Popov Evgeny, Nevière Michel, Bonod Nicolas
Institut Fresnel, Case 161, Unité Mixte de Recherche (UMR 6133), Faculté des Sciences et Techniques de St.-Jérôme, 13397 Marseille Cedex 20, France.
J Opt Soc Am A Opt Image Sci Vis. 2004 Jan;21(1):46-52. doi: 10.1364/josaa.21.000046.
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.
李[《美国光学学会志A》13, 1870 (1996)]的因式分解规则被推广到需要使用贝塞尔函数基的柱面几何结构。一项理论研究证实了劳伦特定则在对两个连续函数的乘积或一个连续函数与一个不连续函数的乘积进行因式分解时的有效性。从理论和数值上证明了在截断基中对两个不连续函数的连续乘积进行因式分解时应用所谓逆规则的必要性。
