A wide-range temperature sensor with a single diode laser based on H₂O absorption spectra near 1850.5 nm

Abstract

We have developed a compact sensor utilizing a tunable diode laser near 1850.5 nm to measure H₂O absorption for wide-range temperature diagnostics. The sensor’s performance was experimentally evaluated in a tube furnace at temperatures ranging from 600 to 1800 K and pressures from 3.5 to 103 kPa, showing a relative error between the measured and set temperatures of −2%–3.5%. The numerical simulations confirmed the sensor’s suitability for temperature measurements between 500 and 2500 K, with the accuracy of absorbance extraction being a critical factor. The above results suggest that the sensor is highly effective for temperature measurement across a broad range and holds potential for applications in aerospace and industrial combustion diagnostics.

1 Introduction

Highly accurate and fast-response measurements of temperature and species concentration are critical in assessing combustion efficiency, which directly influences thermal performance in various combustion systems, such as gas turbines, scramjets, wind tunnels, shock tubes, laboratory flames, and industrial-scale combustors [1–3]. Among the available diagnostic techniques, tunable diode laser absorption spectroscopy (TDLAS) is widely adopted for retrieving combustion temperature and species concentration due to its robustness, high sensitivity, fast response, and non-intrusive measurement capabilities [4–8]. This technique detects specific absorption features of target gases, such as water vapor (H₂O), which is a major product in combustion and has been frequently used as a target gas in TDLAS-based diagnostics [9, 10]. H₂O exhibits several strong absorption bands in the infrared region [11], as illustrated in Figure 1.

FIGURE 1

At a typical combustion temperature of 1,600 K, the line strengths are plotted across a wavelength range from 1 to 10 μm. These absorption bands occur at 1.4 μm (v₁+v₃), 1.8 μm (v₁+v₂+v₃), 2.7 μm (v₁+v₂+v₃), 5.5 μm (v₂), and 6.5 μm (v₁+v₂), with the line strengths at 2.7 μm, 5.5 μm, and 6.5 μm being approximately 10 times stronger than those at 1.4 μm and 1.8 μm. Although these stronger absorption bands in the mid-infrared region provide higher precision for temperature sensing and trace H₂O detection, they require more expensive laser sources, such as quantum cascade lasers (QCLs) [12, 13] and interband cascade lasers (ICLs) [14, 15]. In contrast, the near-infrared absorption bands around 1.4 μm and 1.8 μm can be accessed using fiber-optic diode lasers, offering advantages such as compact size, lower cost, high spectral quality, and room-temperature operation [16–18], and the signals from these lasers can be directly acquired using either a photodetector or a quartz tuning fork detector, which has the merits of wide response range, low cost and tiny size [19–21], making these lasers more attractive for temperature and H₂O concentration measurements in various combustion systems.

Most previous studies have focused on the 1.4 μm region for high-temperature sensing due to the availability of telecommunication-type lasers. For instance, Qu et al. [22] and Liu et al. [23] designed a temperature sensor capable of measuring temperatures using a distributed feedback (DFB) laser with a center wavelength of 1397.8 nm to detect two H₂O absorption lines at 7153.7484 cm⁻¹ and 7154.3534 cm⁻¹. Similarly, Shao et al. [24] developed a gas sensor based on a 1.56 μm laser using wavelength modulation and two-line temperature retrieval to measure temperatures ranging from 200°C to 1000°C. However, these methods are prone to calculation errors due to uncertainties in the HITRAN or HITEMP databases. Increasing the number of H₂O absorption lines can enhance temperature measurement precision. Recent studies by Liu et al. [25] and Li et al. [26] employed three H₂O absorption lines at 7185.597 cm⁻¹, 7444.350 cm⁻¹, and 7444.37 cm⁻¹, respectively, to achieve high-precision temperature measurements in a flat-flame furnace and scramjet engine. Zhang et al. [27] used three DFB lasers operating near 1,343 nm, 1,392 nm, and 1,469 nm to accurately measure engine nozzle temperatures. In our previous work [28], five DFB lasers were employed near 1,392 nm, 1,393 nm, 1,339 nm, 1,343 nm, and 1,469 nm to improve temperature measurement precision in the expansion section of a scramjet engine.

