Fourier Methods with Applications

1975 ◽

Vol 33 ◽

pp. 292-293

Author(s):

D. E. Johnson

Keyword(s):

High Voltage ◽

Prior Information ◽

Block Diagram ◽

Three Dimensional ◽

Real Space ◽

Two Dimensional ◽

Efficient Manner ◽

Fourier Methods ◽

Tilt Series ◽

Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

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An Introduction to Fourier Methods and the Laplace Transformation

American Journal of Physics ◽

10.1119/1.1934901 ◽

1959 ◽

Vol 27 (6) ◽

pp. 433-434 ◽

Cited By ~ 1

Author(s):

Philip Franklin ◽

Horace M. Trent

Keyword(s):

Laplace Transformation ◽

Fourier Methods

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Progressive wavelet correlation using Fourier methods

IEEE Transactions on Signal Processing ◽

10.1109/78.738243 ◽

1999 ◽

Vol 47 (1) ◽

pp. 97-107 ◽

Cited By ~ 23

Author(s):

H.S. Stone

Keyword(s):

Fourier Methods

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Fourier methods for turbomachinery applications

Progress in Aerospace Sciences ◽

10.1016/j.paerosci.2010.04.001 ◽

2010 ◽

Vol 46 (8) ◽

pp. 329-341 ◽

Cited By ~ 78

Author(s):

L. He

Keyword(s):

Fourier Methods

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Reminiscences and discoveries, the introduction of Fourier methods into crystal-structure determination

Notes and Records the Royal Society journal of the history of science ◽

10.1098/rsnr.1990.0021 ◽

1990 ◽

Vol 44 (2) ◽

pp. 257-264

Keyword(s):

Crystal Structure ◽

Structure Determination ◽

Copper Sulphate ◽

Diffraction Grating ◽

Alternative Explanation ◽

Crystal Structure Determination ◽

X Rays ◽

Fourier Methods ◽

Research Student

1. The nature of X-rays X-rays were discovered in 1895 by Rontgen in Wurtzburg. For the next 17 years the nature of these rays was one of the dominant questions in physics: were they particles or were they waves? W.H. Bragg, of Adelaide, found indisputable evidence that they were particles; C.G. Barkla, of Liverpool and Edinburgh, found even more indisputable evidence that they were waves. The decisive experiment was carried out by Friedrich and Knipping (1) in 1912 in Munich, under the guidance of von Laue; they passed a fine beam of X-rays through a crystal of copper sulphate, hoping that it would behave as a diffraction grating. It did! The background was emotionally described bv von Laue in 1948 (2). * W.H. Bragg had a son, W.L. Bragg, who was a research student under J.J. Thomson at Cambridge. He was, as he himself said later, rather upset that his father seemed to have been proved wrong, and he tried to think up an alternative explanation of particles travelling through tunnels in the crystal. But he soon realized that the wave explanation had to be accepted.

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Die Röntgenstrukturanalyse von (CO)9Co3CΟΒΒr2Ν(C5)3. X-ray Structure Analysis of (CO)9Co3COBBr2N(C2H5)3

Zeitschrift für Naturforschung B ◽

10.1515/znb-1976-0313 ◽

1976 ◽

Vol 31 (3) ◽

pp. 342-344 ◽

Cited By ~ 17

Author(s):

Volker Bätzel

Keyword(s):

Least Squares ◽

Structure Analysis ◽

Reliability Index ◽

Three Dimensional ◽

Diagonal Matrix ◽

Crystal Data ◽

Block Diagonal Matrix ◽

Fourier Methods ◽

Space Group ◽

X Ray

Using three dimensional X-ray data collected on a four circle diffractometer, the structure of (CO)9Co3COBBr2N(C2H5)3 was solved by Patterson and Fourier methods. Least squares refinement with a block-diagonal matrix leads to a reliability index of R = 10.7%. Crystal data: α = 13.277(6) Å, b = 10.17(1) Å, c = 9.22(2) Å; α = 91.12(6)°, β = 87.61(4)°, γ = 98.79(2)°; space group P1̅; Z = 2; V = 1229,7 Å3; Dx = 1.97 gcm-3.

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