Spectral Inversion Algorithm of Virtual Image Phase Array Spectrometer Based on Particle Swarm Optimization

Objective Carbon dioxide (CO2) is a principal byproduct of hydrocarbon fuel combustion. Real-time detection of CO2 can evaluate combustion temperature and efficiency, playing a crucial role in combustion diagnosis. Compared with the probe method and other contact techniques, laser absorption spectroscopy offers rapid, precise and non-intrusive measurement of CO2 in combustion environments. This method has attracted increasing attention and research, becoming a mainstream technology for combustion diagnosis. Among various approaches, combining a broadband laser source with broadband absorption spectrum measurement allows capturing more sample absorption characteristics, especially when sample absorption is weak or subject to interference from other absorbents, providing the advantage of multi-wavelength absorption spectrum detection. The virtual image phase array (VIPA) spectrometer, characterized by its wide spectral range and high resolution, represents a novel type of orthogonal dispersion spectrometer. However, when directly applying the VIPA spectrometer to gas parameter inversion, the measured spectral frequency axis exhibits deviations from theoretical values due to the nonlinear dispersion of the VIPA element and discrete sampling by the array detector, leading to reduced accuracy in gas inversion. This paper presents a spectral inversion accuracy optimization algorithm based on particle swarm optimization (PSO) aimed at enhancing the precision of CO2 detection using the VIPA spectrometer for wide-spectrum CO2 detection. Methods The CO2 measurement system, centered around the VIPA spectrometer, primarily consists of two components: the CO2 concentration detection part and the gas preparation part. Light emitted by a supercontinuum light source, after filtration through a 1.42-1.45 mu m filter, combined with a fiber collimator, enters a Chernin-type optical absorption multi-pass cell with an optical path length of 4 m. An optical fiber coupler directs the light exiting the multi-pass cell into a single-mode fiber, which is then connected to the VIPA spectrometer's fiber interface. Initially, the Voigt absorption line model for the CO2 molecule is established by the HITRAN database. The peak position of the absorption model and the experimental peak's pixel position are fitted using a cubic polynomial to achieve preliminary calibration of the frequency axis. Subsequently, the PSO algorithm corrects the peak position of the simulated spectrum line to ensure optimal agreement between the simulated and measured spectra. Finally, the gas volume fraction is determined through the least square method. During peak position correction of PSO algorithm, the spectrum is divided into several sub-intervals using the trough of the spectrum line as the cut-off point. Adjacent sub-intervals with peak spacing less than 1 cm(-1) are grouped into a single fitting interval, and each interval's peak is corrected individually. Results and Discussions The cubic polynomial fitting spectrum extraction algorithm yields a frequency axis with a position deviation ranging from 0?0.1 cm(-1) compared to the theoretical positions [Fig. 4(c)]. Residual analysis indicates that frequency axis calibration deviations are the primary source of these discrepancies. Given the disparity between the measured spectrum's frequency axis and the theoretical spectrum, the PSO algorithm is used to adjust peak positions (Fig. 5). As iterations increase, peak position distribution stabilizes, with the algorithm generally converging by the 30th iteration. The reliability of the PSO peak correction algorithm for gas volume fraction retrieval is examined by measuring CO2 concentrations of 30%, 40%, 50% and 60% within the range of 6900 to 6990 cm(-1). Without PSO correction, the average deviation of inversion is 33.27% (Fig. 8), and the maximum relative error reaches 35.43%. The average deviation of inversion after PSO correction is 1.81%, and the maximum relative error is 2.58%. The accuracy of the inversion is significantly improved after PSO correction of the peak value. Conclusions To address the issue of substantial parameter inversion errors due to insufficient spectrometer frequency axis calibration accuracy, an optimization algorithm of absorption spectrum inversion accuracy based on PSO is introduced in our study. By employing the PSO algorithm to adjust the simulated peak positions of the measured spectrum line of pure gas, an optimal match between simulated and measured spectral lines is achieved. Using corrected peak positions, simulated absorption lines serve as a basis for solving the volume fraction as an independent variable through least squares fitting to experimental lines. Pre- and post-peak correction fitting outcomes for pure CO2 measurement and simulation spectra demonstrate that the PSO-based peak correction algorithm effectively enhances peak location accuracy and reduces fitting residuals. According to CO2 measurement data spinning 30%-60% volume fractions, the average deviation in corrected volume fraction inversion stands at 1.81%, with an average root mean square error of 1.01x10(-5), indicating the method's efficacy in improving the inversion accuracy of volume fraction and verifying the algorithm's applicability to VIPA spectral parameter inversion. This algorithm also offers reference value for gas parameter inversion optimization in other spectrometers.