# TDLAS Monitoring of Carbon Dioxide with Temperature Compensation in Power Plant Exhausts
## 4 Direct Absorption Measurement and Correction  
In this part, the direct absorption spectra with and without temperature corrections are compared to analyze the measurement accuracy by relative errors. The \(x\)-axis of measured spectral data were sampling points, which were time domain signals. The frequency calibration of the spectrum was required to convert the time domain to the frequency domain. The simulations based on HITRAN2012 were used to calibrate the frequency domain. As shown in Figure 3, three wavenumbers in HITRAN2012 correspond to three points in measured spectral. Therefore, the curvilinear equation of quadratic polynomial was obtained to convert the time domain to the frequency domain. Figure 4 plots the measured incident signal \(I_{0}\) and the direct absorption signals \(I_{\mathrm{t}}\) for 10% CO\({}_{2}\) at 318 K. The incident laser intensity \(I_{0}\) was inferred by third-order polynomial fit in the far-wing parts without absorption. The Lorentz profile was chosen to fit the line shape for improving accuracy due to the domination of Lorentzian component at 1 atm. After fitting, the logarithmic ln (\(I_{\mathrm{t}}/I_{0}\)) was integrated over the whole frequency domain to calculate the integrated absorbance A. Thus, the concentration \(X\) can be calculated from Equation (2), with line intensity \(S(T)\) obtained from Equation (4), total pressure \(P\), and path length \(L\) as known parameters. Figure 5 shows the measured absorption spectra of 16% CO\({}_{2}\) in the 6331.8-6333.6 cm\({}^{-1}\) spectral region at five different temperatures from 298 to 338K. The absorption signals in Figure 5 decrease with the increased temperature. Figure 6 plots the CO\({}_{2}\) line shape near 6332.7 cm\({}^{-1}\) (P = 1 atm, T = 298 K, 10% CO\({}_{2}\) in N\({}_{2}\)) well overlaid with the best-fit Lorentz profile. The obtained Lorentzian width of 0.15412 \(\pm\) 0.0042 cm\({}^{-1}\) was broadened by pressure and temperature. The residuals of the curve to data is shown in the bottom panel of Figure 6, showing that the fits are similar. Table 1 shows the relative errors of direct absorption from 298 to 338 K. The error of inferred concentration obtained from the spectroscopic measurement generally rises with the increase of temperature. At 308 K, the biggest relative error was up to 5.66%, which cannot meet the requirement of industrial application. To further explore the cause of measurement errors, line intensities from the HITRAN database were compared with measured line intensities which are calculated by Equation (4). With a certain \(S(T)\), the obtained integrated absorbance \(A\) varies linearly with P\(\cdot\)X\(\cdot\)L where is the product of total pressure (\(P\) = 1 atm), absorption length (\(L\) = 2000 cm), and concentration (\(X\) = 10-20%, interval 2%). The relationship between \(A\) and _P\(\cdot\)X\(\cdot\)L_ can be represented by a linear fitting and the slope of the fitting line is the intensity of the spectral line at the corresponding temperature from 298 K to 338 K, as depicted in Figure 7. Quality of the fit was very good in five temperatures, shown by R squared values from 0.99354 to 0.99875. As shown in Table 2, the calculated values show good agreement with the HITRAN values in variation tendency, but the former's gradient decreases more with the temperature rising. The discrepancy indicates that a 3-10% change of line intensity leads to 1-6% change in the measured CO\({}_{2}\) concentration. Figure 8 depicts that both the integrated absorbance and the line intensity of 14% CO\({}_{2}\) decrease with the increase of temperature. The discrepancy leads to large errors in the concentration measurement, when the total pressure \(P\) and path length \(L\) are invariable. This information can be used to compensate these errors caused by change of temperature. According to the Equation (5), the least squares method is used for linear fitting between \(A/S(T)\) and concentration \(X\) at different temperatures.