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Abstract
The performance of a micro-electro-mechanical system (MEMS) modulator-based dual-channel mid-infrared laser heterodyne radiometer (MIR-LHR) was demonstrated in ground-based solar occultation mode for the first time. A MEMS mirror was employed as an alternative modulator to the traditional mechanical chopper, which makes the system more stable and compact. Two inter-band cascade lasers (ICL) centered at 3.53 µm and 3.93 µm, were employed as local oscillators (LO) to probe absorption lines of methane (CH4), water vapor (H2O) and nitrous oxide (N2O). The system stability greater than 1000 s was evaluated by Allan variance. The experimental MIR-LHR spectra (acquired at Hefei, China, on February 24th 2022) of two channels were compared and were in good agreement with simulation spectra from atmospheric transmission modeling. The mixing ratio of CH4, H2O and N2O were determined to be ∼1.906 ppm, 3069 ppm and ∼338 ppb, respectively. The reported MEMS modulator-based dual-channel MIR-LHR in this manuscript has great potential to be a portable and high spectral resolution instrument for remote sensing of multi-component gases in the atmospheric column.
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1. Introduction
The measurement of vertical concentration profiles of atmospheric trace gases provides a better insight into air pollution, ozone destruction and climate change as well as a method to validate chemical models and satellite observations [1,2]. Global measurements performed from satellite platforms and localized measurements from balloon/aircraft and ground-based platforms can be used for passive remote sensing of vertical concentration profiles of atmospheric trace gases [3]. Compared with the satellite and balloon/aircraft measurements, the ground-based measurements infer the vertical column density of atmospheric trace gas by measuring the amount of sunlight reaching the Earth’s surface, and offer accurate and continuous measurements which can also be used for validation of satellite and balloon/aircraft observations [4]. Meanwhile ground-based observations (such as TCCON, Total Carbon Column Observing Network), usually equipped with a Fourier transform spectrometer (FTS, Bruker, IFS125HR) with a spectral resolution of ∼0.01 cm−1, can provide column-averaged abundances with high precision and accuracy, however the shortfalls (such as large dimensions and high cost of maintenance) limit further expansion of the observing network. A portable Fourier transform infrared (FTIR) spectrometer (Bruker, EM27/SUN) with 0.5/0.2 cm−1 spectral resolution has proven to be a promising complement to the ground-based observations over the last decade, although it sacrifices the spectral resolution for portability [5]. With the objective to develop portable instruments maintained with high spectral resolution (< 0.01 cm−1), ground-based laser heterodyne radiometers (LHR) are widely used for atmospheric remote sensing.
LHR, which extracts absorption information from a broadband light source (such as the Sun) by beating it with a narrow-band local oscillator (LO) on a high speed detector used as a photomixer, has been widely applied for remote sensing of the earth atmosphere and astronomy since the 1970s [6]. Weidmann et al. and Shen et al. established mid-infrared (MIR) LHR systems to measure a variety of GHGs, such as CH4, CO2, H2O, O3 and N2O in the atmospheric column [7,8]. Wilson et al. and Wang et al. developed all-fiber coupled near-infrared (NIR) LHRs for the measurements of CH4 and CO2 in the atmospheric column [9–11]. Robinson et al. demonstrated a hollow waveguide-based miniaturized quantum cascade laser heterodyne spectro-radiometer, and provided an efficient way for the miniaturization of the MIR-LHR [12]. Since the first demonstration in LHR [10], interband cascade lasers (ICL), lasing in continuous wave mode at room temperature at the spectral region between 3 and 6 µm, open a new spectral window for mid-infrared sensing. ICLs offered more reliable alternatives to traditional LOs in the MIR region with the merits of room temperature operation, wide spectral tuning range, compactness, and robustness. In general, the sunlight modulation in a LHR is performed to improve the measurement sensitivity. In the NIR, owing to the progress in the telecommunications industry, a fiber optical switch was usually implemented to modulate the sunlight which made the LHR more compact and robust [13]. In the MIR, limited by the lack of matured fiber optical components or optical waveguides, a traditional mechanical chopper was usually used to realize the sunlight modulation. Recently, a MEMS mirror was employed as an alternative to the mechanical chopper in the earlier work of our own research on the MIR LHR [14].
In the present work, a MEMS modulator-based dual-channel MIR-LHR was developed. Two inter-band cascade lasers (ICL) centered at 3.53 µm and 3.93 µm, are employed as LOs to probe absorption lines of methane (CH4), water vapor (H2O) and nitrous oxide (N2O), respectively. The mixing ratio of CH4, H2O and N2O were obtained by the inversion calculation. The experimental details, instrument performance, data processing, as well as analysis results and validation through comparison with atmospheric transmission modeling will be presented and discussed.
