Abstract
This paper introduces a high-precision, calibration-free method for reconstructing molecular absorbance profile. The method employs a scanning wavelength modulation strategy that integrates low-frequency triangular wave scanning with high-frequency sine wave modulation. Specifically, it utilizes harmonic signals corresponding to the spectral lines at the scanning frequency to reconstruct transmittance information centered around that frequency, using the modulation depth as the half-width frequency range. By incorporating low-frequency scanning, the transmittance information of the spectral lines can be accurately obtained. Finally, through interpolation and averaging of the transmittance in overlapping frequency regions, the molecular absorbance profile is reconstructed.The main content of this paper is structured into three key components: theoretical derivation, numerical simulation, and experimental validation of the harmonic reconstruction method. In the theoretical derivation section, the instantaneous laser frequency is represented as a parameter "x" using a cosine function and is subsequently substituted into the Fourier expansion of the laser transmittance. Then the transmittance function is reconstructed based on Chebyshev polynomials. In the numerical simulation section, we illustrate the comprehensive process of the harmonic reconstruction method, including harmonic detection, data matrix reconstruction, and the interpolation and averaging of data matrix slices to ultimately obtain the transmittance function. Following this, systematic errors in the reconstructed transmittance functions are analyzed and compared for various harmonic orders and modulation depths through numerical simulations. The results show that the systematic error decreases with the harmonic order and increases with the modulation depth. In the experimental verification section, to evaluate the measurement accuracy of this method, we reconstructed the absorbance profile for different concentrations of CO<sub>2</sub> using the 6330.821 cm<sup>-1</sup> spectral line. The standard deviation of the fitting residual of the absorbance profile is in the order of 10<sup>-5</sup>. The signal-to-noise ratios were 503 and 222 for the strong and weak absorptions, respectively. We conducted 3000 consecutive online measurements and compared the harmonic reconstruction method with both the direct absorption method and the second harmonic peak method. Statistical analyses were made regarding the standard deviations and Gaussian distributions of the deduced concentration results. The results indicate that the standard deviation from the harmonic reconstruction method is less than half of those from the direct absorption method and the second harmonic peak method, demonstrating significantly superior measurement stability. This method holds promise as a new reliable approach for the high-precision measurement of spectral line parameters and online monitoring of weakly absorbing gas parameters in complex industrial environments.
Published Version
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