A spectroscopic analysis method in which spectral data of mixtures obtained from a plurality of points on a sample surface are resolved into component spectra and concentrations. A new alternating least squares multivariate curve resolution technique is presented which iteratively resolves the components. The technique starts from an initial estimate that the spectral values of a first component of the sample are all equal (an ‘empty model’), and resolves that component. Then successive further components are iteratively resolved, from initial ‘empty model’ estimates of those components and from previously resolved spectra. In the common case where the main component is present in nearly pure form in the data set, this empty modelling technique results in more accurate resolution of the components. This is due to the ability of the technique to resolve the pure spectra of minor components without modelling concentrations of the main component into them.