Open Access
Add to BibSonomy
Abstract
We developed a near-infrared (NIR) dual-channel oxygen-corrected laser heterodyne radiometer (LHR) in the ground-based solar occultation mode for measuring vertical profile of wind field in the troposphere and low stratosphere. Two distributed feedback (DFB) lasers centered at 1.27 µm and 1.603 µm were used as local oscillators (LO) to probe absorption of oxygen (O2) and carbon dioxide (CO2), respectively. High-resolution atmospheric O2 and CO2 transmission spectra were measured simultaneously. The atmospheric O2 transmission spectrum was used to correct the temperature and pressure profiles based on a constrained Nelder-Mead’s simplex method. Vertical profiles of atmospheric wind field with an accuracy of ∼5 m/s were retrieved based on the optimal estimation method (OEM). The results reveal that the dual-channel oxygen-corrected LHR has high development potential in portable and miniaturized wind field measurement.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The performance of global numerical weather prediction (NWP) models has been continuously improving over the last two decades. The NWP model essentially describes the rule of atmospheric motion, which is widely applied in short-term and medium-term weather forecast, environmental change, climate prediction and other fields, and can provide the basis for 7-day weather forecast. Atmospheric wind field is one of the most significant initial inputs for NWP models, and its accuracy has a significant impact on the NWP performance. The requirements of the global wind field observation requested by the World Meteorological Organization (WMO) are those the vertical resolution and the measurement accuracy should be 0.2-5 km and 1.5-5 m/s, respectively [1]. Additionally, the study of the atmospheric wind field can not only provide useful insights into the atmospheric dynamics processes, promote atmospheric space research, but also ensure the safety of space activities [2].
Optical techniques are the most common methods for measuring atmospheric wind field. Doppler laser radar is an active detection technology that measures atmospheric wind speed and atmospheric temperature through molecular scattering. In this technology, the effective detectable height is from the ground to 20 km with a vertical resolution of 1 km [3]. Fabry-Perot interferometer (FPI), Michelson interferometer and Doppler Asymmetric Spatial Heterodyne (DASH) are primary passive technologies for measuring the atmospheric wind field, they are deployed in ground-based or space-borne platforms. The FPI retrieves wind speed by accurately measuring the center and radius of interference fringes. Subsequently, miniaturized ground-based FPI was utilized in the USA and Japan for investigating wind and temperature in the thermosphere. Wang et al. reported a ground-based FPI using a band-pass filter behind the etalon and Galilean telescope system. The upper atmospheric wind field was retrieved based on the measurement data and an inversion algorithm [4–6]. Unlike the principle of FPI, the Michelson interferometer realizes the wind field detection by measuring the phase change in the interference fringes. The Wind Imaging Interferometer (WINDII) is the first space-borne instrument to use a Michelson interferometer for passive wind field detection, and it successfully measured atmospheric wind field in the altitude of 80-300 km [7]. DASH technology is developed based on spatial heterodyne spectroscopy, which is a new technology specifically designed for passive measurement of middle and upper atmospheric wind fields. In 2013, Solheim and Shepherd at York University developed a Stratospheric Wind Interferometer for Transport studies DASH (SWIFT-DASH) prototype, which was used for sensing stratospheric wind field and infrared ozone [8]. Nevertheless, disadvantages such as the complex optical structure and instrument size of high-resolution FPI and DASH limit their further application in complex geographic environments.
Laser heterodyne radiometer (LHR), which has the characteristics of high spectral resolution, can easily detect the slight Doppler shift of transmission spectrum caused by wind field. LHR is also lightweight, reliable, portable and low cost, which has received considerable attention in recent years [9–15]. LHR was first applied to wind field measurement in the 1970s. Absolute wind velocities in the thermosphere of Venus (100–120 km) were retrieved by the NASA team in 1991. They measured the CO2 Doppler shift in the Venus thermosphere using NASA/Goddard light Center infrared heterodyne spectrometer. In 2007, a team at the University of Cologne in Germany measured the Mars equatorial wind field by using a mid-infrared (MIR) tunable CO2 laser as local oscillator (LO). In 2020, Rodin’s team proposed a new remote sensing method for vertical wind profile measurement along the observation line of sight based on a high-resolution LHR in the solar occultation mode [16–18]. In the previous work, the vertical wind profiles were retrieved from the forward model and the measured transmission spectrum with Doppler shift. The data of the forward model includes atmospheric parameters and prior data. The error of atmospheric parameters reduces reliability of the retrieved wind profiles. Therefore, real-time atmospheric temperature and pressure profiles play an important role in building an accurate forward model and improving the reliability of retrieval. Oxygen (O2) concentration is stable throughout the troposphere and lower stratosphere and typically used to provide dry air correction and real-time determine temperature and pressure profiles [19,20].
