Minimum harmonic detection order for Rayleigh resolution in modulation spectroscopy

摘要

Wavelength Modulation Spectroscopy (WMS) utilizes low frequency modulation of the probe, followed by synchronous detection at the modulation frequency or at one of the harmonics. WMS provides a particularly useful tool for resolving highly disparate overlapping lines, because the high-order derivative-like structure of higher harmonics results in an enhancement of features, not possible with conventional ("direct") absorption spectroscopy. An important question, not yet systematically addressed in the literature is, "Given that in any measurement seeking to resolve overlapping spectra there is always a minimum harmonic detection order, how does one determine this order?" To address this issue, a Rayleigh-like criterion is defined and used to determine when two lines are barely resolved. Shannon's information theoretical principles are then used to calculate the information obtained when overlapping spectra are barely resolved at a particular harmonic. The results obtained allow one to predict the minimal harmonic detection order that should be used to resolve overlapping lines.