Despite the stronger absorption at high temperatures in the 1.8 μm band compared to the 1.4 μm band [11], TDLAS measurements near 1.8 μm have been rarely reported. The 1.8 μm band holds promise for more sensitive H₂O detection and higher-precision temperature measurements. Therefore, in this study, we employed a single DFB laser operating near 1.85 μm as a TDLAS sensor to scan multiple H₂O absorption lines, with the lower-state energy levels ranging from 70 to 6,581 cm⁻¹. This sensor, featuring a high signal-to-noise ratio and strong line strength over a wide temperature range, enables high-precision temperature measurements across a broad temperature range.

2 Measurement basis of the sensor

2.1 Selection of H₂O absorption lines

The precision of laser-based sensors largely depends on the absorption strength of the selected target lines, which directly influences measurement accuracy. Therefore, selecting optimized absorption lines is critical. In this study, I will elaborate on the specific line selection criteria: 1) Target Molecule Selection: H₂O was chosen as the target molecule for TDLAS-based temperature measurement, with a designated temperature range of 500–2500 K. This range not only covers the operational temperatures of our laboratory tube furnace for experimental validation but also extends to meet the requirements of future combustion flow field studies in aerospace engines. 2) Band Selection: The chosen spectral band lacks interference from major combustion products such as CO and CO₂, and features uniformly distributed lower-state energy levels, enabling measurements across a wide temperature span. 3) Laser Selection and Initial Line Database: Based on the above analysis of Figure 1 and selection criteria (1) and (2), a DFB laser operating near 1,850 nm (1.8–2 μm) was selected, covering the 5,400–5,409 cm⁻¹ range. Absorption lines were initially chosen from HITEMP2010 with line strengths at 296 K meeting a threshold of S (T₀)≥1.0 × 10⁻³⁵ cm^-2 atm⁻¹. (4) Temperature-Based Line Screening: Within this initial database, line strengths were calculated at 100 K intervals, and line strengths meeting S(T)≥1.0 × 10⁻⁶ cm⁻² atm⁻¹ were selected to create temperature-specific databases from 500 to 2,500 K. (5) Signal-to-Noise Ratio (SNR) Optimization: For each temperature interval, lines with peak absorbance values yielding signal-to-noise ratios above 10 were further selected and consolidated to form an optimized absorption line database for temperature calculations over the 500–2,500 K range. Based on the criteria, H₂O absorption lines between 5,400.5 cm⁻¹ and 5,405.7 cm⁻¹ were selected. Because the line selection incorporated the temperature dependence of line strengths, each line in the final combined database exhibits varying intensities across temperatures, enabling accurate measurements from low to high temperatures.

Based on the line selection criteria, the simulated H₂O absorption spectra at 1,600 K (in blue) are shown in Figure 2A. Additionally, in combustion flow environments, such as aerospace engines and gas turbines, hydrocarbon-based fuels are commonly used, resulting in maximum potential interference concentrations of approximately 20% CO₂, 10% CO, and 10% CH₄. Hence, potential interference from carbon dioxide (CO₂), carbon monoxide (CO), and methane (CH₄) was considered, with their simulated absorption spectra displayed in black, red, and green, respectively. The H₂O absorption is significantly stronger than that of other gases, indicating that spectral interference from these gases can be ignored. Figure 2B further illustrates the normalized line strength distribution of the selected absorption lines for temperatures ranging from 500 to 2500 K. The variation in line strengths for each absorption line at different temperatures is distinguished by the color gradient in the heatmap, clearly indicating the applicable temperature calculation range for each line and demonstrating how the line strengths and detectable absorption lines vary with temperature, enabling temperature measurement over a wide range.

FIGURE 2

2.2 Temperature retrieval method

The most common methods for retrieving temperature in TDLAS combustion diagnostics are two-line thermometry [29, 30] and the Boltzmann Plot method [31–33]. However, these approaches involve computing the integrated absorbance over a wide spectral range, which can be computationally intensive. In this study, we developed a broadband spectral fitting model based on the univariate search method [34, 35] to determine temperature and H₂O concentration. This model fits multiple H₂O absorption lines across the absorption spectrum and continuous spectral bands, which has been reported in our previous work [36].

