<i>Fourier Transforms and their Physical Applications</i>

Champeney, D. C.; Fuoss, Raymond M.

doi:10.1063/1.3128283

Cited by 318 publications

(212 citation statements)

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“…By the Wiener-Khintchine theorem [6] we see this is equivalent to A − → k 2 = const, i.e. the incident spectrum is broad compared to that selected by the instrument.…”

Section: A New Look At Scattering From Many Particle Systemsmentioning

confidence: 99%

“…δ y is the component of − → δ perpendicular to the incident beam (see fig.4). The result (16) is known as the van Cittert-Zernike theorem, [2], [6], [7] and has the form of the Fraunhofer formula. Note that this formula is applicable to geometries where one would not normally observe a Fraunhofer diffraction pattern, except in the case of a spherical wave converging on the point of observation.…”

Section: Elastic Scattering In Real Spacementioning

confidence: 99%

“…The problem is then to show that this length can arise in the case of Fresnel diffraction (finite distance L). This is the content of the van-Cittert Zernike theorem ( [2], [6], [7]) mentioned above. In this way we can describe the scattering process in terms of diffraction at the defining slits and the correlation length of the incident beam.…”

Section: Examples Of Correlation Lengths and Timesmentioning

confidence: 99%

“…The correlation properties of a beam as a result of the optical properties of its preparing devices are known as the van Cittert-Zernike theorem [2], [6] and [7] and we will see how this can be applied to both timedependent and -independent scattering.…”

Section: Correlation Functions and Scatteringmentioning

confidence: 99%

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Space-time approach to scattering from many-body systems

Gähler

Felber

Mezei³

et al. 1998

Phys. Rev. A

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We present scattering from many body systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the scattering amplitude as a space-time integral over the scattering sample for an incident wave characterized by its correlation function which results from the shaping of the wave field by the apparatus. Instrument resolution effects -seen as due to the loss of correlation caused by the path differences in the different arms of the instrument are automatically included and analytic forms of the resolution function for different instruments are obtained. Each element of the apparatus is associated with a correlation length (or time). These correlation lengths, determined by the dimensions of the apparatus are generally much smaller than these dimensions and larger than the wavelength. As is well known, these are the conditions for the validity of geometrical optics so that the conventional treatment, where the scattering is calculated by the van Hove plane wave approach and the trajectories through the instrument are treated classically, is usually valid. In the present approach analytic expressions for the correlation functions are obtained. The intersection of the moving correlation volumes (those regions where the correlation functions are significant) associated with the different elements of the apparatus determines the maximum correlation lengths (times) that can be observed in a sample, and hence, the momentum (energy) resolution of the measurement. This geometrical picture of moving correlation volumes derived by our technique shows how the interaction of the scatterer with the wave field shaped by the apparatus proceeds in space and time. Matching of the correlation volumes so as to maximize the intersection region yields a transparent, graphical method of instrument design. PACS: 03.65. Nk, 3.80 +r, 03.75, 61.12.B

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“…By the Wiener-Khintchine theorem [6] we see this is equivalent to A − → k 2 = const, i.e. the incident spectrum is broad compared to that selected by the instrument.…”

Section: A New Look At Scattering From Many Particle Systemsmentioning

confidence: 99%

Section: Elastic Scattering In Real Spacementioning

confidence: 99%

Section: Examples Of Correlation Lengths and Timesmentioning

confidence: 99%

Section: Correlation Functions and Scatteringmentioning

confidence: 99%

See 2 more Smart Citations

Space-time approach to scattering from many-body systems

Gähler

Felber

Mezei³

et al. 1998

Phys. Rev. A

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“…P Õ (u) the stochastic process /(t), which is the Fourier transform of (see, e.g., Champeney 1973). It follows from the Par-R Õ (t) cevalÏs theorem that…”

Section: Stochastic Drivingmentioning

confidence: 99%

Coronal Loop Heating by Torsional Alfven Waves Directly Driven by Footpoint Motions: Harmonic Driving versus Stochastic Driving

Рудерман

1999

ApJ

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Two scenarios of coronal loop heating by directly driven torsional waves are considered. In the Alfven Ðrst scenario the driving is assumed to be harmonic. In the steady state of oscillations, wave energy dissipation mainly occurs in a narrow dissipative layer embracing an ideal resonant magnetic surface. The wave motion in the dissipative layer is characterized by very large amplitudes. It is assumed that the radiative and thermoconductive losses from loops are exactly covered by wave energy dissipation. This assumption allows expression of the maximum value of the velocity in the dissipative layer in terms of the energy losses and the loop parameters. It turns out that this maximum velocity is proportional to R1@3, where R is the total Reynolds number accounting for both viscosity and resistivity. For typical coronal loops and R \ 106, the maximum velocity in the dissipative layer is between 800 and 1000 km s~1. In the second scenario the driving is assumed to be a stationary stochastic process. Once again it is assumed that energy losses from the loop are covered by wave energy dissipation. The maximum value of the mean square velocity turns out to be proportional to R1@6. This value is also very sensitive to the width of the driver frequency spectrum. In two considered examples, one with a narrow spectrum and another with a wide spectrum, the maximum values of the mean square velocity between 300 and 400 km s~1 and between 150 and 200 km s~1 were obtained, respectively, for typical coronal loops and R \ 106. Since the observed nonthermal velocities in coronal loops never exceed a few tens of km s~1, these results lead to the conclusion that both scenarios do not satisfy the observational constraints.

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Electron Microscopy and Image Processing: Essential Tools for Structural Analysis of Macromolecules

Belnap

2015

CP Protein Science

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Macromolecular electron microscopy typically depicts the structures of macromolecular complexes ranging from ∼200 kDa to hundreds of MDa. The amount of specimen required, a few micrograms, is typically 100 to 1000 times less than needed for X-ray crystallography or nuclear magnetic resonance spectroscopy. Micrographs of frozen-hydrated (cryogenic) specimens portray native structures, but the original images are noisy. Computational averaging reduces noise, and three-dimensional reconstructions are calculated by combining different views of free-standing particles ("single-particle analysis"). Electron crystallography is used to characterize two-dimensional arrays of membrane proteins and very small three-dimensional crystals. Under favorable circumstances, near-atomic resolutions are achieved. For structures at somewhat lower resolution, pseudo-atomic models are obtained by fitting high-resolution components into the density. Time-resolved experiments describe dynamic processes. Electron tomography allows reconstruction of pleiomorphic complexes and subcellular structures and modeling of macromolecules in their cellular context. Significant information is also obtained from metal-coated and dehydrated specimens.

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Fourier Transforms and their Physical Applications

Cited by 318 publications

References 0 publications

Space-time approach to scattering from many-body systems

Space-time approach to scattering from many-body systems

Coronal Loop Heating by Torsional Alfven Waves Directly Driven by Footpoint Motions: Harmonic Driving versus Stochastic Driving

Electron Microscopy and Image Processing: Essential Tools for Structural Analysis of Macromolecules

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