In this work, we developed a high-resolution oxygen-corrected dual-channel LHR for stratospheric and tropospheric wind field detection. High-resolution CO2 transmission spectrum in the atmospheric column was obtained using the developed LHR with a balanced detector as a photomixer. O2 transmission spectrum was simultaneously obtained during the observation, which is used to real-time correct the atmospheric pressure and temperature profiles. The vertical profiles of wind field were finally retrieved from the CO2 transmission spectra using the optimal estimation method (OEM). In the subsequent sections, theoretical background, experimental setup, data processing, inversion methods and results will be presented and discussed.
2. Theoretical background
The principle of LHR has been described in the existing literature [21,22]. The fields of the sunlight ES and the LO ELO can be expressed as:
where ALO and AS are the amplitudes of the LO and the signal, respectively. ωS and ωLO are the corresponding angular frequencies, φ is the phase. The two superimposed fields are imaged onto a photodetector serving as a photomixer. The response current of the photodetector can be expressed as:The atmospheric transmission spectrum can be obtained by recording the IF signal. It is worth noting that the spectral line-shape of molecular absorption, determined by absorption center frequency, Doppler broadening and Lorentz broadening, and line intensity, would be affected by the presence of a wind field [23]. Doppler shift in the absorption center frequency related to wind speed can be described as:
where ν is the center frequency of the molecular absorption, νwin is the center frequency of the molecular absorption in the presence of wind, Vwin is the wind speed at different heights, and c is light velocity.The atmospheric CO2 absorption spectra at different altitudes in the presence of wind field are simulated, as shown in Fig. 1. The CO2 absorption spectrum is affected by wind speed and wind direction. The faster the wind speed is, the more obvious the Doppler shift of CO2 absorption spectrum is. And the Doppler shift direction of CO2 absorption spectrum is determined by the wind direction. The atmospheric transmission spectrum measured by the ground-based LHR is the convolution of absorption spectra at different altitudes. The relationship between the CO2 absorption at different altitudes and the transmission τ (ν, z) through the troposphere and low stratosphere can be expressed as follows [24,25]:
Fig. 1. CO2 absorption spectra at different altitudes without (black line) and with (red line) influence of the wind field. The arrow direction represents the direction of the wind field with arrow length representing the wind speed.
Therefore, the measured atmospheric transmission spectrum provides an unambiguous relationship between the shift from the line center and the altitude at which part of the line profile is formed. The spectral resolution of the LHR depends on the bandwidth of the RF filter in the system. Considering that the linewidth of the DFB laser is 2 MHz while the filter bandwidth is 10 MHz, the accuracy of IF signal analysis is enough to measure the Doppler shift of absorption spectrum in the atmosphere caused by wind speed on the line of sight greater than 3 m/s.
3. Experimental setup and data processing
The near-infrared (NIR) dual-channel LHR is schematically shown in Fig. 2. A homemade solar tracker with an accuracy of 7 arc seconds is used to track the Sun. The solar radiation absorbed by CO2 and O2 is coupled into a single-mode fiber via a collimator (Thorlabs, F810-APC, f = 37.13 mm). A fiber optical switch divides the solar radiation into two amplitude-modulated signals whose the modulation frequency is set to 125 Hz via the drive circuit of the fiber switch.
Fig. 2. Schematic of the NIR dual-channel LHR. FOS: fiber optical switch; FC: fiber coupler; FS: fiber beam splitter; PD: photodetector; BPF: band-pass filter, Amp: amplifier; SD: Schottky diode; LIA: lock-in amplifier; SC-Pro: Supercontinuum laser source; DAQ: data acquisition.