The flowchart for the broadband spectral fitting model is shown in Figure 3. First, a measured broadband spectral absorbance (denoted as Abs_mea) is recorded, and a model-based spectral absorbance (denoted as Abs_model), using Voigt profile, is simulated based on input fitting parameters such as H₂O line parameters from HITEMP2010 and experimental conditions (e.g., pressure, optical path length). A nonlinear univariate method (using the fminbnd function in MATLAB) is then employed to search for the optimal temperature (denoted as T_opt) under an initial concentration (denoted as X₀) and initial temperature (denoted as T_initial). A linear fitting between Abs_mea and Abs_model is performed to obtain the slope () and intercept () of the linear fit according to the relationship of = . The concentration is then updated as = . After jth iterations, the second norm of the fitting residuals (r_normr) is minimized and the convergence condition (| - |<1、| - |<1 × 10⁻³) is satisfied, yielding the optimal temperature and concentration. Here, the r_normr value represents the second norm of the spectral fitting residuals, which is the square root of the sum of squared residuals. The r_normr is shown in Equation 1:Where is Abs_mea during the jth iteration, is the fitting result = .

FIGURE 3

and are respectively the optimal temperature and concentration, then r_normr can be further expressed by Equation 2:Where is during the jth iteration, represents the objective function dependent on temperature . The term indicates the value of that minimizes the objective function. Specifically, is an operator that finds the variable value at which the function reaches its minimum, and refers to this variable in the context.

The typical example illustrating this method is shown in Figures 4, 5. To fit the actual experimental conditions, an H₂O absorbance spectrum was simulated under the conditions of Pressure = 1 atm, X_H2O = 0.06, L = 23 cm and T = 1200 K. Gaussian noise with an amplitude of ±0.005 and a 20% error in H₂O absorption line parameters were added in the H₂O absorbance spectrum regarded as measured spectrum. Then it was input into the broadband spectral fitting model to obtain the trends for temperature, concentration, and r_normr during each iteration, as shown in Figure 4.

FIGURE 4

FIGURE 5

In the first iteration (blue curve in Figure 4A), the optimal temperature differs significantly from the true value of 1200 K, and the corresponding r_normr (green curve in Figure 4B) is also at its maximum. Figure 5A shows the Abs_mea (blue curve) and Abs_model (red curve) for the first iteration, where a poor fit between the measured and model-based spectrum is evident. Similarly, Figure 5B presents the linear fit of the spectral data for the first iteration, demonstrating a clear deviation between the measured data and the linear fit. These results indicate that the temperature and the concentration are not optimal in the first iteration. After several iterations, the temperature and concentration in the 11th iteration converge closely to the true values of 1200 K and 0.06, respectively. Furthermore, the r_normr is minimized. The spectra (Figure 5C) and the linear fit of the spectral data (Figure 5D) confirm a much-improved fit, indicating that the optimal temperature and concentration have been successfully determined.

3 Experimental setup and discussions

3.1 Experimental setup

A DFB laser (Nanoplus, S/N: 2899/03-02) operating near 1850.5 nm was selected as the laser source. A commercial laser controller (LDC501, Stanford Research Systems) was used to regulate the laser operating temperature, and a sawtooth wave signal generated by a commercial function generator (SDG2082X, SIGLENT) was applied to continuously scan the absorption lines of H₂O. The temperature measurement performance of the sensor was evaluated using a commercial tube furnace platform (GSL-1800X-III-₵50). The laser beam was split into two parts using a fiber splitter, as shown in Figure 6. Fifty percent of the beam was collimated by a fiber collimator, transmitted through the temperature test region in the furnace, and then detected by a photodetector (Thorlabs PDA10D-E-C). The other half of the beam passed through a quartz Fabry-Pérot etalon for frequency calibration and was detected by another photodetector. The generated photocurrents were converted into voltage signals using a custom-made transimpedance amplifier. The signals were then digitized using a 16-bit data acquisition card (NI PXIe-5172). To ensure a stable temperature region within the furnace, the sapphire tube was inserted into both ends of the furnace tube. Additionally, a pair of structures incorporating internal gas pipes was designed to mount the collimator. The structures allowed for purging the internal air gap with high-purity nitrogen (99.99%) to eliminate absorption interference from residual H₂O.

