The treatment of errors in the deconvolution of line profile measurements

Abstract
A new approach to the problem of estimating the errors introduced when experimental line-shape data are deconvoluted is presented. The experimental measurements are fitted with a finite sine/cosine series so that deconvolution and other processing can be performed analytically. The error on the deconvoluted curve is described in terms of a confidence band drawn so that the true curve lies entirely within the band with probability, say, 07middot;95. Various criteria which may be used to decide the number of terms to be used in the series are considered in detail. Examples are given in which the method has been applied to the analysis of x-ray Compton line profile measurements.