One amplitude-modulated solar beam from the fiber switch is separated by a 10:90 fiber splitter (FS1), where the 90% parts is coupled with a LO beam from a DFB laser centered at ∼1.27 µm (DL1, NEL, 2 MHz) through a fiber coupler (FC1), and then connected to a photodetector (PD1, Thorlabs, DET08CFC/M) for measuring O2 transmission spectrum, while the 10% part is connected to a photodetector (PD2, Thorlabs, PDA20CS2) for monitoring the solar power. The other amplitude-modulated solar beam is coupled with a LO beam from another DFB laser (DL2, NEL,2 MHz) centered at 1.603 µm through a 2 × 2 fiber coupler (FC2) and then connected to a balanced detector (Thorlabs, PDB410C) for measuring CO2 transmission spectrum. Angled physical contact (APC) interfaces are employed to reduce the reflection. The IF signals generated from PD1 and balanced detector are processed by RF processing modules (RM1, RM2), where RM1 consists of a Bias-T, a 290-400 MHz band-pass filter followed by three-stage low noise amplifiers (Mini-Circuits, ZX60-4016E-S+) with a gain of 21 dB each. After that, the amplified IF signal is fed to a square-law detector (Herotek, DHM020BB) for measurement of the IF signal power. RM2 consists of a 0.3-10 MHz band-pass filter and a square-law detector (Herotek, DHM020BB). Both output signals from the RM1 and RM2 are demodulated using two LIAs (Stanford Research Systems, SR830). Compared with the conventional photodetector applied as the photomixer in the O2 channel, the balanced detector used as the photomixer in CO2 channel can suppress the LO-induced noise. The bandwidth of filter defines the instrument line shape (ILS) of the LHR. As shown in Fig. 3, a 0.23-10 MHz band-pass filter is chosen, resulting in a 20 MHz (0.00067 cm-1) double-sideband spectral resolution of the CO2 channel [26]. The inset of Fig. 3 shows the used ILS for wind field retrieval. For the O2 channel, the bandwidth of the band-pass filter is 200 MHz.
Compared to the LO frequency, the Doppler shift caused by the wind field is very slight, therefore, frequency calibration is very important for analyzing the Doppler shift of atmospheric transmission spectrum. The frequency calibration module is shown in Fig. 2 (in red dotted box). Interference fringes from a fiber Mach-Zehnder interferometer with a free spectral range (FSR) of 0.0017 cm−1 is detected by the photodetector (PD3) and used for the relative frequency calibration. Due to the weak line intensity (1.73e-23cm-1/ (molec·cm-2)) of the CO2 at 6238.77 cm-1, a laboratory-made multi-pass cell is used to increase the optical path length to 7.5 m. The radiation from the supercontinuum laser source (Anyang laser, SC-Pro) passing through the multi-pass cell filled with CO2 is superimposed with the laser radiation from DL2. The combined two laser beams are fed into the photodetector (PD4, Thorlabs, DET08CFC/M) and then processed by RM3 to obtain the CO2 absorption spectrum. RM3 and RM1 have the same configuration except that the bandwidth of the band-pass filter is changed to 225-400 MHz. The absolute frequency is determined with the help of CO2 absorption frequency (at 6238.77 cm-1) provided by the HITRAN2016 database [27].
For instrumental control (solar tracker, SC-Pro and laser controllers) and data acquisition & processing, a personal computer equipped with a DAQ card (National Instruments, USB-6210) and a Python software are employed.
The solar occultation measurements were performed in Building 1 at the Anhui Institute of Optics and Mechanics (31.9°N, 117.16°E, and 40 m above sea level) on some sunny and cloudless days in December 2021. The observation details are listed in Table 1.
Table 1. Observation details (Observations of CO2 absorption line profile)
The CO2 atmospheric transmission spectra were obtained by tuning laser injection current in 0.2 mA increments across the absorption feature. LIA time constant was set to 1 s. The data processing method is shown in Fig. 4.
Fig. 4. Data processing flow chart: (a) raw data and baseline fit; (b) solar power; (c) CO2 transmission spectrum obtained by normalization.
