Application of Abel inversion in real-time calculations for circularly and elliptically symmetric radiation sources

New Abel inversion methods were developed for real-time calculations of emissions from circularly and elliptically symmetric radiation sources. Using the geometrical relationship between the plasma and the measuring device, an upper triangular area matrix was introduced to determine the local plasma emissivity from the measured irradiation value. Fast calculations of Abel inversion could be achieved using this area matrix since there was no need to fit the data for inversion. Inversion correctness was checked by the use of a given test function. This fast calculation algorithm could also be applied for the radiation source with the elliptical symmetry. This technique was applied to the measurement of arc plasma intensity in flat and V-grooved arc welding.