Abel inversion using Legendre polynomials approximations

An improved Abel inversion method based on Legendre polynomials approximations is presented for reconstructing the original radial distribution of plasma emission coefficients from projected intensities. The method uses the technique of overlapping two near segments for obtaining an excellent approximation of the intensity distribution. The approximated function of the intensity profile is a combination of various shifted Legendre polynomials which in the Abel inverse equation can be integrated exactly to deduce the emission coefficient. It is shown, using simulated intensity data with and without noise inverted for a comparison with those obtained by other methods, that the method is more accurate and has a better property of noise resistance. It is well suited for applying to experimental intensities distorted by noise.