Improvement of Concentration Inversion Model Based on Second Harmonic Valley Spacing in Wavelength Modulation Spectroscopy

In tunable diode laser absorption spectroscopy (TDLAS), the wavelength modulation spectroscopy (WMS) is widely employed. However, when measuring the gas concentration with the second harmonic signal, errors will occur and the inversion accuracy will be reduced, because the change of the modulation depth will lead to the change of the second harmonic peak value, and the value of modulation depth cannot be calculated directly in the absence of gas component. To improve the inversion accuracy of WMS technology, we calibrate the modulation depth and take it as a parameter to the concentration inversion model. In this article, the relationship between the modulation depth and the valley spacing of the second harmonic is first derived, and used to calibrate the modulation depth in the measurement; then, an improved concentration inversion model is established by adding the calibrated modulation depth to the traditional model. Through simulations in Simulink and gas concentration measurement experiments with carbon monoxide (CO), the effectiveness of modulation depth calibration using valley spacing and the accuracy of the improved model are verified. The gas concentration measurement error of the improved model (relative error <; 0.37%, root-mean-square error (RMSE): 5.468 × 10
^-5
) is reduced by nearly one order of magnitude compared to the traditional model without calibration of the modulation depth (relative error <; 1.70%, RMSE: 2.178 × 10
^-4
). The correction method of modulation depth in this article does not need the priori information of the gas component, and the improved model produces a better determination of gas concentration immune to the variations of modulation depth, which is important for field measurements especially those with large environmental variations.