DETERMINATION OF SINGLE-SCATTERING LINE PROFILE FROM OBSERVED SPECTRUM

An analysis is given for the calculation of the single-scattering profile S1(x, y, z, ...) from the observed spectrum I(x, y, z, ...), when I(x, y, z, ...) contains contributions from plural- scattering events. No assumptions are made concerning the line shape for S1(x, y, z, ...), but a value for the unscattered intensity is required. Further, the analysis given requires that all the scattered intensity is collected, so that Poisson statistics are applicable to the scattering processes occurring in the specimen. The solution for S1(x, y, z ...) is then given as a series in I(x, y, z, ...), with appropriate weighting coefficients. The spectrum I(x, y, z, ...) must be corrected for the finite resolution of the spectrometer, before a solution can be obtained for S1(x, y, z, ...). Computational tests and the limitations of the present analysis are given.