Application of calibration-free wavelength modulated spectral absorption technique in temperature measurement under ultra-short optical path

The measurement of gas temperature parameters is of great significance in scientific research and industrial production. Wavelength modulation technology, as a non-contact optical detection means, has the characteristics of strong anti-interference ability and is widely used in various complex and harsh environments. The accuracy of temperature measurement is affected by short optical paths and weak absorption. In this paper, a calibration-free wavelength modulated ultra-short optical path measurement system is established, and the selection rules of spectral lines under the ultra-short optical path and weak absorption are proposed. The measurement results of wavelength modulation without calibration are in good agreement with those of thermocouple temperature measurement, and the relative error is less than 10%.


Introduction
Tunable diode laser absorption spectroscopy (TDLAS) has the advantages of non-intrusive measurement, high sensitivity, multi-parameter synchronous measurement, etc. Therefore it is widely used in the measurement of flow field temperature [1] without interfering with the original flow form and getting the real description of objectives.Absorption spectroscopy includes two methods, namely the direct absorption spectroscopy (DAS) and the wavelength modulation spectroscopy (WMS).Wavelength modulation technology can greatly suppress the low-frequency noise in the absorbed signal because of the superposition of high-frequency signal on the low-frequency signal, which makes wavelength modulation suitable for the poor flow field environment with weak absorption.
In wavelength modulation technology, the absorbed signal and the linear function are coupled to each other, and there is no complete decoupling method at present.Therefore, when using WMS for temperature detection, it is generally necessary to calibrate the demodulated harmonic signal [2] .In the case of temperature measurement in a bad environment, direct calibration is difficult, so researchers have done a lot of work on wavelength modulation without calibration.Li et al. developed a fast response coordinated diode laser absorption sensor and measured the temperature in a shock tube with an optical path L=15.24 cm using the peak inversion flow field parameter method.The measured results were consistent with the theoretical value, and the relative error was less than 1.2% [3] .Sun et al. proposed a new calibration-free full-linear fitting wavelength modulated absorption spectrum temperature measurement method, which compares simulated normalized second harmonic signals with measured results to determine the properties of gases [4] .Goldenstein et al. used the calibration-free method proposed by K SUN to measure the temperature, velocity, and static pressure of the gas in the Stanford expansion tube with optical path L=7.5 cm.The result showed that the residual difference between the simulated harmonic signal and the measured signal was less than 2.5%.The temperature, pressure, and velocity measured by the experiment are consistent within the range of 5%, 3.8%, and 1.5% predicted by the theory [5] .
In the above experiments measured by calibration-free wavelength modulation technology, the measured optical path is large, and the optical path is not interfered with by other substances such as glass.The accuracy of temperature measurement by wavelength modulation technology is affected by the intensity of the absorbed signal, which declines as the optical path decreases for the same spectral line.When the laser passes through the glass, absorption will be reduced.Therefore, more attention needs to be paid to the selection of spectral lines.In this paper, the selection criteria of spectral lines under short optical path and weak absorption are systematically studied, and the calibration-free measurement system at room temperature is verified.

The basic principle of calibration-free wavelength modulation technology for temperature measurement
Wavelength modulation technology refers to the laser in the low-frequency sawtooth signal and the high-frequency sine signal driven by the laser.The light intensity signal to be measured by the flow field is accepted by the detector and then demodulated through the lock amplifier to absorb signals at a specific frequency.From these absorbed signals, information such as the flow field temperature and constituent concentrations can be obtained.The specific formula has been elaborated in many literatures and will not be described too much here [6,7] .This section mainly describes the specific steps of uncalibrated wavelength modulation.
The relationship between the intensity of the incident laser  () and the intensity of the absorbed laser  () can be described by the Beer-Lambert law: (2) Figure 1 shows the solution of the wavelength modulation temperature without calibration is mainly divided into the following steps [8] : (1) The relationship between the actual absorbed laser intensity and time  () is measured.(2) The relationship between the wave number of the laser () and the change of intensity with time  () is measured.(3) The intensity of the transmitted laser light is simulated according to the Beer-Lambert law.(4) The actual laser intensity and the simulated laser intensity are fed into the same lock-in amplifier to obtain the harmonic signal.(5) The simulated harmonic signal is approximated to the actual by iterating the free parameters to find the temperature T.

