Theory and operational rules for the discrete Hankel transform

被引:42
作者
Baddour, Natalie [1 ]
Chouinard, Ugo [1 ]
机构
[1] Univ Ottawa, Dept Mech Engn, Ottawa, ON K1N 6N5, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
NUMERICAL EVALUATION; CONVOLUTION PROPERTIES; FOURIER-TRANSFORMS; INTEGER-ORDER; ALGORITHM; COMPUTATION; RECONSTRUCTION; PROPAGATION; MATRIX;
D O I
10.1364/JOSAA.32.000611
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform. (C) 2015 Optical Society of America
引用
收藏
页码:611 / 622
页数:12
相关论文
共 57 条
[1]   NUMERICAL EVALUATION OF THE HANKEL TRANSFORM - REMARKS [J].
AGNESI, A ;
REALI, GC ;
PATRINI, G ;
TOMASELLI, A .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1993, 10 (09) :1872-1874
[2]   END CORRECTION IN THE QUASI-FAST HANKEL TRANSFORM FOR OPTICAL-PROPAGATION PROBLEMS [J].
AGRAWAL, GP ;
LAX, M .
OPTICS LETTERS, 1981, 6 (04) :171-173
[3]  
[Anonymous], ENCY MATH
[4]  
[Anonymous], INTEGRAL TRANSFORMS
[5]  
[Anonymous], FRONTIERS OPTICS
[6]   Application of the generalized shift operator to the Hankel transform [J].
Baddour, Natalie .
SPRINGERPLUS, 2014, 3 :1-6
[7]   Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates [J].
Baddour, Natalie .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2010, 27 (10) :2144-2155
[8]   Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates [J].
Baddour, Natalie .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 2009, 26 (08) :1767-1777
[9]   Zero-order Hankel transformation algorithms based on Filon quadrature philosophy for diffraction optics and beam propagation [J].
Barakat, R ;
Parshall, E ;
Sandler, BH .
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION, 1998, 15 (03) :652-659
[10]   Hankel convolution operators on entire functions and distributions [J].
Belhadj, M ;
Betancor, JJ .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 276 (01) :40-63