Finite element Fourier and Abbe transform methods for generalization of aperture function and geometry in Fraunhofer diffraction theory

The paper introduces a new method, integral summation algorithm, to measure superfine scale based on Fraunhofer Diffraction. Be different from the traditional method, the paper simulates a series of curve of diffraction luminance distribution on different given size based on Fraunhofer Diffraction theory and researches the closest one to the diffraction curve of unknown slot measured. In order to get more accurate measurement result, the curve is taken by the integral summation algorithm and be compared on the integration area difference instead of comparing the standard deviation. The result shows that the size of given slot is closer to the size of unknown slot than standard deviation method, which somewhat improves the accuracy of the measurement.

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Monochromatic X-ray-induced thermal effect on four-reflection “nested” meV-monochromators: dynamical diffraction theory and finite-element analysis

Chinese Physics C ◽

10.1088/1674-1137/39/9/096004 ◽

2015 ◽

Vol 39 (9) ◽

pp. 096004

Author(s):

Ling-Fei Hu ◽

Li-Dan Gao ◽

Zhen-Jie Li ◽

Shan-Feng Wang ◽

Wei-Fan Sheng ◽

...

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Thermal Effect ◽

Diffraction Theory ◽

Element Analysis ◽

Dynamical Diffraction ◽

X Ray

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Relative Intensities in ED Patterns From Thin Gold Films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096436 ◽

1972 ◽

Vol 30 ◽

pp. 636-637

Author(s):

R. H. Morriss ◽

J. D. C. Peng ◽

C. D. Melvin

Keyword(s):

Theoretical Calculations ◽

Diffraction Theory ◽

Gold Films ◽

Reasonable Accuracy ◽

Experimental Conditions ◽

Crystal Perfection ◽

Heavy Atoms ◽

Fine Focus ◽

Convergent Beam ◽

Beam Diffraction

Although dynamical diffraction theory was modified for electrons by Bethe in 1928, relatively few calculations have been carried out because of computational difficulties. Even fewer attempts have been made to correlate experimental data with theoretical calculations. The experimental conditions are indeed stringent - not only is a knowledge of crystal perfection, morphology, and orientation necessary, but other factors such as specimen contamination are important and must be carefully controlled. The experimental method of fine-focus convergent-beam electron diffraction has been successfully applied by Goodman and Lehmpfuhl to single crystals of MgO containing light atoms and more recently by Lynch to single crystalline (111) gold films which contain heavy atoms. In both experiments intensity distributions were calculated using the multislice method of n-beam diffraction theory. In order to obtain reasonable accuracy Lynch found it necessary to include 139 beams in the calculations for gold with all but 43 corresponding to beams out of the [111] zone.

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“Preparation of Single Crystalline Gold Films for ED Studies”

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096424 ◽

1972 ◽

Vol 30 ◽

pp. 634-635

Author(s):

Joseph D. C. Peng

Keyword(s):

Crystal Morphology ◽

Diffraction Theory ◽

Scattering Matrix ◽

Vacuum Evaporation ◽

Gold Films ◽

Matrix Formulation ◽

Silver Films ◽

Single Crystalline ◽

Grating Pattern ◽

Stacking Disorder

The relative intensities of the ED spots in a cross-grating pattern can be calculated using N-beam electron diffraction theory. The scattering matrix formulation of N-beam ED theory has been previously applied to imperfect microcrystals of gold containing stacking disorder (coherent twinning) in the (111) crystal plane. In the present experiment an effort has been made to grow single-crystalline, defect-free (111) gold films of a uniform and accurately know thickness using vacuum evaporation techniques. These represent stringent conditions to be met experimentally; however, if a meaningful comparison is to be made between theory and experiment, these factors must be carefully controlled. It is well-known that crystal morphology, perfection, and orientation each have pronounced effects on relative intensities in single crystals.The double evaporation method first suggested by Pashley was employed with some modifications. Oriented silver films of a thickness of about 1500Å were first grown by vacuum evaporation on freshly cleaved mica, with the substrate temperature at 285° C during evaporation with the deposition rate at 500-800Å/sec.

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