2. Experimental details
The dual-channel MIR-LHR system is schematically shown in Fig. 1. Sunlight containing atmospheric absorption information is captured with a home-made high-precision solar tracker. The solar motion is tracked by photoelectric tracking and proportion-integral-derivative (PID) control with an accuracy of 7 arc seconds. A MEMS mirror (S12237-03P, Hamamatsu, 2.6 mm in diameter) is used to replace the conventional mechanical chopper to modulate the sunlight, and its modulation frequency is determined by the control circuit. One modulated beam from the MEMS mirror module is coupled with a LO beam from an ICL1 centered at ∼3.93 µm (Nanoplus) on a beam splitter (BS1). The mixed beams pass through the filter (OF1) and are focused onto a high speed photo-detector with a bandwidth of 100 MHz (Detector 1, PV-2TE-4, VIGO System S.A.) for N2O detection. The other modulated beam from the MEMS mirror module is coupled with a LO beam from another ICL2 centered at ∼3.53 µm (Nanoplus) on a beam splitter (BS2), and the mixed beams pass through the filter (OF2), then are focused onto another high speed photo-detector (Detector 2) for CH4 and H2O detection. Subsequently, the beat signals generated from Detector 1 and Detector 2 are processed by two radio frequency (RF) processing modules. In the RF processing modules, the RF signal is first filtered by a band-pass filter, then converted to a DC signal by a Schottky diode (HEROTEK, DHM020BB), and finally amplified by a low-noise preamplifier (SR560, Stanford Research Systems). The processed signals from the RF modules are demodulated using two lock-in amplifiers (LIA) (SR850, Stanford Research Systems) at the first harmonic with the modulation frequency of the MEMS mirror module as a reference. The DC outputs of Detector 1 and Detector 2 are used to monitor the LO powers, respectively. A personal computer (PC) equipped with a DAQ card (USB-6210, National Instruments) and a LabVIEW software was employed for data acquisition & processing and instrumental control (solar tracker, MEMS mirror, wavelength meter and laser controllers). According to the divergence angle of the sunlight (∼9.2 mrad), three OAPMs are used to focus and collimate the sunlight to ensure sufficient signal power for the MIR-LHR, and the MEMS mirror is placed at the focal point of OAPMs. The solar power injected into the LHR system was increased by a factor of ∼2.5 via the collimation and focus of the OAPMs [14]. The dual-channel MIR-LHR receiver size is 60 × 30 × 20 cm3.
Fig. 1. Schematic diagram of the experimental setup, OAPM: off-axis parabolic mirror; BS 1,2: beam splitter; OF 1,2: Optical filter; FL 1,2: Focus lens; DAQ: data acquisition card; LIA: lock-in amplifier; PC: personal computer.
3. Instrument performance and data processing
To obtain the higher signal-to-noise ratio (SNR), modulating frequency of the MEMS mirror was investigated. Broadband radiation from a solar tracker or blackbody was focused on the MEMS mirror and modulated into two square wave signals with mutually exclusive phases in two detection channels (3.53 µm and 3.93 µm channel), as shown in Fig. 2. The frequency and duty cycle of the modulation signal can be adjusted by the driver circuit of the MEMS mirror. According to the operating principle of the MEMS mirror, lower modulation frequency should be used to obtain a better modulated signal. Since resonance occurs when the mirror exhibits square wave motion, it is important to set the period of the square wave as close as possible to the integer multiple of the resonant frequency's reciprocal [15,16]. The characteristic resonant frequency of the used MEMS mirror is approximately 530 Hz. Therefore, the modulation frequency used in the MIR-LHR is 5.3 Hz (the corresponding period ∼0.188679 s), and the duty cycle is nearly 50%.
The instrument line-shape (ILS) is a highly important instrumental parameter of LHR [17]. The ILS is a key integral part of the forward model, and as such one must ensure that it is as representative as possible of the real spectrometer to avoid additional measurement biases [18,19]. In the LO tuning mode, the ILS is primarily defined by the pass-band filter used to select the part of the intermediate frequency (IF) spectral power to contribute to the signal. The schematic in Fig. 3 shows the RF signal processing in the MIR-LHR. The LO field and the amplitude modulated (at the frequency fmod) source field are imaged onto the photomixer. The DC component is rejected to let only the heterodyne IF signal through amplification. A band-pass filter determines the instrument spectral resolution and the transmitted IF power is measured by a square law detector. The total IF power is measured using a phase-sensitive detector (PSD), in which fmod is used as the reference. The heterodyne voltage signal Vhet at the output of the PSD can be expressed by Eq. (1), where ksdrepresents the responsivity of the square law detector, η is the quantum efficiency of the detector, e is the elementary electric charge, h is the Planck constant, v is the photon frequency, G is the gain of the amplifier and Z is the input impedance. PS and PLO are the source power and the LO power [20].
