In multicomponent analysis we have the IR spectrum of an unknown mixture of gases, for which we have no knowledge of the constituent gases, not to mention their partial pressures. Instead we know a large set of library spectra of pure molecular gases, measured in known pressures and with the same interferometer as the unknown sample. By using these pure spectra we ought to be able to calculate the partial pressures of the pure gases in the mixture, with error limits. The errors in the obtained values arise from the measurement noise in the spectra. Because the calculation of such partial pressures that best explain the mixture spectrum is a relatively simple task, we shall consider it only briefly and will concentrate on the calculation of their error limits. We shall also consider the optimal choice for a resolution that will provide error limits as small as possible and the application of the non-negativity constraint for the partial pressures. In addition to gas spectra, all the calculations apply to spectra of noninteracting liquids as well.
Pekka Saarinen and Jyrki Kauppinen, "Multicomponent Analysis of FT-IR Spectra," Appl. Spectrosc. 45, 953-963 (1991)
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