AbstractWith the appropriate excitation, a specimen will emit an X‐ray spectrum where the characteristic line intensities are strongly dependent on the elemental composition. The measurement of these intensities thus affords a method of accurate quantitative elemental analysis. A digitized record of the spectrum may be obtained using a lithium drifted silicon detector, associated electronics and some storage medium. The recorded data is the original spectrum convoluted by the appropriate instrumental function. This paper describes several procedures which may be applied to this data to obtain accurate estimates of the individual X‐ray line intensities, mainly with reference to the spectra obtained by electron excitation of thick specimens. The choice of a particular procedure depends on the quality of the data acquistion system, and the likely systematic errors which have been calculated for illustrative examples with special reference to the effects of drift and resolution changes in the electronics. Background subtraction techniques involving interpolation, extrapolation and filtering are discussed, together with methods for deconvolution of overlapping peaks, in particular least squares regression. A versatile new procedure, iterative stripping, is presented which simultaneously accomplishes background subtraction and peak deconvolut