Improved Abel Inversion Method for Analysis of Spectral and Photo-Optical Data of Magnetic Influenced Plasma Flows

摘要

This paper presents the derivation of an alternative method called spline method to perform inverse Abel transformation of measured data sets. At first the general approach of Abel transformation is shown. The following section shows the principle of operation of the existing methods. Then the new spline method is derived, which is a combination of the known Fourier method and f-Interpolation method with polynomials with an analytical solution of the forward Abel transform. All methods are tested on three test cases: an off centered Gaussian function, a cubic function and photo-optical data of a plasma flow in front of a spherical probe head. The results of the different methods are compared, limitations are shown and their advantages are pointed out. The new method is advantageous for noisy data and due to its spline based approach no assumptions about the local distribution are needed.