FIGURE 6

Seven equally spaced temperatures ranging from 600 K to 1800 K were set within the furnace’s maximum tolerance temperature of 2000 K. After reaching the preset temperatures, pure water vapor (100% purity) at three different pressures (P1–P3: 3.5–6.5 KPa) was introduced into the furnace, with the pressures monitored using a manometer (MKS628). For each temperature and pressure, 500 raw spectral signals were recorded once the pressure stabilized. Additional tests were conducted at higher pressures (P4–P6: 10–103 KPa) using a mixture of pure water vapor and high-purity nitrogen, with 500 spectral signals captured for each set condition. Non-absorbing regions of the raw spectral signals were fitted using a third-order polynomial to extract the H₂O absorbance. Figure 7A displays the measured raw data and the corresponding extracted H₂O absorbance. A spectral fitting result using the broadband spectral fitting model is shown in Figure 7B, demonstrating close agreement between the fitted and measured H₂O absorbance. But there is still a deviation between −0.02 and 0.02 as shown in Figure 7C. The reason of this deviation can be concluded as follows. DFB laser’s wide scanning range combined with spectral broadening and weak absorption lines, introduces errors in selecting non-absorbing regions, resulting in irregular baseline fluctuations that subsequently cause baseline shifts during spectral fitting, and this effect will be discussed in Section 3.2. Moreover, the spectral line parameters in HITEMP2010 have errors ranging from 5% to 20%, or even higher, and unavoidable spectral noise also contributes to the deviation. Calibration of spectral parameters and an increase in the SNR can reduce these errors, but due to the large number of lines involved, this process is still ongoing. However, as illustrated in Figure 7D, even with a deviation between −0.02 and 0.02, r_normr converges to a minimum after 13 iterations, allowing optimal temperature and concentration values to be obtained.

FIGURE 7

3.2 Results and discussions

3.2.1 Analysis of experimental results

To further validate the sensor’s performance, temperature measurements were carried out in the furnace across a range of 600–1800 K and pressures from 3.5 to 103 KPa. An example of the extracted H₂O absorption spectrum at temperatures between 600 K and 1800 K (at P3) is shown in Figure 8A. The absorption intensity varies across this temperature range, corresponding to the trend in line strength with temperature, as depicted in Figure 2B.

FIGURE 8

The extracted H₂O absorption spectra were processed using the broadband spectral fitting model to determine the measured temperatures, with error bars and relative errors at different temperatures and pressures shown in Figure 8B. At a constant temperature, the standard deviations at different pressures remain relatively consistent and close to the average values. The relative error fluctuates within 2% for pressures ranging from 3.5 to 6.5 KPa, indicating stable temperature measurement performance. At higher pressures (10–103 KPa), the maximum standard deviation is 34.6 K (at 1800 K, 102.9 KPa), and the relative error ranges from −1% to 3.5%. The relative error increases significantly at temperatures above 1000 K and pressures exceeding 50 KPa. The wide wavelength scanning range of the laser, combined with weak spectral lines and spectral broadening, complicates the accurate fitting of non-absorbing regions using polynomial methods, leading to errors in absorbance extraction and temperature measurement.

3.2.2 Simulation analysis

To evaluate the impact of absorbance extraction errors on temperature accuracy, the absorption-free laser intensity (I₀) was determined by extracted baselines at different temperatures and pressures in Section 3.2.1. H₂O absorption spectra (denoted as ) were simulated at seven equal-interval temperatures between 600 and 1800 K and six different pressures (3.5–150 KPa), with Gaussian noise (amplitude ±0.005) and a 20% error in the H₂O line parameters added to the simulated spectra. The transmitted intensity () is calculated by Equation 3.where B(υ) represents the added Gaussian noise.

Figure 9A shows an example of the simulated transmitted intensity at 1000 K and 150 kPa, along with the extracted spectrum. The error bars and relative errors are plotted in Figure 9B, showing a maximum standard deviation of 60.1 K (at 1800 K, 150 KPa). The relative error fluctuates within ±1% at pressures between 3.5 KPa and 10 kPa, but rises to 3% at pressures between 50 and 150 kPa, which is largely consistent with the experimental results. This indicates that incorrect selection of non-absorbing regions can reduce accuracy of absorbance extraction and temperature measurements.

