Dependence of harmonic signals on sample-gas parameters in wavelength-modulation spectroscopy for precise absorption measurements

The dependence of the amplitude of phase-sensitive harmonic signals in wavelength-modulation spectroscopy on the optical depth, temperature, and pressure of the sample gas as well as the modulation amplitude is investigated theoretically to estimate the tolerance of these parameters in precise absorption measurements. First, the amplitudes of harmonic signals of both Lorentzian and Gaussian lines are calculated analytically and numerically for arbitrary optical depths and modulation amplitudes. From these results it is shown, in particular, that the second-harmonic signal normalized by the zeroth-harmonic (dc) signal restores the unsaturated signal to a good approximation. Then, the effects of temperature and pressure on the second-harmonic signal are analyzed for high-pressure and low-pressure samples. Finally, some numerical examples of the effects of these parameters in precise concentration and isotope-ratio measurements of environmental molecules, CH4 and N2O, are given.