Abstract

In a typical inductively coupled plasma (ICP) with cylindrical symmetry, the physical system is best characterized in terms of the radial coordinate <i>r</i> and the height <i>h</i> measured from the induction coil. However, the emission (or absorption) intensity is usually measured as a function of lateral coordinate, <i>x</i>, and height, <i>h</i>, and the Abel integral equation is used to transform the lateral intensity, <i>I</i>(<i>x</i>), into the radial intensity, <i>i</i>(<i>r</i>). Therefore, an accurate Abel inversion is a prerequisite for physical characterizations of ICP at any levels of sophistication. And it follows that the error in the inverted radial intensity must be properly evaluated.

Optical system for the automatic Abel inversion of emission from a cylindrical volume radiator

Gerald L. Rogoff
J. Opt. Soc. Am. 67(1) 44-47 (1977)

Abel inversion of knife-edge data from radially symmetric pulsed laser beams

Robert M. O’Connell and Roger A. Vogel
Appl. Opt. 26(13) 2528-2532 (1987)

Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques

Pankaj S. Kolhe and Ajay K. Agrawal
Appl. Opt. 48(20) 3894-3902 (2009)

Abel inversion applied to plasma spectroscopy: a new interactive method

J. Glasser, J. Chapelle, and J. C. Boettner
Appl. Opt. 17(23) 3750-3754 (1978)

Inversion of interferometric data from cylindrically symmetric, refraction less plasmas

D. W. Oldenburg and J. C. Samson
J. Opt. Soc. Am. 69(7) 927-942 (1979)