During the wind field measurement, the interference caused by clouds reduces the signal-to-noise ratio (SNR), thereby adversely affecting the retrieval results. Therefore, the solar power is real-time monitored by the photodetector (PD2). As shown in Fig. 4(b), the variation of the solar power is less than 2%), therefore the recorded LHR signal is effective. The heterodyne signal (Fig. 4(a), red curve) is then subtracted from the corresponding background noise (Fig. 4(a), black curve), which is measured with the fiber optical switch being off. The final atmospheric transmission spectrum ((Fig. 4(c), black curve)) is obtained by normalizing the heterodyne signal to the baseline (Fig. 4(a), blue curve), where baseline is approximated by a third-order polynomial.
4. Inversion method and results
4.1 Forward model and inversion method
The flow chart of atmospheric wind field inversion based on O2 correction, which includes forward model and inversion algorithm, is shown in Fig. 5.
Based on Hitran2016 and Geisa databases and Py4cats (Python scripts for Computational Atmospheric Spectroscopy), we established a line-by-line atmospheric radiative transfer model [28]. Py4cats is a Python reimplementation of a general purpose atmospheric radiative transfer line-by-line infrared-microwave code (GARLIC).
The radiative transfer calculation is implemented in the following three steps: 1) Extracting the lines of relevant molecules in the scanning range of laser frequency in the experiment; 2) Calculating the line-by-line cross sections under given atmospheric wind speed, pressure, and temperature; 3) Combining the cross sections with absorption coefficient and optical depth, and integrating them along the line of sight. During the step-by-step calculation process, various parameters can be visualized through the Python extension package to obtain a clear understanding of the physical process of wind field affecting atmospheric transmission spectrum [29].
The spectral line-shape of atmospheric CO2 absorption is affected by atmospheric temperature and pressure, and precise temperature and pressure profiles are crucial for the establishment of the forward model. O2 is uniformly distributed in the atmosphere, so the O2 transmission spectrum can be used to correct atmospheric temperature and pressure profiles. As shown in Fig. 6, the prior profiles of temperature and pressure in Hefei, were obtained according to the latitude and longitude interpolation of the European Center for Medium-Range Weather Forecasts (ECWMF) and China Meteorological Data Service Center (CMCC).
According to the meteorological data of Hefei area in recent years, the uncertainty of prior temperature and pressure are determined. In order to retrieve atmospheric temperature and pressure profiles, the temperature and pressure profiles from the troposphere to the low stratosphere are fit as polynomial function of altitude:
where Z is the altitude, c is a constant. The pressure and temperature profiles from the troposphere to the low stratosphere are retrieved based on a constrained Nelder-Mead’s simplex method, where the uncertainties of temperature and pressure are set as the constrained intervals [20]. The Nelder-Mead simplex algorithm is a search algorithm for solving multi-parameter optimization problems. With the advantages of simple computation, fast convergence, and strong local search ability, the algorithm is widely used to solve multi-parameter curve fitting problems. By modifying the fitting coefficients a and b, the residual δ between the fitted and measured O2 transmission spectra is less than the default value k. The temperature and pressure profiles are retrieved, which are used as the atmospheric parameters in the forward model of the wind field retrieval.The prior profile of CO2 concentration is gained from the GOSAT data. For other major atmospheric species such as O3, H2O, CO, NH3, N2O, and CH4, there are no strong absorption in the target absorption detection region, which can be ignored when establishing the forward model. Note that atmosphere is divided into 16 layers from surface to 30 km with an altitude grid of 1, 2, and 5 km, separately. The relationship between pre-processed LHR data and the forward model is described as:
where ym is the measurement vector, xn is the state vector considered in the forward model, ε is the error vector, and m and n are the dimensions of the measurement vector and the state vector, respectively. The retrieval of the atmospheric vertical wind field is based on the optimal estimation method (OEM) [30]. The OEM-based data retrieval is an iterative process and uses Bayesian statistics with Gaussian probability density functions to minimize the cost function (χ2):Fig. 8. Retrieval results of O2, (a) pre-processed (black curve), and fitted (red curve) LHR transmission spectrum; (b) the residuals.
