The detection of weak absorption changes induced by an external excitation is often hindered by intense background absorptions as well as by noise. Modulation spectroscopy is an adequate tool to be applied in such a case, provided the system may be periodically stimulated, leading to a periodic reversible or pseudoreversible response. In modulated excitation (ME) Fourier transform infrared spectroscopy the phase sensitive detection (PSD) used for the demodulation of the periodic system response is generally performed during data acquisition, i.e., applied to the intensity of the interferogram. This leads to a number of problems in quantitative analysis and the requirement of optional equipment. In this article, a method is presented to perform an off-line vector PSD of conventional time-resolved spectra after data acquisition. A detailed mathematical analysis of PSD applied to the spectral intensity, the interferogram intensity, and to time-resolved spectra is presented. It is shown, that vector PSD applied to a set of time-resolved spectra is straightforward and avoids any additional mathematical corrections. Furthermore, it will be shown how ME spectroscopy can be used for experimental separation of overlapping bands and a detailed description for the determination of absolute modulation amplitudes and phase lags is given.

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