Broadband Absorbers Measurement Based on Wavelength Modulation Spectroscopy with Logarithmic Transformation and Analysis of the FirstHarmonic Signal

We proposed a method for measuring the concentration of broadband absorbers based on wavelength modulation spectroscopy (WMS), logarithmic transformation of the absorption signal, and analysis of the first harmonic (1f) signal. We found that the second harmonic (2f) signal of broadband absorbers is weak, while the 1f signal is much stronger. However, conventional WMS relies on an idealized Voigt absorption line profile for approximation, while the demodulated 1f signal intensity remains concentration-independent. Thus, we proposed a modified WMS method in which, through logarithmic transformation of the absorption signal, the intensity of the 1f signal is linear to the absorbance regardless of the gas absorption line shape. This allowed for the retrieval of broadband absorbers' concentration by measuring the 1f signal. To locate the detection wavelength, we introduced a reference gas that exhibits a narrow absorption peak within the absorption band of the broadband absorbers and utilized the peak of its 2f signal for wavelength calibration. We validated the effectiveness of the method by experiments, where isobutane was measured while ethane was selected as the reference gas. The 1f signal intensity demonstrated a strong linear correlation with isobutane concentration across different ethane background concentrations (R² =0.9989). Based on Allan deviation analysis, the system achieved a minimum detectable concentration of 97 ppb at the optimal averaging time of 19.7 s. Compared to the 2f-based approach, the 1f-based method improved the detection limit by more than 40 times.