An algorithm for the differentiation of arbitrary order in the solution of inversion problems in applied spectroscopy

Abstract

We describe algorithms for the solution of inversion problems in atomic absorption and resonance fluorescence. Also derived is the thin-layer approximation for solution of Abel's equation, with or without absorption. The basis for these procedures is the algorithm of differentiation to arbitrary order, including fractional differentiation. Mathematical experiments demonstrating the efficiency of the suggested algorithm have been carried out. © 1989.