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Abstract
Tunable diode laser absorption spectroscopy has been widely employed for gas sensing, where the gas concentration is often obtained from the absorption signal with a known or a fixed absorption path length. Nevertheless, there are also numerous applications in which the absorption path length is very challenging to retrieve, e.g., open path remote sensing and gas absorption in scattering media. In this work, a new approach, based on the wavelength modulation spectroscopy (WMS), has been developed to measure the gas absorption signal and the corresponding absorption path length simultaneously. The phase angle of the first harmonic signal (1f phase angle) in the WMS technique is utilized for retrieving the absorption path length as well as the gas absorption signal. This approach has been experimentally validated by measuring carbon dioxide (CO2) concentration in open path environment. The CO2 concentration is evaluated by measuring the reflectance signal from a distant object with hundreds of meters away from the system. The measurement accuracy of the absorption path length, evaluated from a 7-day continuous measurement, can reach up to 1%. The promising result has shown a great potential of utilizing the 1f phase angle for gas concentration measurements, e.g., open path remote sensing applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As the rapid development of infrared diode laser technologies, tunable diode laser absorption spectroscopy (TDLAS) has been widely applied in greenhouse gas and air pollution monitoring, combustion diagnostics, industrial processes control, etc. [1–6]. In laser absorption spectroscopy, the absorbance is proportional to the product of the gas concentration and the absorption path length. In other words, the uncertainty of the absorption path length significantly influences the retrieval accuracy of the gas concentration. In a single-pass or multi-pass cell based measurement configuration, the absorption path length is well defined or can be calibrated by e.g., reference measurements with known gas concentrations. Nevertheless, the absorption path length in sophisticated multi-pass gas cells could also vary due to e.g., mechanical instabilities, leading to increased uncertainties of gas concentration for long-term measurements [7]. Moreover, the absorption path length may be unknown or very difficult to retrieve in many applications, e.g., gas in scattering media absorption spectroscopy (GASMAS) [8], open path remote sensing of gas concentration [9,10], etc. Thus, it has been of great interest to measure the absorption path length while measuring gas absorption signals in order to retrieve the gas concentration precisely.
Gianfrani et al. measured the absorption path length of multi-pass cell by a Michelson interferometer with high precision and accuracy [11]. Du et al. utilized the optical frequency domain reflectometer (OFDR) to measure the absorption path length of a multi-pass cell [12]. Recently, Lou et al. demonstrated an approach for simultaneous measurement of the gas absorption spectrum and the absorption path length by employing the optical frequency-modulated continuous-wave (FMCW) interferometry in a multi-pass cell [13]. Although a high precision can be achieved, the measurement range is limited by the linewidth of the diode laser, e.g., tens of meters for a typical linewidth of about 10 MHz. In GASMAS techniques, the laser beam has been significantly scattered in the porous scattering media, leading to an unknown absorption path length. Mei et al. measured the gas absorption and the path length in scattering media with the frequency domain photon migration (FDPM) technique and the FMCW technique [14–16], which requires additional optoelectronics for performing path length measurements. In open path remote sensing applications, the absorption path length is generally measured by separate GPS or range-finder modules [17,18], which is impractical for remote measurements with undefined open paths. Although the differential absorption lidar technique can measure range-resolved absorption signals, expensive high-energy, narrow-band tunable laser source has to be employed, which is rather complicated and requires intensive maintenance [9,10].
In this paper, we have developed a new approach, which is based on the first harmonic phase angle (1f-PA) of the wavelength modulation spectroscopy (WMS) [19], to measure the gas absorption and the path length simultaneously in open path remote sensing applications. The absorption path length was obtained from the non-absorption region of the 1f-PA signal, while the differential of the 1f-PA signal was utilized for the calibration-free retrieval of gas concentration. The method has been theoretically investigated and then validated by measuring carbon dioxide (CO2) concentration in open path environment. The measurement accuracy of the path length has also been evaluated thoroughly.