The ILS is given by the response of the IF filter and embedded into the expression of PS (Eq.2) when the LO frequency sweep is slow enough compared to rate of change induced by the spectral features, where L(σ) is the spectral radiance, $\kappa$ accounts for the optical transmission losses down to the detector chip, and ${\lambda ^2}$ represents the single spatial mode throughput the LHR is sensitive to.
In order to choose an appropriate pass-band filter, frequency spectrum analysis of the heterodyne signals was performed to separate the MIR-LHR signal from unwanted noises using a RF signal analyzer (N9000A, Agilent Technologies). For the purpose of the compromise between SNR and spectral resolution, band-pass filters with 10-70 MHz and 45-81 MHz were chosen for 3.53 µm and 3.93 µm channels, respectively, which resulted in ∼140 MHz (0.0047 cm−1) and ∼162 MHz (0.0054 cm−1) double-sideband spectral resolution. The measured ILSs for the two channels in the MIR-LHR are shown in Fig. 4 (a) and (b), where the blue curves are the heterodyne signals and the red curves are the band-pass signals.
Fig. 4. Spectral analysis of heterodyne signal (blue curve); band-pass signal (red curve), (a) 3.53 µm detection channel (b) 3.93 µm detection channel.
The other aspect to investigate before deployment is instrument stability. To that end, the concept of Allan variance is used [21,22]. In the laboratory setting, a blackbody radiation (T = 1323K) is used as the source radiation and spectra are acquired with a 300 ms lock-in time constant per point. Sequential acquisitions are done for a total measurement time of ∼25 min. From the experimental data, the Allan variance maps of the dual-channel MIR-LHR are calculated and shown in Fig. 5. The heterodyne voltage signals Vhet at the in-phase output of the LIA were measured and the recorded raw data of the two detection channels are plotted in the upper panels. In a log-log plot, the Allan variance decreases linearly with the time constant. The lower panel shows the Allan variance as a function of the measurement time, and the theoretically expected behavior of the system mainly comes from white noise when the time constant is short. The Allan variance indicates that the system is truly white noise limited between 100 and 200 s. After 200s, the rollover point where drifts dominate the noise statistics are not yet reached. That indicates that an instrument stable over more than 1000 s at least.
Fig. 5. Raw measurement results of 3.53 µm and 3.93 µm detection channels (upper panels); Allan variance curves as a function of the LIA time constant (lower panel).
4. Results analysis and validation
The experimental results, measured in our institute (Hefei, China, 31.9°N/117.166°E, 40 m above sea level) on February 24th 2022 (a sunny and cloudless day), are shown in Fig. 6. In one LO frequency scan, the temperatures of the two LOs were first set at 10 °C and 14.5 °C, respectively. Then the current was tuned in a point-by-point mode (34-44 mA, 0.1 mA interval) to probe the target absorption features around 2831.92 cm−1 and 2538.34 cm−1 via laser controllers (LDC-3724, ILX Lightwave). As shown in the Allan variance (Fig. 5), at the same time constant, the deviation of 3.93 µm channel is lower than that of 3.53 µm channel. It can be concluded that the SNR of the LHR spectrum should be well matched to the selection of the time constant as well as the scanning time (depends on the time constant, acquisition time and acquisition intervals). When the time constant is small, the noise could not be efficiently removed. While a longer time constant (than the optimal one) would result in longer scanning time and thus change the absorption path, and the inversion results would be affected [23]. It should be noted that, when tuning the laser working currents, an acquisition time interval (∼3 times of the lock-in time constant) was set to avoid distortion of the MIR-LHR spectral line-shape. To compromise between the SNR and the scanning time, the time constant of the system was set to 1s and one typical scanning time is about 300 s. The MIR-LHR signals of 3.53 µm and 3.93 µm detection channels are shown in Fig. 6 (a, red curve) and (b, blue curve). The black curves in Fig. 6 (a) and (b) are the DC signals of detector 1 and detector 2 to normalize the power variations caused by the LOs. Figure 6 (c) shows the laser calibration curves of the laser wavenumber as a function of the laser injection current via a wavemeter (621B-XIR, Birstol). In the ground-based solar occultation mode, the SNRs of 3.53 µm and 3.93 µm detection channels are 67 and 89, respectively, which exactly agree with the Allan variance analysis of the blackbody simulation experiment.