FIGURE 9

To further verify the impact of these factors and evaluate the sensor’s performance at temperatures above 1800 K, H₂O absorption spectra were simulated for ten equal-interval temperatures between 500 and 2500 K at six different pressures (3.5–150 KPa). Gaussian noise (amplitude ±0.005) and a 20% error in spectral parameters were added to the H₂O absorbance, where the process assumes accurate absorbance extraction. Figure 10A shows an example of the simulated spectra, while Figure 10B presents the corresponding error bars and relative errors. The maximum standard deviation of temperature is 105.14 K (at 2500 K, 150 KPa), and the relative error fluctuates between 1.5% and 2%, which is lower than the error shown in Figure 9B for the same conditions. These results demonstrate that the sensor performs effectively over the 500–2500 K range, and that improper selection of non-absorbing regions directly reduces the accuracy of absorbance extraction and temperature measurements, which will be addressed in future work by developing a broadband baseline fitting model to enhance temperature measurement accuracy.

FIGURE 10

4 Conclusion

In this study, we developed a TDLAS sensor operating near 1850.5 nm to scan multiple H₂O absorption lines within the 5,400–5,406 cm⁻¹ range for wide-range temperature measurement. The sensor’s performance was experimentally validated in a tube furnace at temperatures ranging from 600 to 1800 K and pressures from 3.5 to 103 kPa, where the relative error of temperature is within 3.5%. Additionally, numerical simulations demonstrated that the sensor is capable of accurate temperature measurements from 500 to 2500 K. The accuracy of the extracted absorbance plays a crucial role in the overall measurement precision, and factors such as the wide scanning range, weak spectral lines, and spectral line broadening can influence the selection of non-absorbing regions and the quality of absorbance extraction. Future work will focus on the development of a broadband baseline fitting model to mitigate the effects of spectral interference and further improve temperature measurement accuracy. Overall, the sensor exhibits high measurement accuracy over a wide temperature range and is well-suited for applications in combustion environments with large temperature gradients, such as the isolation and expansion sections of scramjet engines. Additionally, this sensor provides a promising solution for multiline temperature distribution measurements in future diagnostics.

References

• 1.

  KimGShimHJungSParkGLeeD. Robustness and performance evaluation of TDLAS sensor for scramjet intake. Aerospace Sci Technol (2023) 141:108561. 10.1016/j.ast.2023.108561

  • CrossRef
  • Google Scholar

• 2.

  NieWXuZRaoGLinXLuJDongMet alMethods of tunable diode laser absorption saturation spectroscopy to gas sensing under optically thick conditions. Microw Opt Technol Lett (2021) 63(8):2063–7. 10.1002/mop.32840

  • CrossRef
  • Google Scholar

• 3.

  FisherEMDBenoyTHumphriesGWilsonDLengdenMJohnstoneWet alA custom, high-channel count data acquisition system for chemical species tomography of aero-jet engine exhaust plumes. IEEE Trans Instrum Meas (2020) 69(2):549–58. 10.1109/tim.2019.2895932

  • CrossRef
  • Google Scholar

• 4.

  WerleP. A review of recent advances in semiconductor laser based gas monitors. Spectrochim Acta A (1998) 54(2):197–236. 10.1016/s1386-1425(97)00227-8

  • CrossRef
  • Google Scholar

• 5.

  LacknerM. Tunable diode laser absorption spectroscopy(TDLAS) in the process industries-A Review. Rev Chem Eng (2007) 23(2). 10.1515/revce.2007.23.2.65

  • CrossRef
  • Google Scholar

• 6.

  SchulzCDreizlerAEbertVWolfrumJ. Combustion diagnostics. In: TropeaC, editor. Handbook of experimental fluid mechanics. Berlin, Heidelberg: Springer (2007). p. 1241–315. 10.1007/978-3-540-30299-5_20

  • CrossRef
  • Google Scholar

• 7.

  BolshovMAYuAKYuVR. Tunable diode laser spectroscopy as a technique for combustion diagnostics. Spectrochim Acta B (2015) 106:45–66. 10.1016/j.sab.2015.01.010

  • CrossRef
  • Google Scholar

• 8.

