Quantum noise in 2D projections and 3D reconstructions

Saxberg, Brendan; Saxton, W. O.

doi:10.1016/s0304-3991(81)80182-9

Cited by 52 publications

(20 citation statements)

References 5 publications

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“…To collect a regular tilt series for the reconstruction of single (as opposed to crystalline) asymmetrical particles, the specimen is tilted by equal angular increments, and a micrograph of the same particle is recorded in each position. Besides the dose requirements determined by the signal-tonoise ratio needed in the reconstruction (e.g., Hoppe et al, 1973;Saxberg and Saxton, 1981;van Heel, 1986), there is a constraint imposed by the minimum exposure necessary to cross-correlate two images to enable the determination of the position with respect t o a common origin (Saxton and Frank, 1977):…”

Section: Reconstruction Methods For Random Tilt Seriesmentioning

confidence: 99%

Three‐Dimensional reconstruction of single particles from random and nonrandom tilt series

Radermacher

1988

J. Elec. Microsc. Tech.

484

337

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To overcome the radiation damage-induced limitations to the resolution of three-dimensional reconstructions from electron microscopic tilt series, novel reconstruction schemes have been developed that require only a single exposure of the specimen. The tilt series collected with these methods have random projection directions. First, three-dimensional reconstruction techniques are described that are applicable to data obtained from tilt series with regular tilt geometry, followed by the extensions of these techniques to permit analysis of projection series with randomly spaced tilts. The main emphasis is placed on the weighted back-projection methods, which have recently been extended so as to be applicable to random tilt series. Besides a description of the algorithms, the complete procedure for a three-dimensional reconstruction from a single-exposure, random conical tilt series is explained, including the determination of the azimuthal angles, the alignment scheme for conical tilt series, the dependence of the achievable resolution on the number of projections for regular conical and single-axis geometries, and the method to calculate the actual resolution of two-dimensional image averages and of three-dimensional reconstructions using the phase residual and Fourier ring correlation criteria. Examples are given of biological specimens to which these three-dimensional reconstruction methods have been applied.

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Section: Reconstruction Methods For Random Tilt Seriesmentioning

confidence: 99%

Three‐Dimensional reconstruction of single particles from random and nonrandom tilt series

Radermacher

1988

J. Elec. Microsc. Tech.

484

337

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“…Solving the structure of biological macromolecules or small molecular at atomic level is even more challenging 6 . The main problem is that, as a consequence of Poisson statistics, the required illumination dose is inversely proportional to the square of the spatial resolution 7 , and thus improving spatial resolution means quadratically higher doses. The increased dose may destroy the structure of the sample before sufficient image signalto-noise is reached.…”

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confidence: 99%

Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose

et al. 2020

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Both high resolution and high precision are required to quantitatively determine the atomic structure of complex nanostructured materials. However, for conventional imaging methods in scanning transmission electron microscopy (STEM), atomic resolution with picometer precision cannot usually be achieved for weakly-scattering samples or radiation-sensitive materials, such as 2D materials. Here, we demonstrate low-dose, sub-angstrom resolution imaging with picometer precision using mixed-state electron ptychography. We show that correctly accounting for the partial coherence of the electron beam is a prerequisite for highquality structural reconstructions due to the intrinsic partial coherence of the electron beam. The mixed-state reconstruction gains importance especially when simultaneously pursuing high resolution, high precision and large field-of-view imaging. Compared with conventional atomic-resolution STEM imaging techniques, the mixed-state ptychographic approach simultaneously provides a four-times-faster acquisition, with double the information limit at the same dose, or up to a fifty-fold reduction in dose at the same resolution.

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“…where N q is the number of quanta (here, electrons) per unit area; d is the diameter of the image disc; and C is the contrast. Essentially, the same required electron exposure is calculated by the equation used in Saxberg and Saxton (1981) for the value at which the image of an 0.3-nm feature would be three times the shot noise, if its mass density was 1 g/cm 3 (i.e., water). The density of protein (ϳ1.3 g/cm 3 ) is only a little bit higher than this.…”

Section: What Is the Minimum Number Of Molecules That Is Required To mentioning

confidence: 99%

Review: Electron Crystallography: Present Excitement, a Nod to the Past, Anticipating the Future

Glaeser

1999

Journal of Structural Biology

139

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Quantum noise in 2D projections and 3D reconstructions

Cited by 52 publications

References 5 publications

Three‐Dimensional reconstruction of single particles from random and nonrandom tilt series

Three‐Dimensional reconstruction of single particles from random and nonrandom tilt series

Mixed-state electron ptychography enables sub-angstrom resolution imaging with picometer precision at low dose

Review: Electron Crystallography: Present Excitement, a Nod to the Past, Anticipating the Future

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