Geodesic
Efficient quadrature for fast oscillating integral of paraxial optics
Mathematica Applicanda, Tome 43 (2015) no. 2, pp. 253-267.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The study concerns of determination of a quadrature for the integral solution of the paraxial wave equation. The difficulty in computation of the integral is associated with rapid change of the integrand phase. The developed quadrature takes into account fast oscillatiing character of the integrand. The presented method is an alternative to the commonly used methods based on use of the Fourier transform. The determination of the quadrature is discussed on the example of the integral arisen in the theory of propagation and focusing of hard X-rays waves. Due to the generality of the presented quadrature, it may also be applied to issues related to standard optics and acoustics.
DOI : 10.14708/ma.v43i2.688
Classification : 65D32, 65E05, 65Z05, 35Q60
Mots-clés : paraxial wave equation, quadrature, quick oscilating integrands, X-ray optics 
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Sergey Kshevetskii; Pawel Wojda. Efficient quadrature for fast oscillating integral of paraxial optics. Mathematica Applicanda, Tome 43 (2015) no. 2, pp.  253-267. doi : 10.14708/ma.v43i2.688. http://geodesic.mathdoc.fr/articles/10.14708/ma.v43i2.688/

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