Efficient quadrature for fast oscillating integral of paraxial optics

• Autorzy: Kshevetskii S. , Wojda P.

Identyfikatory

DOI

10.14708/ma.v43i2.688

Warianty tytułu

PL

Wydajna kwadratura dla całkowania szybko oscylujących funkcji optyki rentgenowskiej

• Języki publikacji: EN

Abstrakty

EN

The study concerns the determination of quadrature for the integral solution of the paraxial wave equation. The difficulty in computation of the integral is associated with the rapid change of the integrand phase. The developed quadrature takes into account the fast oscillating character of the integrand. The presented method is an alternative to the commonly used methods based on the 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 on 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.

PL

Praca jest poświęcona wyznaczaniu kwadratury dla rozwiązań całkowych równania przewodnictwa cieplnego z zespolonym potencjałem. Trudność w wyznaczaniu tego typu całek jest związana z szybkimi oscylacjami funkcji całkowanej. Prezentowana metoda jest alternatywa dla powszechnie stosowanej metody opartej o zastosowanie transformacji Fouriera. Sprecyzowanie kwadratury jest przedyskutowane na przykładzie całek występujących przy badaniu teorii propagacji i skupiania promieniowania rentgenowskiego. Dzięki ogólności prezentowanej kwadratury, może być ona także zastosowana do zagadnień związanych z optyką i akustyką.

Słowa kluczowe

EN

paraxial wave equation; quadrature; quick oscillating integrands; X-ray optics

PL

równanie przewodnictwa cieplnego z zespolonym potencjałem; kwadratura; całkowanie szybko oscylującej funkcji; optyka rentgenowska

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2015
• Tom: Vol. 43, No. 2
• Strony: 253--267
• Opis fizyczny: Bibliogr. 35 poz., rys., wykr.

Twórcy

autor

Kshevetskii S.

• Baltic I. Kant Federal University, Kaliningrad, Russia

autor

Wojda P.

• Gdańsk University of Technology, Faculty of Applied Physics and Mathematics, 11/12 G. Narutowicza str., 80-233 Gdańsk, Poland

Bibliografia

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