Objective  Tuned laser absorption spectroscopy (TLAS) technology has advantages such as non-contact, anti-interference, and high sensitivity, which can be used for gas concentration, temperature, and pressure measurement. In the existing pressure detection models, limited feature points of spectral lines are mostly extracted and calculated, which can lead to problems such as susceptibility to interference in measurement results and significant measurement errors. Therefore, it is necessary to establish a new anti-interference and stable pressure detection model. To solve this problem, a mathematical model was proposed for fitting the pressure and spectral line shape function within the low and high pressure ranges based on the gas pressure measurement method of absorption line width.

  Methods  Simulation research on the second harmonic absorption lines under different pressures was conducted based on the principle of spectral line broadening. In order to simulate the pressure changes by adjusting the Gauss/Lorentz halfwidth ratio, the second-order derivative signal was obtained by convolution of Gauss and Lorentz functions to simulate the second harmonic of the absorption spectral line. By establishing a mathematical model of the Gauss/Lorentz line fitting ratio and pressure, the fitting relationship between the two was obtained under ideal conditions and the influence of laser line width, white noise, and background interference. The comparative analysis on the stability of the fitting ratio with eigenvalues used to calculate pressure in existing models such as the peak width and 2f/4f amplitude under dynamic noise and background interference were conducted. Finally, the measured signal at 1 580 nm of CO₂ gas was processed to verify the simulation results.

  Results and Discussions   The simulation results show that under ideal conditions and the influence of laser linewidth, white noise, and background interference, there is a third-order fitting relationship between the Gauss/Lorentz line fitting ratio and pressure, and the fitting degree remains above 0.998 0 (Fig.3-6). Compared with traditional models, it has better stability under dynamic noise and background interference (Tab.1). The experimental results show that the third-order fit between the Gauss/Lorentz line fitting ratio of the actual detection spectral line and the pressure is 0.986 3 (Fig.9), slightly lower than the simulated fit of 0.998 7 (Fig.2), which is consistent with the simulation analysis results.

  Conclusions  In order to establish a more effective pressure detection method, based on the principle of spectral line broadening, the pressure change is simulated using the ratio of Gauss function half width to Lorentz function half width, and the Voigt function is used to describe the absorption spectral line shape. A mathematical model was established for the pressure to fitting ratio under ideal conditions, laser linewidth, white noise, and background interference. Through simulation analysis, the relationship between pressure and fitting ratio satisfies a third-order fitting relationship, which is not only affected by laser linewidth, white noise, and background interference, but also maintain stability under dynamic noise and background interference, which exhibits advantages in pressure detection compared to traditional models. The experimental validation was carried out using CO₂ absorption spectra. The curve fitting obtained from analyzing the experimental data was slightly lower, but its trend was consistent, which indicated the effectiveness of the established mathematical model. The proposed method has certain theoretical significance and practical value in pressure measurement, providing new ideas for pressure detection.