Since the wind field is different at each layer, the sensitivity of transmittance to the wind field is therefore different. In the inversion iteration process, the Jacobian matrix of the wind field should be calculated in each cycle. After i iterations, the stopping criterion for iteration is that χ2/m = ∼1. The retrieved wind profile is the state vector xi + 1, and the best fitted CO2 and O2 transmission spectra can be calculated by using the forward model with the retrieved wind profile.
4.2 Inversion results and analysis
A set of typical transmission spectra were analyzed to determine atmospheric temperature and pressure and retrieve atmospheric wind fields. The transmission spectra of O2 and CO2 were measured at 10:54 on 21 December 2021, with a solar zenith angle of 56. 63°.The pre-processed LHR data were obtained by convolution of the transmission spectrum with corresponding ILS. The retrieval results of O2 and CO2 are shown in Fig. 8 (a) and (b) and Fig. 9 (a) and (b), respectively, where the processed LHR data (black curve), the fitted spectra (red curve), and residuals (blue curve) are presented with an interval of 0.0001 cm−1. As expected, the fitted spectra are basically consistent with the LHR spectra and the residuals are randomly distributed, which indicates a well configured fit.
The prior wind field is imported in the inversion algorithm for iteration. The retrieved wind profiles on the line of sight are shown in Fig. 10. Left panels show the atmospheric CO2 transmission spectrum measured by LHR. Prior wind profiles (blue curve) and the retrieved wind profiles on the line of sight (red dashed) are displayed in right panels.
Fig. 9. Retrieval results of CO2, (a) pre-processed (black curve), and fitted (red curve) LHR transmission spectrum; (b) the residuals.
Fig. 10. The left panels show the measured atmospheric transmission spectra; the right panels show the prior vertical wind profiles (blue curve) and the retrieved wind profiles on the line of sight (red dashed).
The inversion error mainly includes smoothing error Ss and measurement error Sm. The measurement error Sm is caused by random noise during measurement. In our case, the smoothing error Ss is considered to determine whether the atmospheric altitude grid is reasonable. The smoothing error Ss, caused by the smoothed actual profile, can be expressed as:
As shown in Fig. 11, the smoothing error decreases with altitude below 3 km, reaches the maximum at 10 km, and tends to be gradual in the range of 15-30 km. This indicates that the altitude grid at altitude below 3 km or above 15 km is consistent with the theoretical height resolution, while at 3 km-15 km, the altitude grid is less than the theoretical height resolution, and the wind field profile is smoothed. Therefore, detailed wind field meteorological data will be further quoted to determine a reasonable altitude grid in order to reduce the smoothing error.
5. Conclusion
We presented a NIR dual channel oxygen-corrected LHR for the measurement of atmospheric vertical wind field in the troposphere and low stratosphere. A 0.3-10 MHz band-pass filter used in the LHR CO2 channel resulted in a spectral resolution of 0.00067 cm-1. The transmission spectra of O2 and CO2 in Hefei were obtained, and an SNR of 100 was achieved in a recording time of 12 min. The temperature and pressure profiles were corrected by O2 transmission spectrum using a constrained Nelder-Mead’s simplex method. The atmospheric wind field profiles on the line of sight were retrieved based on OEM with an accuracy of ∼5 m/s at Hefei. More detailed meteorological data and long-term observations can be applied to improve the accuracy of measurement and inversion result. In future work, we will focus on deploying LHR at different latitudinal and longitudinal sites to measure the wind field in the UV direction.
Funding
Key Programme (41730103); National Natural Science Foundation of China (42075128, U1909211); Natural Science Foundation of Anhui Province (2208085QF218).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. F. Smith, S. Havemann, A. Hoffmann, W. Bell, D. Weidmann, and S. Newman, “Evaluation of laser heterodyne radiometry for numerical weather prediction applications,” Q. J. Roy. Meteor. Soc. 144(715), 1831–1850 (2018). [CrossRef]
2. L. Zhang, C. Zhang, and X. Jian, “Passive detection of upper atmospheric wind field based on the Lorentzian line shape profile,” Acta. Phys. Sin. 59(2), 899–906 (2010). [CrossRef]
3. J. Fu, J. Li, and Q. Wu, “Application and prospect of Doppler lidar in the wind field observation,” Acta. Aerodynamica. Sinica. 39(4), 172–179 (2021).
