Reconstruction of local emissivity profile from line integrated data using Abel transform.

Abstract

An efficient and stable Abel inversion method is developed using Zernike polynomials to reconstruct the local emissivity profile from line integrated data. We reconstructed emissivity for parabolic, Gaussian, and non-monotonic profiles. By leveraging Cormack's method, we skip evaluating the integrals numerically, reducing error in reconstruction. This method is derivative-free and singularity-free. The standard deviation of the reconstructed profiles is estimated and found to be small. For a parabolic profile with n = 3, the standard deviation is 0.0887, and the Kolmogorov-Smirnov test yields a KS statistic value of 0.002, with a reduced chi-square value of 0.857. A chi-square test and a Kolmogorov-Smirnov test are performed to reject the null hypothesis, adding another verification layer to the efficiency of our method along with a standard deviation test.