Efficient quadrature for fast oscillating integral of paraxial optics

Paweł Wojda, С. П. Кшевецкий · Roczniki Polskiego Towarzystwa Matematycznego. Seria 3, Matematyka Stosowana/Matematyka Stosowana/Mathematica Applicanda · 2016

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Type: article
Published: 2016-01-26
Cited by: 1
References: 35
DOI: https://doi.org/10.14708/ma.v43i2.688
OpenAlex: https://openalex.org/W2336987963
Semantic Scholar: https://api.semanticscholar.org/CorpusID:59389153

Keywords

Paraxial approximation, Quadrature (astronomy), Mathematics, Physics, Optics

References

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Introduction to Optics and Optical ImagingCraig R. Scott — 1997
The Fourier transform and its applications to opticsP. M. Duffieux — 1983
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory IntegralsElias M. Stein, Timothy S Murphy — 1993
Fourier Series and Optical Transform Techniques in Contemporary Optics: An IntroductionRaymond G. Wilson, Sean M. McCreary — 1995
Fast integration of rapidly oscillatory functionsDavid Levin — 1996
A method for numerical integration on an automatic computerC. W. Clenshaw, A. R. Curtis — 1960
Numerical approximation of Fourier-transformsHans J. Stetter — 1966
Initial phase and free-particle wave packet evolutionT. L. Beach — 2009
On the numerical quadrature of highly-oscillating integrals II: Irregular oscillatorsA. Iserles — 2005
Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillationsDavid I. W. Levin — 1982
Analysis of a collocation method for integrating rapidly oscillatory functionsDavid Levin — 1997
A high order, progressive method for the evaluation of irregular oscillatory integralsG. A. Evans, J.R. Webster — 1997
Moment-free numerical integration of highly oscillatory functionsSheehan Olver — 2006
Computer analysis of two-dimensional images in the Zernike phase contrast method for hard X raysV. G. Kohn, М. А. Орлов — 2012
On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiationA. Snigirev, I. Snigireva, V. G. Kohn — 1995
Phase-contrast microtomography with coherent high-energy synchrotron x raysC. Raven, A. Snigirev, I. Snigireva — 1996
High energy X-ray nanofocusing by silicon planar lensesA. Snigirev, I. Snigireva, Maxim V. Grigoriev — 2009
On the numerical quadrature of highly‐oscillating integrals I: Fourier transformsArieh Iserles — 2004
A method for the numerical evaluation of finite integrals of oscillatory functionsI. M. Longman — 1960

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Asymptotic stability of a dual-scale compact method for approximating highly oscillatory Helmholtz solutionsTiffany Jones, Qin Sheng — 2019

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