Selection of spectral lines
The most important step in WMS-2f/1f temperature measurement is to select the appropriate spectral line.Zhou X et al. described the line selection criteria for temperature measurement using wavelength modulation technology [9,10,11] .In this section, we briefly discuss the principle of line selection for measuring the temperature of the flow field in the case of a short optical path through quartz glass.
When selecting the spectral line, we must first ensure that the laser can have enough absorption after passing through the glass, and then select the spectral line with lower cost under the premise of ensuring strong absorption.At the same time to avoid the interference of adjacent spectral lines, the two spectral lines should have a large enough low-state energy level difference to ensure a high-temperature measurement sensitivity.When there is no way to ensure sufficient absorption and high-temperature measurement sensitivity at the same time, priority should be given to ensuring sufficient absorption while trying to get closer to high sensitivity.
Based on the above rules, a pair of absorption lines were selected from the HITRAN2012 database, as shown in Table 1

Experimental system
The experimental equipment is shown in Figure 2, and the real image of the experiment is shown in Figure 3.The measuring system includes a signal generator, two DFB lasers, a laser mounting base, two pieces of high-purity quartz glass, two photodetectors, N purge device, germanium etalon, wavemeter, and data acquisition system.The two DFB lasers operating near 1392.5 nm and 1359.5 nm are installed on the laser mounting mount and the flow field temperature is monitored with a thermocouple.By adjusting the drive seat output center current and measuring with a wavemeter, the laser center wavelength is adjusted to 1392.534 nm and 1359.512nm respectively, which are located near the center of the water molecule absorption line.The signal generator outputs a sawtooth signal and a modulation signal to the laser drive seat.The modulation signal selects the normalized second harmonic peak maximum corresponding to the modulation signal, and the size of the scan signal should be able to make the second harmonic shape completely display a cycle.The signal size of the signal generator input to the laser controller is shown in Table 2.

Analysis and discussion of experimental results
The initial laser intensity of the laser  () is measured without absorption by N purging.The change of laser wavenumber with time () is measured by the standard and the wavemeter.First of all, the wavelength of the laser at the initial time needs to be determined by the wavelength meter, and it is converted into the wavenumber.Secondly, the interference signal was measured by using germanium etalon, and the relative wavenumber change relationship with time was obtained by using the program developed by Li et al [12] .The specific processing steps can be referred to Li et al.'s work and Du et al.'s work [12,13] .
The actual absorbed signal and the analog absorbed signal are passed into the same phase-locked amplifier program for demodulation.The parameter Settings of the phase-locked amplifier are shown in the table.After three iterations, the normalized second harmonics obtained by the final demodulation are shown in Figure 4.It can be seen that the simulated and actual normalized second harmonics of the two lasers fit very well.
The measurement results of wavelength modulation temperature without calibration are shown in Figure 5.The temperature measured by the thermocouple is 296 K, and the experimental results are basically the same as those measured by the thermocouple, with a relative error of less than 5%.The experimental results show that the spectral line pairs of 1392.5 nm and 1359.5 nm are feasible for the measurement of temperature under an ultra-short optical path.

Conclusion
The temperature measuring platform was built by using the wavelength modulation technique of a laser passing through quartz glass under the background of an ultra-short optical path.Weak absorption caused by short optical range and glass can be improved by selecting spectral lines with strong line strength, strong absorption, and high thermometric sensitivity, while interference from neighboring spectral lines should be avoided.When there is a contradiction with the traditional spectral line selection rules, the premise should be to ensure sufficient absorption.Taking H O absorption as an example, the temperature of the laboratory environment was measured using 1392.5 nm and 1359.5 nm lasers, and the relative error was less than 5% compared with the thermocouple temperature measurement results.The experimental results show that the surface calibration wavelength modulation technique has the advantages of strong reliability and high precision in the measurement of the ultra-short optical temperature range.The next step is to apply this system to the temperature measurement of an ultra-short optical path oscillating tube (similar to a shock tube).
) where  () represents the incident laser intensity signal, ∅ represents the linear function of absorbed component j, () represents the change of laser wave number with time, and  refers to the integral absorbance of absorbed component j, which can be expressed as:  = ∫ () = ∫  ()

Figure 2 .
Figure 2. Schematic of TDLAS measurement device.Figure 3. Real image of the experiment.

Figure 3 .
Figure 2. Schematic of TDLAS measurement device.Figure 3. Real image of the experiment.

Figure 4 .
Figure 4. Comparison between simulated absorption normalized second harmonic and actual situation.

Table 2 .
Load to laser controller signal size.