The fast way for calculation of first class rayleigh-sommerfeld integral
A.V. Ustinov

Image Processing Systems Institute of the RAS

Full text of article: Russian language.

Abstract:
Ways for acceleration of Kirchhoff integral owing to using of analytical transformations and the effective program realization are described in present article. Consecutive steps of the speed increase after every transformation are shown. Application conditions of different approximations are obtained. It should be noted that after an application of all transformations the time of program performance weakly depends on the distance between input and output planes.

Key words: Kirchhoff integral, paraxiality, quadrature formula, asymptotic expansion.

References:

  1. Totzeck, M. Validity of the scalar Kirchhoff and Rayleigh-Sommerfeld diffraction theories in the near field of small phase obiects // J. Opt. Soc. Am. – 1991.- Vol.8, N1. – P.27-32
  2. Melnikov, L.A. The use of Kirchhoff approach for the calculation of the near field amplitudes of electromagnetic field / Melnikov L.A., Tsoy V.I. // Optics Communications. – 2005. – Vol.256 – P.1-9
  3. Veerman, J.A.C.- Calculation of the Rayleigh-Sommerfeld diffraction integral by exact integration of the fast oscillating factor / J.A.C.Veerman, J.J.Rusch, H.P.Urbach // J. Opt. Soc. Am. – 2005.- Vol.22, N4. – P.636-646
  4. Vinogradova, M.B. Waves theory / Vinogradova M.B., Rudenko O.V., Suhorukov A.P.– Moscow: Science, 1979. – 383 p. – (in Russian).
  5. Balalayev, S.А. Realization of fast algorithm of Kirchhoff's diffraction integral on an example of Bessel modes / S.A.Balalayev, S.N.Khonina. // Computer Optics. – 2006. – Vol.30 - P.69-73. – ISSN 0134-2452. – (in Russian)/
  6. Lanczos, C. Applied Analysis / Prentice Hall, Inc., 1956. – 524 p.

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