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Implementation of fast kirchhoff transformation algorithm exemplified for bessel beams
S.A. Balalaev1,2, S.N. Khonina

1Image Processing Systems Institute оf the RAS,
2Samara State Aerospace University (SSAU)

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Full text of article: Russian language.

The paper analyzes high-performance non-paraxial algorithms for computation of a complex field of a laser beam at various distances from the source. A comparative analysis of previously used and newly developed algorithms is provided. Despite the generality of application of the developed algorithms, their efficiency is achieved under certain conditions. The study provides the characteristics of accuracy and speed of the algorithms when applied to particular tasks.

non-paraxial propagation, Kirchhoff transformation, fast calculation algorithms, Bessel beams.

Balalaev SA, Khonina SN. Implementation of Fast Kirchhoff Transformation Algorithm Exemplified for Bessel Beams. Computer Optics 2006; 30: 69-73.

This work was supported by the Russian-American program “Basic Research and Higher Education” (CRDF Project SA-014-02), a grant from the КАИК 05-01-96505, and also a grant from INTAS 04-77-7198.


  1. Vinogradova MB, Rudenko OV, Sukhorukov AP. The wave theory [In Russian]. Moscow: "Nauka" Publisher; 1979.
  2. Bahvalov NS. Numerical methods (analysis, algebra, ordinary differential equations) [In Russian]. Moscow: "Nauka" Publisher; 1975.
  3. Drozdov MA, Khonina SN. Investigation of the limits of applicability of the paraxial approximation for describing the propagation of laser light in free space [In Russian]. Natural science, economics, management 2003; 4: 47-55.

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