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
[Optical Society of America ]
(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
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)