Abel inversion with a simple analytic representation for experimental data

Abstract

The advantages of using a simple analytic representation for experimental data requiring Abel inversion are explored. A simple yet versatile function is proposed, and its Abel inverse derived. Its use allows not only a fast and accurate inversion of the data but also a simple, straightforward calculation of the magnitude of the error in the inverted values in terms of the mean standard deviations of the parameters defining the proposed function. A full discussion of the sources of error and their relative importance is also presented, as well as a numerical example using simulated data. The analysis indicates that unless the measured data is error free to an extremely high degree, no amplification of the experimental error, inherent in the data, occurs with this inversion method even if only three or four adjustable parameters are employed in defining the analytic function.