4. J. G. Heinz, R. S. Wilbert, B. H. Paul, and A. G. David, “Atmospheric wind measurements with the high-resolution Doppler imager,” J. Spacecr. Rockets 32(1), 169–176 (1995). [CrossRef]
5. J. J. Makela, J. W. Meriwether, Y. Huang, and P. J. Sherwood, “Simulation and analysis of a multi-order imaging Fabry–Perot interferometer for the study of thermospheric winds and temperatures,” Appl. Opt. 50(22), 4403–4416 (2011). [CrossRef]
6. H. Wang, Y. Wang, J. Fu, and Z. Zhang, “A New Ground-based Fabry-Perot Interferometer for Measurement of the Thermospheric Wind,” Chinese Journal of Space Science 36(3), 352–357 (2016).
7. G. G. Shepherd, G. Thuillier, Y. M. Cho, M. L. Duboin, W. F. J. Evans, W. A. Gault, C. Hersom, D. J. W. Kendall, C. Lathuillère, R. P. Lowe, I. C. McDade, Y. J. Rochon, M. G. Shepherd, B. H. Solheim, D. Y. Wang, and W. E. War, “The Wind Imaging Interferometer (WINDII) on the Upper Atmosphere Research Satellite: A 20 Year Perspective,” Rev. Geophys 50, RG2007 (2012). [CrossRef]
8. B. Solheim, S. Brown, C. Sioris, and G. G. Shepherd, “SWIFT-DASH: Spatial Heterodyne Spectroscopy Approach to Stratospheric Wind and Ozone Measurement,” Atmos.-Ocean 53(1), 50–57 (2015). [CrossRef]
9. D. Weidmann and G. Wysocki, “High-resolution broadband (>100 cm-1) infrared heterodyne spectro-radiometry using an external cavity quantum cascade laser,” Opt. Express 17(1), 248–259 (2009). [CrossRef]
10. D. Weidmann, B. J. Perrett, N. A. Macleod, and R. M. Jenkins, “Hollow waveguide photomixing for quantum cascade laser heterodyne spectro-radiometry,” Opt. Express 19(10), 9074–9085 (2011). [CrossRef]
11. D. Weidmann, T. Tsai, N. A. Macleod, and G. Wysocki, “Atmospheric observations of multiple molecular species using ultra-high-resolution external cavity quantum cascade laser heterodyne radiometry,” Opt. Lett. 36(11), 1951–1953 (2011). [CrossRef]
12. G. B. Clarke, E. L. Wilson, J. H. Miller, and H. R. Melroy, “Uncertainty analysis for the miniaturized laser heterodyne radiometer (mini-LHR) for the measurement of carbon dioxide in the atmospheric column,” Meas. Sci. Technol. 25(5), 055204 (2014). [CrossRef]
13. D. Weidmann, A. Hoffmann, N. Macleod, K. Middleton, J. Kurtz, S. Barraclough, and D. Griffin, “The methane isotopologues by solar occultation (miso) nanosatellite mission: spectral channel optimization and early performance analysis,” Remote Sens. 9(10), 1073 (2017). [CrossRef]
14. E. L. Wilson, A. J. DiGregorio, V. J. Riot, M. S. Ammons, W. W. Bruner, D. Carter, J. P. Mao, S. E. Ramanathan, L. D. Strahan, C. Oman, R. M. Hoffman, and Garner, “A 4U laser heterodyne radiometer for methane (CH4) and carbon dioxide (CO2) measurements from an occultation-viewing CubeSat,” Meas. Sci. Technol. 28(3), 035902 (2017). [CrossRef]
15. J. Wang, G. Wang, T. Tan, G. Zhu, C. Sun, Z. Cao, W. Chen, and X. Gao, “Mid-infrared laser heterodyne radiometer (LHR) based on a 3.53 µm room-temperature interband cascade laser,” Opt. Express 27(7), 9610–9619 (2019). [CrossRef]
