A LabVIEW program for determining confidence intervals of Abel-inverted radial emission profiles

A LabVIEW-based program for the determination of confidence intervals in Abel inversion is described in detail. Confidence intervals are determined from the noise level in the input lateral-emission profile. It is first assumed that the noise-free lateral profile is a smooth and continuous function which can be satisfactorily approximated by a polynomial fit. Random noise is then added to produce a profile that is statistically identical to the experimental lateral profile. Because the number of generated lateral profiles can be as large as desired, the corresponding Abel-inverted radial profiles provide a basis for determination of the confidence intervals. The program is capable of determining the optimal order of the fitting polynomial for the input lateral profile. Two methods for computing the Abel inversion calculation, the Nestor-Olsen and the Hankel-Fourier algorithms, are built into the program. If necessary, the input lateral profile can be smoothed by a built-in moving-average function. A detailed description of the program and its associated functions is presented, followed by a characterization of its performance in the determination of Abel-inversion confidence intervals for several test emission profiles.