The Hankel transform in n-dimensions and its applications in optical propagation and imaging

Colin J.R. Sheppard, Shan S. Kou, Jiao Lin

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Researchpeer-review

Abstract

Researchers discuss the Hankel transform in n-dimensions and its applications in optical propagation and imaging. The researchers aim to extend the approach to the n-dimensional case by considering the nD hyperspherically symmetrical Fourier transform in nD space, which can be expressed as a Hankel transform. They derive various relationships for general n, and then give specific examples for 1, 2, 3, and 4 dimensions. Tables of Hankel transforms particularly relevant for imaging and wave propagation applications, which include many transforms not given in standard tables. The 2D case has many practical applications in optics, especially for cylindrical focusing, fringe analysis, planar wave guides, and plasmonics.

Original languageEnglish
Title of host publicationAdvances in Imaging and Electron Physics
EditorsPeter W. Hawkes
Place of PublicationMassachusetts USA
PublisherAcademic Press
Chapter4
Pages135-184
Number of pages50
Edition1st
ISBN (Print)9780128022542
DOIs
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameAdvances in Imaging and Electron Physics
PublisherElsevier
Volume188
ISSN (Print)1076-5670

Keywords

  • diffraction propagation
  • Fourier transform
  • fringe analysis
  • Green function
  • Hankel transform
  • planar
  • plasmonics
  • waveguides

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