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When molecules whose collision induced vibrational decay rates are small areprobed by molecular absorption spectroscopic (MAS) techniques the absorptionsignal can, under certain conditions, be reduced and distorted. The reason hasbeen attributed to the fact that a substantial fraction of the molecules in theinteraction region will reside in excited vibrational states, which leads to adepletion of the vibrational ground state. One type of molecule in which thiscan take place is methane. A model for this phenomenon, based on $\text{CH}_4$in trace concentrations in either $\text{N}_2$ or dry air in a cylindrical gascell, detected by mid-infrared light in the 1 - 100 Torr pressure range, ispresented. Due to a fast collisional coupling between various rotational statesand velocity groups we suggest that depletion in MAS can be modeled adequatelyby a simple three-level system to which the transport of molecules in thesystem is coupled as diffusion according to Fick's law, applied to each levelindividually. The model is verified in a separate work [Hausmaninger T et al.,J Quant Spectrosc Radiat Tr. 2017;205:59-70] with good agreement. It predictsthat depletion has a strong pressure dependence in the 1 - 30 Torr range, thatit is significantly more pronounced in $\text{N}_2$ than in air, and thatconsiderable degrees of depletion can be obtained for mW powers of light (> 10%for powers > 20 mW). The findings indicate that, unless precautions are taken,depletion can adversely affect quantitative assessments performed by MAS. Meansof how to reduce depletion are given.

Model for molecular absorption spectroscopy in the 1-100 Torr range in  the presence of vibrational depletion - Applied to $\text{CH}_4$ in  $\text{N}_2$ and dry air