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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 9 — Mar. 20, 2008
  • pp: 1350–1357

Modified Fourier–Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques

Shuiliang Ma, Hongming Gao, and Lin Wu  »View Author Affiliations

Applied Optics, Vol. 47, Issue 9, pp. 1350-1357 (2008)

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Errors in discrete Abel inversion methods using Fourier transform techniques have been analyzed. The Fourier expansion method is very accurate but sensitive to noise. The Fourier–Hankel method has a significant systematic negative deviation, which increases with the radius; inversion error of the method can be reduced by adjusting the value of a factor. With a decrease of the factor both methods show a noise filtering property. Based on the analysis, a modified Fourier–Hankel method that is accurate, computationally efficient, and has the ability to filter noise in the inversion process is proposed for applying to experimental data.

© 2008 Optical Society of America

OCIS Codes
(110.6960) Imaging systems : Tomography
(120.1740) Instrumentation, measurement, and metrology : Combustion diagnostics

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: October 15, 2007
Revised Manuscript: December 26, 2007
Manuscript Accepted: February 1, 2008
Published: March 20, 2008

Shuiliang Ma, Hongming Gao, and Lin Wu, "Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques," Appl. Opt. 47, 1350-1357 (2008)

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