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
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)