Modeling of the n-th harmonic spectra used in wavelength modulation spectroscopy and their properties

In this paper a convolution model for the harmonic spectra and harmonic signals used in wavelength modulation spectroscopy (WMS) with arbitrary transmission function is given. This implies a straightforward description of the harmonic spectra in the Fourier domain, which also allows for a new general computation method. Furthermore, the model can be extended to include non-ideal behavior of practical systems by assuming a modified transmission function, e.g. a nonzero laser linewidth, laser intensity modulation during wavelength tuning and additional filtering of the harmonic signals. A recursion formula and a mean value property for n-th harmonic spectra has been found. The harmonic signals occurring in practical systems can be modeled with a system theoretic approach, where these are given as the output of a filter that represents the WMS system and the transmission is regarded as the input signal of the filter. This gives a very intuitive view of WMS systems.