  WitzelOKleinAWagnerSMeffertCSchulzCEbertV. High-speed tunable diode laser absorption spectroscopy for sampling-free in-cylinder water vapor concentration measurements in an optical IC engine. Appl Phys B (2012) 109(3):521–32. 10.1007/s00340-012-5225-0

  • CrossRef
  • Google Scholar

• 9.

  GoldensteinCSSpearrinRMJeffriesJBHansonRK. Infrared laser-absorption sensing for combustion gases. Prog Energ Combust Sci (2017) 60:132–76. 10.1016/j.pecs.2016.12.002

  • CrossRef
  • Google Scholar

• 10.

  WolfrumJ. Lasers in combustion: from basic theory to practical devices. Proc Combust Inst (1998) 27(1):1–41. 10.1016/s0082-0784(98)80387-1

  • CrossRef
  • Google Scholar

• 11.

  TaoMMWangYMWuHLLiGHWangSTaoBet alHyperspectral absorption of water around 2 μm based on a boradband tunable, narrow linewidth Tm-doped fiber laser. Acta Phys Sin (2022) 71(11):114203. 10.7498/aps.71.20212127

  • CrossRef
  • Google Scholar

• 12.

  LiJDengHSunJYuBFischerH. Simultaneous atmospheric CO, N₂O and H₂O detection using a single quantum cascade laser sensor based on dual-spectroscopy techniques. Sens Actuators B Chem (2016) 231:723–32. 10.1016/j.snb.2016.03.089

  • CrossRef
  • Google Scholar

• 13.

  ZhouXTangYZhaoSChenHLiH. Water vapor detection based on three-line TDLAS with a continuous wave quantum cascade laser. Optik (2023) 287:171126. 10.1016/j.ijleo.2023.171126

  • CrossRef
  • Google Scholar

• 14.

  LiJDuZAnY. Frequency modulation characteristics for interband cascade lasers emitting at 3 μm. Appl Phys B (2015) 121(1):7–17. 10.1007/s00340-015-6195-9

  • CrossRef
  • Google Scholar

• 15.

  NorthernJHO’HaganSFletcherBGrasBEwartPKimCSet alMid-infrared multi-mode absorption spectroscopy using interband cascade lasers for multi-species sensing. Opt Lett (2015) 40(17):4186. 10.1364/ol.40.004186

  • CrossRef
  • Google Scholar

• 16.

  XingFHuangYZhaoMZhaoJ. The brief introduction of different laser diagnostics methods used in aeroengine combustion research. J Sens (2016) 2016:1–13. 10.1155/2016/2183569

  • CrossRef
  • Google Scholar

• 17.

  LiBXueLJiNWeiDH. Research on spectroscopy modulation of a distributed feedback laser diode based on the TDLAS technique. Int J Opt (2021)2021) 2021:1–9. 10.1155/2021/8829790

  • CrossRef
  • Google Scholar

• 18.

  LiuXZhouXJeffriesJBHansonRK. Experimental study of H2O spectroscopic parameters in the near-IR (6940–7440cm⁻¹) for gas sensing applications at elevated temperature. J Quant Spectrosc Radiat Transf (2007) 103(3):565–77. 10.1016/j.jqsrt.2006.07.008

  • CrossRef
  • Google Scholar

• 19.

  MaYQiaoSWangRHeYFangCLiangT. A novel tapered quartz tuning fork-based laser spectroscopy sensing. Appl Phys Re (2024) 11(4). 10.1063/5.0214874

  • CrossRef
  • Google Scholar

• 20.

  LiuYQiaoSFangCHeYSunHLiuJet alA highly sensitive LITES sensor based on a multi-pass cell with dense spot pattern and a novel quartz tuning fork with low frequency. Opto-electron Adv (2024) 7(3):230230. 10.29026/oea.2024.230230

  • CrossRef
  • Google Scholar

• 21.

  WangJWuHSampaoloAPatimiscoPSpagnoloVJiaSet alQuartz-enhanced multiheterodyne resonant photoacoustic spectroscopy. Light Sci Appl (2024) 13(1):77. 10.1038/s41377-024-01425-1

  • CrossRef
  • Google Scholar

• 22.

