Calibration-free wavelength modulation spectroscopy for gas concentration measurements under low-absorbance conditions

<正>We derive the expressions of the first and second harmonic signals on the basis of absorption spectral and lock-in theories,and determine the gas concentration according to the ratio of second and first harmonic signals.It is found that the X and Y components of the harmonic signals are influenced by the phase shift between the detection and reference signal,and the phase shift can be any value in a range from 0 to 2π,which is different from the results obtained previously.Meanwhile,an additional item caused by the residual amplitude modulation will make a great contribution to the second harmonic signal,and may not be neglected under low absorbance conditions.Theoretical analysis indicates that subtracting back-ground signal from the second harmonic signal can remove the influence of this item,and can improve the measurement accuracy of gas concentration.On this basis,we select the transition of CO₂ at 6527.64 cm^-1 to analyse the approximation errors during the derivation by numerical simulation and then measure the CO₂ concentration under low absorbance conditions,with absorbance varying from l%o to 6‰.