A method for determining the size of a source from the diffraction image on the basis of a Chebyshev approximation criterion

1978 ◽  
Vol 21 (6) ◽  
pp. 626-631
Author(s):  
A. A. Rubenok
Keyword(s):  
Chebyshev Approximation ◽  
Diffraction Image ◽  
Approximation Criterion

Research on a Model of Reverberation

2013 ◽  
Vol 321-324 ◽  
pp. 1117-1122
Author(s):  
Li Cai Zhang ◽  
Xiao Juan Tong
Keyword(s):  
High Frequency ◽  
Simple Structure ◽  
Complex Structure ◽  
Chebyshev Approximation ◽  
Comb Filter ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Low Pass ◽  
Absorption Characteristics ◽  
Approximation Criterion

Against defects of lacking consideration of air absorption characteristics to the high frequency signal in Schroeder reverberation model, and the more complex structure in Moorer reverberation model, use equiripple Chebyshev approximation criterion to design 4 FIR comb filter with low-pass characteristics and make the FIR filters in parallel, to get a pure parallel reverberation model. This reverberation model considers the absorption characteristics of air to the high-frequency signal, and has a more simple structure.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

Chebyshev approximation to data by geometric elements

1993 ◽  
Vol 5 (10) ◽  
pp. 509-522 ◽  
Author(s):  
Rudolf Drieschner
Keyword(s):  
Chebyshev Approximation ◽  
Geometric Elements

Algorithm for Spatial Straightness Evaluation Using Theories of Linear Complex Chebyshev Approximation and Semi-infinite Linear Programming

2005 ◽  
Vol 128 (1) ◽  
pp. 167-174 ◽  
Author(s):  
LiMin Zhu ◽  
Ye Ding ◽  
Han Ding
Keyword(s):  
Linear Programming ◽  
Chebyshev Approximation ◽  
Approximation Problem ◽  
Linear Complex ◽  
Infinite Linear Programming ◽  
Minimum Zone ◽  
Effectiveness And Efficiency ◽  
Primal And Dual ◽  
Straightness Error ◽  
Infinite Linear

This paper presents a novel methodology for evaluating spatial straightness error based on the minimum zone criterion. Spatial straightness evaluation is formulated as a linear complex Chebyshev approximation problem, and then reformulated as a semi-infinite linear programming problem. Both models for the primal and dual programs are developed. An efficient simplex-based algorithm is employed to solve the dual linear program to yield the straightness value. Also a general algebraic criterion for checking the optimality of the solution is proposed. Numerical experiments are given to verify the effectiveness and efficiency of the presented algorithm.

Polynomial Chebyshev approximation of a complex transfer function

Computing ◽  
1971 ◽  
Vol 8 (3-4) ◽  
pp. 335-342
Author(s):  
C. Dierick ◽  
Y. Kamp
Keyword(s):  
Transfer Function ◽  
Chebyshev Approximation
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