  QuZSchmidtFM. In situ H₂O and temperature detection close to burning biomass pellets using calibration-free wavelength modulation spectroscopy. Appl Phys B (2015) 119(1):45–53. 10.1007/s00340-015-6026-z

  • CrossRef
  • Google Scholar

• 23.

  LiuXMaY. Tunable diode laser absorption spectroscopy based temperature measurement with a single diode laser near 1.4 μm. Sensors (2022) 22(16):6095. 10.3390/s22166095

  • CrossRef
  • Google Scholar

• 24.

  ShaoJLathdavongLKluczynskiPLundqvistSAxnerO. Methodology for temperature measurements in water vapor using wavelength-modulation tunable diode laser absorption spectrometry in the telecom C-band. Appl Phys B (2009) 97(3):727–48. 10.1007/s00340-009-3721-7

  • CrossRef
  • Google Scholar

• 25.

  LiuCCaoZLiFLinYXuL. Flame monitoring of a model swirl injector using 1D tunable diode laser absorption spectroscopy tomography. Meas Sci Technol (2017) 28(5):054002. 10.1088/1361-6501/aa5aee

  • CrossRef
  • Google Scholar

• 26.

  LiFYuXGuHLiZZhaoYMaLet alSimultaneous measurements of multiple flow parameters for scramjet characterization using tunable diode-laser sensors. Appl Opt (2011) 50(36):6697. 10.1364/ao.50.006697

  • CrossRef
  • Google Scholar

• 27.

  ZhangBQXuZYLiuJGYaoLRuanJHuJYet alTemperature measurement method of high temperature and high pressure flow field based on wavelength modulation spectroscopy technology. Acta Phys Sin (2019) 68(23):233301. 10.7498/aps.68.20190515

  • CrossRef
  • Google Scholar

• 28.

  HuangAXuZYDengHYangWBQiXHLiJet alHigh‐pressure gas temperature sensing for exit plane of aero‐engine combustor using tunable diode laser absorption spectroscopy. Microw Opt Technol Lett (2023) 66(1). 10.1002/mop.33897

  • CrossRef
  • Google Scholar

• 29.

  BürkleSBiondoLDingCPHonzaREbertVBöhmBet alIn-Cylinder temperature measurements in a motored IC engine using TDLAS. Flow Turbul Combust (2018) 101(1):139–59. 10.1007/s10494-017-9886-y

  • CrossRef
  • Google Scholar

• 30.

  MaLNingHWuJRenW. In situ flame temperature measurements using a mid-infrared two-line H₂O laser-absorption thermometry. Combust Sci Technol (2017) 190(3):393–408. 10.1080/00102202.2017.1392515

  • CrossRef
  • Google Scholar

• 31.

  LindstromCDJacksonKRWilliamsSGivensRBaileyWFTamCJet alShock-train structure resolved with absorption spectroscopy Part I: system design and validation. AIAA J (2009) 47(10):2368–78. 10.2514/1.41074

  • CrossRef
  • Google Scholar

• 32.

  LindstromCDDavisDWilliamsSTamCJ. Shock-train structure resolved with absorption spectroscopy Part II: analysis and CFD comparison. AIAA J (2009) 47(10):2379–90. 10.2514/1.41077

  • CrossRef
  • Google Scholar

• 33.

  SappeyADMastersonPHowellJEstesMOwenbyDSutherlandL. Tomographic reconstruction of multipath tunable diode laser spectroscopy measurements in turbine engines. J Propuls Power (2014) 30(1):24–8. 10.2514/1.b34212

  • CrossRef
  • Google Scholar

• 34.

  D’SouzaEJ. Accelerated convergence of the error back-propagation training algorithm using univariate search[dissertation]. Philadelphia(PA: Drexel University (1991) 10.17918/00008716

  • CrossRef
  • Google Scholar

• 35.

  RhinehartRR. Engineering optimization: applications, methods, and analysis. New York: ASME Press (2018). p. 34. 10.1115/1.861opt

  • CrossRef
  • Google Scholar

• 36.

  AiSDengHHuangAXiaHHChenCGKanRFet alNemerical study on influencing factors of thermometry method based broadband absorption spectra. Acta Opt Sin (2022) 42(18):1830003. [in Chinese]. 10.3788/aos202242.1830003

  • CrossRef
  • Google Scholar