On a Constrained Fourier Extrapolation Method for Numerical Deconvolution

1983 ◽  
pp. 65-80 ◽  
Author(s):  
A. Russell Davies
Keyword(s):  
Extrapolation Method ◽  
Numerical Deconvolution

point-Analysis Using the Extrapolation Method in the Analytical Electron microscope

1990 ◽  
Vol 48 (2) ◽  
pp. 430-431
Author(s):  
Zenji Horita ◽  
Ryuzo Nishimachi ◽  
Takeshi Sano ◽  
Minoru Nemoto
Keyword(s):  
Electron Microscope ◽  
Extrapolation Method ◽  
X Ray ◽  
Absorption Correction ◽  
Point Analysis ◽  
Analytical Electron ◽  
Analytical Electron Microscope ◽  
Data Points ◽  
Identical Composition ◽  
X Ray Absorption

Absorption correction is often required in quantitative x-ray microanalysis of thin specimens using the analytical electron microscope. For such correction, it is convenient to use the extrapolation method[l] because the thickness, density and mass absorption coefficient are not necessary in the method. The characteristic x-ray intensities measured for the analysis are only requirement for the absorption correction. However, to achieve extrapolation, it is imperative to obtain data points more than two at different thicknesses in the identical composition. Thus, the method encounters difficulty in analyzing a region equivalent to beam size or the specimen with uniform thickness. The purpose of this study is to modify the method so that extrapolation becomes feasible in such limited conditions. Applicability of the new form is examined by using a standard sample and then it is applied to quantification of phases in a Ni-Al-W ternary alloy.The earlier equation for the extrapolation method was formulated based on the facts that the magnitude of x-ray absorption increases with increasing thickness and that the intensity of a characteristic x-ray exhibiting negligible absorption in the specimen is used as a measure of thickness.

Quantitative x-ray microanalysis and thickness determination using ζ factor

1996 ◽  
Vol 54 ◽  
pp. 580-581
Author(s):  
M. Watanabe ◽  
Z. Horita ◽  
M. Nemoto
Keyword(s):  
Diffusion Couple ◽  
Extrapolation Method ◽  
Thin Specimen ◽  
Beam Position ◽  
X Ray ◽  
Thickness Determination ◽  
Experimental Limitation ◽  
X Ray Absorption

X-ray absorption in quantitative x-ray microanalysis of thin specimens may be corrected without knowledge of thickness when the extrapolation method or the differential x-ray absorption (DXA) method is used. However, there is an experimental limitation involved in each method. In this study, a method is proposed to overcome such a limitation. The method is developed by introducing the ζ factor and by combining the extrapolation method and DXA method. The method using the ζ factor, which is called the ζ-DXA method in this study, is applied to diffusion-couple experiments in the Ni-Al system.For a thin specimen where incident electrons are fully transparent, the characteristic x-ray intensity generated from a beam position, I, may be represented as I = (NρW/A)Qωaist.

Time-domain extrapolation method for tractor drive shaft loads in stationary operating conditions

2021 ◽  
Vol 210 ◽  
pp. 143-155
Author(s):  
Zihan Yang ◽  
Zhenghe Song ◽  
Xueyan Zhao ◽  
Xingxiang Zhou
Keyword(s):  
Time Domain ◽  
Operating Conditions ◽  
Drive Shaft ◽  
Extrapolation Method

Extrapolation method to extend the dynamic range of the Shack-Hartmann wave-front sensor

2007 ◽  
Author(s):  
Huaqiang Li ◽  
Helun Song ◽  
Xuejun Rao ◽  
Changhui Rao ◽  
Jinsheng Yang
Keyword(s):  
Wave Front ◽  
Dynamic Range ◽  
Extrapolation Method

The Cl + Bk extrapolation method. Application to hydrogen fluoride

1979 ◽  
Vol 42 (3) ◽  
pp. 249-258 ◽  
Author(s):  
Thom H. Dunning
Keyword(s):  
Hydrogen Fluoride ◽  
Extrapolation Method

An Extrapolation Method to Compute Far-Field Pressures From Near-Field Pressures Obtained by Finite Element Method

1995 ◽  
Author(s):  
Jamal Assaad ◽  
Christian Bruneel ◽  
Jean-Michel Rouvaen ◽  
Régis Bossut
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Near Field ◽  
Radiation Condition ◽  
Directivity Pattern ◽  
Extrapolation Method ◽  
External Boundary ◽  
Finite Width ◽  
Far Field ◽  
Element Method

Abstract The finite element method is widely used for the modeling of piezoelectric transducers. With respect to the radiation loading, the fluid is meshed and terminated by an external nonreflecting surface. This reflecting surface can be made up with dipolar damping elements that absorb approximately the outgoing acoustic wave. In fact, with dipolar dampers the fluid mesh can be quite limited. This method can provides a direct computation of the near-field pressure inside the selected external boundary. This paper describes an original extrapolation method to compute far-field pressures from near-field pressures in the two-dimensional (2-D) case. In fact, using the 2-D Helmholtz equation and its solution obeying the Sommerfeld radiation condition, the far-field directivity pattern can be expressed in terms of the near-field directivity pattern. These developments are valid for any radiation problem in 2D. One test example is described which consists of a finite width planar source mounted in a rigid or a soft baffle. Experimental results concerning the far-field directivity pattern of lithium niobate bars (Y-cut) are also presented.

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