Calculation of the Ratio Between the Second and First Harmonic Signals in Wavelength-Modulation Spectroscopy for Absorption Measurement

The dependence of the ratio between the second and first harmonic signals in wavelength-modulation spectroscopy is calculated for the precise absorption measurement that is applied to gas sensing. In the calculation, the amplitude modulation of the laser is considered as well as the frequency modulation. First, the dependence of signals on peak optical depth is discussed for the Lorentzian and Gaussian lines. Next, the dependence of signals on gas concentration is calculated in a weak absorption-limit. Finally, a numerical example is explained taking into consideration both peak optical depth and gas concentration.