Comparison of Different Methods of Abel Inversion Using Computer Simulated and Experimental Side-On Data

Abstract

A recently devised new method for numerical Abel inversion is compared with four other commonly used methods. One of them, the convolution method, is employed in computer tomography for reconstructing asymmetrical objects. It is investigated whether this method can be adapted for the case of radial symmetry.As a first approach the comparison is performed by computer simulation. Special attention is given to the propagation of errors according to their origin. The result is a recipe for minimizing errors and for choosing the optimal method for reconstruction.The second step is a comparison of experimentally obtained radial profiles with functions resulting from Abel inversion of measured side-on data. Thus it is shown that the concept developed by computer simulation can be applied in practice.

Characterization of gelatinized corn starch suspensions and resulting drop size distributions after effervescent atomization

“…Abel inversion allows calculation of radial dependent data from corresponding integral data. The application of Abel inversion on rotational symmetric measurement data is based on the work of Hipp et al (2004) and Pretzler et al (1992). Eq.…”

“…Eq. (1) displays the calculation of an unknown radial dependent function f(r) from a function h(y) based on integral measured data by Abel inversion (Pretzler et al, 1992).…”

Excitation Temperature and Constituent Concentration Profiles of the Plasma Jet Under Plasma Spray-PVD Conditions

“…Because the measured I(y) is not given analytically but in discrete data points, both the differentiation and the integration in equation (5) Fourier method shows the best results because it also works as a low-pass filter [33].…”

The Metal-Halide Lamp Under Varying Gravity Conditions Measured by Emission and Laser Absorption Spectroscopy

“…Note that the density plots shown are line-of-sight (column) densities. In future these will be converted into radial profiles by means of Abel inversion (Bakker 2000;Buie et al 1996;Pretzler et al 1992;Sudharsanan 1986;Kak and Slaney 1988).…”