A laser-induced plasma analysis based on the inversion of Abel transformation.

A numerical method for the inverse Abel transformation that can reconstruct plasma emissivity from a projected intensity profile is proposed. After calculating the derivatives of the projected intensity profile using a Volterra integral equation of the first kind, we approximate the derivative function in the Abel inversion transform using discrete least-squares approximation, and then, we obtain the emissivity profile using a numerical integral formula. It is shown that this process is numerically stable and efficient, and it is also resistant to noise when applied to experimental data, as demonstrated by our numerical results. [ABSTRACT FROM AUTHOR]