16. J. J. Goldstein, M. J. Mumma, T. Kostiuk, D. Deming, F. Espenak, and D. Zipoy, “Absolute wind velocities in the lower thermosphere of Venus using infrared heterodyne spectroscopy,” Icarus 94(1), 45–63 (1991). [CrossRef]
17. M. Sorniga, T. Livengood, G. Sonnabend, P. Kroetz, D. Stupar, T. Kostiuk, and R. Schieder, “Venus upper atmosphere winds from ground-based heterodyne spectroscopy of CO2 at 10µm wavelength,” Planet. Space Sci. 56(10), 1399–1406 (2008). [CrossRef]
18. A. V. Rodin, D. V. Churbanov, S. G. Zenevich, A. Y. Klimchuk, V. M. Semenov, M. V. Spiridonov, and I. S. Gazizov, “Vertical wind profiling from the troposphere to the lower mesosphere based on high-resolution heterodyne near-infrared spectroradiometry,” Meas. Sci. Technol. 13(5), 2299–2308 (2020). [CrossRef]
19. H. Deng, C. Yang, Z. Xu, M. Li, A. Huang, L. Yao, M. Hu, B. Chen, Y. He, R. Kan, and J. Liu, “Development of a laser heterodyne spectroradiometer for high-resolution measurements of CO2, CH4, H2O and O2 in the atmospheric column,” Opt. Express 29(2), 2003–2013 (2021). [CrossRef]
20. S. B. David, E. T. Jared, and M. F. J Monica, “Precision heterodyne oxygen-corrected spectrometry: vertical profiling of water and carbon dioxide in the troposphere and lower stratosphere,” Appl. Opt. 59(7), B10–B17 (2020). [CrossRef]
21. F. Shen, G. Wang, Z. Xue, T. Tan, Z. Cao, X. Gao, and W. Chen, “Impact of Lock-In Time Constant on Remote Monitoring of Trace Gas in the Atmospheric Column Using Laser Heterodyne Radiometer (LHR),” Remote Sens-Basel 14(12), 2923 (2022). [CrossRef]
22. E. L. Wilson, M. L. McLinden, J. H. Miller, G. R. Allan, L. E. Ott, H. R. Melroy, and G. B. Clarke, “Miniaturized laser heterodyne radiometer for measurements of CO2 in the atmospheric column,” Appl. Phys. B 114(3), 385–393 (2014). [CrossRef]
23. Z. Yin, C. Wu, W. Gong, Z. Gong, and Y. Wang, “Voigt profile function and its maximum,” Acta. Phys. Sin. 62(12), 123301 (2013). [CrossRef]
24. W. Xu and Z. Fang, “The Application of Doppler Broadening and Doppler Shift to Spectral Analysis,” Spectrosc. Spect. Anal. 4, 667–669 (2002).
25. M. Premuda, E. Palazzi, F. Ravegnani, D. Bortoli, S. Masieri, and G. Giovanelli, “MOCRA: a Monte Carlo code for the simulation of radiative transfer in the atmosphere,” Opt. Express 20(7), 7973–7993 (2012). [CrossRef]
26. J. Wang, C. Sun, G. Wang, M. Zou, T. Tan, K. Liu, W. Chen, and X. Gao, “A fibered near-infrared laser heterodyne radiometer for simultaneous remote sensing of atmospheric CO2 and CH4,” Opt. Laser. Eng. 129, 106083 (2020). [CrossRef]
27. I. E. Gordon, L. S. Rothman, C. Hill, et al., “The HITRAN2016 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 203, 3–69 (2017). [CrossRef]
28. R. V. Kochanov, I. E. Gordon, L. S. Rothman, P. Wcisło, C. Hill, and J. S. Wilzewski, “HITRAN Application Programming Interface (HAPI): A comprehensive approach to working with spectroscopic data,” J. Quant. Spectrosc. Radiat. Transfer 177, 15–30 (2016). [CrossRef]
29. A. Dudhia, “The Reference Forward Model (RFM),” J. Quant. Spectrosc. Radiat. Transfer 186, 243–253 (2017). [CrossRef]
30. C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, (World Scientific, 2000).
