron microscopy imaging, are used to provide structural information. Transmission electron microscopy (TEM), one of the most popular analytic tools, has been widely used for structural analysis in both physical and biological sciences for many decades, in which 3D objects are projected into two-dimensional (2D) images. In many cases, 2D-projection images are insufficient to understand the relationship between the 3D structure and the function of nanoscale objects. Electron tomography (ET) is a technique that retrieves 3D structural information from a tilt series of 2D projections, and is gradually becoming a mature technology with sub-nanometer resolution. Distinct methods to overcome sample-based limitations have been separately developed in both physical and biological science, although they share some basic concepts of ET. This review discusses the common basis for 3D characterization, and specifies difficulties and solutions regarding both hard and soft materials research. It is hoped that novel solutions based on current state-of-the-art techniques for advanced applications in hybrid matter systems can be motivated.

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Equally sloped tomography with oversampling reconstruction

Cited by 158 publications

References 17 publications

Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Macromolecular structures probed by combining single-shot free-electron laser diffraction with synchrotron coherent X-ray imaging

Electron Tomography: A Three‐Dimensional Analytic Tool for Hard and Soft Materials Research

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