Fig. 6. Raw signals acquired in one scan, (a) 3.53 µm LHR signal (red curve) and DC output of detector 1 (black curve); (b) 3.93 µm LHR signal (blue curve) and DC output of detector 2 (black curve); (c) 3.53 µm (red curve) and 3.93 µm (blue curve) laser wavelength calibration.
After intensity normalization and wavenumber calibration, the atmospheric transmission spectrum of the solar radiance can be obtained from the developed system. The retrieval results of CH4, H2O and N2O are shown in Fig. 7 (a) and (b) and Fig. 8 (a) and (b), respectively, where the processed LHR data (blue curve), the fitted spectra (red curve), and residuals (black curve) are presented with an interval of 0.001 cm−1. As expected, the LHR spectra of the two detection channels based on the MEMS mirror modulator are basically consistent with the fitted spectra. Since the laboratory is located in the middle of the round island, affected by the interference of geographical position, water vapor absorption and absorption path (solar zenith angle), the line-shape and absorption depth of 3.53 µm HDO absorption spectrum (Fig. 7, blue curve) are slightly different from those of the fitted spectrum (Fig. 7, red curve) [24].
Fig. 7. Retrieval results of CH4 and HDO, (a) processed (blue curve), and fitted (red curve) 3.53 µm LHR transmittance spectra; (b) the residuals.
Fig. 8. Retrieval results of N2O, (a) processed (blue curve), and fitted (red curve) 3.93 µm LHR transmittance spectra; (b) the residuals.
Data retrievals were performed using the optimal estimation method (OEM), described by Rodgers [25] and it was applied to the LHR data retrievals by Weidmann for the first time [26]. A brief recall is presented here. The atmospheric transmission spectrum of the solar radiance can be calculated by calling a radiative transfer forward model (F), where F is built based on the reference forward model (RFM, version 4.34), which is a fast line-by-line radiative transfer model [18]. The relationship between processed LHR data and the atmospheric state vectors is described as the following:
where y is the measurement vector, x is the state vector considered in the forward calculation, and ɛ is the error vector. The OEM-based data retrieval is a Levenberg–Marquardt (LM) iterative process, using Bayesian statistics with Gaussian probability density functions, to minimize the cost function (χ2):The pressure and temperature profiles used for the data retrieval are shown in Fig. 10, which were obtained from the China Meteorological Data Service Center (CMCC) and the Europe Center for Medium-Range Weather Forecast (ECMWF). For the methane and water vapor profiles, the data were interpolated from the typical mid-latitude daytime profiles. And a priori profile of nitrous oxide was obtained from the Earth Observing System (EOS). Note that the atmosphere is separated into 45 layers from the surface to 70 km. The HDO/H2O ratio of Vienna Standard Mean Ocean Water (VSMOW) was used to obtain the water vapor profile. Figure 11 shows the retrieved vertical concentration profiles of (a) CH4, (b) water vapor and (c) N2O, respectively. Based on the retrieved CH4, water vapor and N2O profiles, the mixing ratio of CH4 is found to be ∼1.906 ppm (or ∼3.862E+20 molecules/cm2), the mixing ratio of H2O is calculated to be ∼3069 ppm (or ∼6.206E+23 molecules/cm2), and the mixing ratio of N2O was found to be ∼338 ppb (or ∼6.834E+19 molecules/cm2), respectively. The smoothing error matrix and the measurement error matrix are considered to perform an error analysis. And the total retrieval errors were calculated to be ∼1% (CH4), 7% (H2O) and ∼0.8% (N2O), respectively.
5. Conclusion
In the study, a MEMS modulator-based dual-channel MIR-LHR was developed for simultaneous remote sensing of atmospheric CH4, H2O and N2O. Two ICLs centered at 3.53 µm and 3.93 µm, were employed as LOs to probe absorption lines of CH4, H2O and N2O, respectively. The developed system shows good performance in terms of its high spectral resolution for the two detection channels. The stability of the system was evaluated by the Allan variance. The measured LHR spectra were consistent with simulation spectra from atmospheric transmission modeling and the mixing ratio of CH4, H2O and N2O were determined to be ∼1.906 ppm, 3069 ppm and ∼338 ppb, respectively. The MIR-LHR demonstrated in this manuscript has great potential to be a portable and high spectral resolution instrument for atmospheric multi-component gases. In the future, long-term simultaneous detection and source-receptor analysis will be carried out for the study of atmospheric trace gases and isotopes in the MIR. Additionally, a FPGA-based integrated circuits will be employed to replace the laser controllers and RF signal processing circuit in the LHR system.
Funding
Key Project of the National Natural Science Foundation of China (41730103); National Natural Science Foundation of China (42075128); Natural Science Foundation of Anhui Province (2208085QF218); Talent fund of Hefei University under Grant (20RC02).
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.
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