Method and apparatus for using non-linear spectral fitting procedures on gamma-ray spectral data

摘要

A method and an apparatus for decomposing a gamma spectrum representative of an unknown material for determining the contribution of each constituent postulated to constitute the material, wherein an energy spectrum of the gamma rays issued from the material is formed, as well as a composite spectrum made up of individual standard spectra of the postulated constituents and comprising elemental yields being representative of the proportion of the corresponding constituents; the best fit between the measured spectrum and the composite spectrum is determined by modifying simultaneously at least one elemental yield and at least one parameter representative of the conditions under which the measured spectrum and the composite spectrum have been obtained. The best fit may be based on any non linear least squares search for a global minimum of X.sup.2 =(S Y-U).sup.T W(S Y-U), where "U" is a matrix representing the measured spectrum, "S" is a matrix representing the composite spectrum, "Y" is a matrix representative of the elemental yields and "W" is a weight matrix. The non linear fitting method used may be e.g. a gradient search or the Marquardt method.