Determination of bandwidth and frequency changes by Raman difference spectroscopy

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Abstract
The mathematical expressions necessary for analyzing the Raman difference spectra resulting from bandwidth and/or frequency differences between two samples have been derived for both Lorentzian and Gaussian band shapes. Intermediate bands may be analyzed using interpolation. The results show that the difference spectra have two maxima separated by a minimum near zero intensity whenever bandwidth changes are dominant. If the frequency shift is zero, these two maxima have the same intensity. Nonzero frequency shifts result in two unequal maxima and their intensity difference may be used to calculate the magnitude of the shift. Three examples of experimental spectra have been analyzed in order to demonstrate the applicability of the technique.