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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 1 — Jan. 1, 2004
  • pp: 46–52

Factorization of products of discontinuous functions applied to Fourier–Bessel basis

Evgeny Popov, Michel Nevière, and Nicolas Bonod  »View Author Affiliations

JOSA A, Vol. 21, Issue 1, pp. 46-52 (2004)

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The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.

© 2004 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.1940) Diffraction and gratings : Diffraction
(070.2590) Fourier optics and signal processing : ABCD transforms

Original Manuscript: May 13, 2003
Revised Manuscript: August 1, 2003
Manuscript Accepted: September 8, 2003
Published: January 1, 2004

Evgeny Popov, Michel Nevière, and Nicolas Bonod, "Factorization of products of discontinuous functions applied to Fourier–Bessel basis," J. Opt. Soc. Am. A 21, 46-52 (2004)

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