2. Methods
In WMS technique, the laser wavelength is simultaneously modulated by a linearly scanning signal and a high frequency sinusoidal wave (typically in the kilohertz range). Because of the nonlinear characteristic of the gas absorption cross section, harmonics of the absorption signal are generated as the wavelength-modulated laser beam is absorbed by the target gas. By employing digital or analogue lock-in techniques, high harmonics of the absorption signal can be picked up with the 1/f noise greatly suppressed. Meanwhile, the optical wavelength modulation is often accompanied by a modulation of the laser intensity for laser diodes. In general, the laser intensity-modulation signal can be written in Fourier series
The transmitted laser beam is absorbed by the target gas and then detected by a photodetector. The received absorption signal is demodulated with an in-phase reference signal and an out-of-phase reference signal. The first or second harmonic absorption signal can then be obtained through the Fourier analysis. According to [20], the first harmonic signal vector $\overrightarrow {{R_{1f}}}$can be expressed as the sum of three vectors
In previous work, the absorption signal is directly obtained from the 1f-PA signal, which, however, suffers from the non-absorption baseline. In fact, since ${\tau _I}$ can be considered as a constant in Eq. (6), the differential of the 1f-PA can be expressed as
3. Experiments and results
3.1 Experimental setup
The proposed approach for simultaneous measurement of gas absorption and path length was validated by measuring CO2 concentration in open path environment. The experimental setup is shown in Fig. 1. A tunable diode laser (NEL NLK1L5EAAA) was employed to probe the absorption of CO2 at 6358.64 cm−1 (1572.66 nm). A 100 Hz, 1.16 Vpp (peak-to-peak voltage) triangular-wave scanning signal and a 50 kHz, 400 mV sine-wave modulation signal, generated by the multifunction data acquisition card (DAQ, NI, USB-6363) with 2MS/s sample rate, were sent to the laser controller (SRS, LDC502) to drive the diode laser. The laser beam was divided by a fiber splitter into two parts, i.e., the measurement beam and the reference beam. The measurement beam was transmitted by the collimator to the reflective sheet (3M diamond-grade prismatic reflective sheeting 3910), which was made from plastic with triangular pyramid array structure. The reflective beam was collected by a commercial telescope (Meade LX90) and then detected by a photodiode (PD1, GAP 1000). As shown in Fig. 1(b), two reflective sheets were mounted at different distances. The distances between the receiving telescope and the two reflective sheets, which were measured by a commercial laser range finder, were 350 ± 2 m and 76 ± 0.2 m, respectively. The detected signal is acquired by the same DAQ card with 2MS/s sampling rate. The reference signal was addressed to a homemade quartz etalon, with a free spectral range of 0.0173 cm−1. The interference signal detected by the other photodiode (PD2, Thorlabs, PDA 10DT-EC) was acquired by an oscilloscope with 100 MS/s sampling rate to measure the frequency modulation response. The digital demodulation process was accomplished by employing the Fast Fourier Transform, which is described in [20].
Fig. 1. (a) Diagram of the experiment setup for carbon dioxide measurement in open path environment; (b) Photograph of the experimental field; (c) Map of the experimental field. DFB-distributed feedback diode laser, AO-Analog Output, AI-Analog Input, PD-photo diode, PC-Personal Computer.
3.2 Absorption path length measurement based on the 1f-PA
Calibration measurements have been carried to retrieve the phase or time delay due to the system response (i.e., ${\theta _{1f - \textrm{zero}}}$) by directly measuring the intensity of the laser beam with PD1, without transmitting the laser beam into atmosphere. Under this circumstance, the absorption path length as well as the CO2 absorption signal is negligible, which can be considered as a zero absorption path-length (zero-path) measurement. The open-path measurements were carried out by pointing the laser beam to the reflective sheet at site NO.2 (or NO.1). The detected signals of the zero-path measurement and the open-path measurement, as well as the corresponding 1f-PA signals are shown in Fig. 2. The difference between the open-path 1f-PA (${\theta _{1f - \textrm{open}}}$) and the zero-path 1f-PA (${\theta _{1f - \textrm{zero}}}$) shown in Fig. 2(b), i.e., $\theta _{1f - \textrm{open}}^\ast $ has relatively flat baseline. The mean value of its non-absorption region, outlined by a rectangle in Fig. 2(b), equals to -0.73 rad. The corresponding absorption path length was evaluated according to Eq. (9), i.e., 699.3 m.
Fig. 2. (a) The original open-path and zero-path signals; (b) the open-path 1f-PA (${\theta _{1f - \textrm{open}}}$), zero-path 1f-PA (${\theta _{1f - \textrm{zero}}}$), and the difference between them ($\theta _{1f - \textrm{open}}^\ast $). The red box illustrates the non-absorption region for calculating absorption length path.
The minimum deviation of absorption path length is limited by the time accuracy of the DAQ card, 50 ppm of sampling rate (25 ps) for NI USB-6363 used in the experiment. The temporal fluctuation of the absorption path length has been analyzed by Allan deviation, as shown in Fig. 3. The fluctuation of the absorption path length for the near-range measurement (NO.1, 76 m) is about 0.3 m, which is much less than that for the far-range measurement (NO.2, 350 m). This could be due to enhanced atmospheric turbulence for long-distance measurements. The optimum integration time of the path-length measurement was about 100 seconds according to the Allan deviation analysis. The trend of Allan Deviation after 100 seconds could be attributed to the drift of the diode laser and other electronic devices, variation of environmental temperature and pressure, etc.
Continuous measurement has been carried out to investigate the long-term stability of the measured absorption path-length, as shown in Fig. 4. The zero-path 1f-PA signal is acquired on 2 September 2019. The long-term fluctuation of the absorption path length is mainly caused by the fluctuation of the ambient temperature and pressure, the shift of the laser response and the detector, etc. According to the temporal analysis on the absorption path length shown in Fig. 4, it has been found out that the shift of path length is less than 2 m for one day and is less than 7 m for 7 days (1%). It should be emphasized that the drifting of the absorption path length could be significantly reduced by adding an in site reference measurement (e.g., a beam splitter and an identical photodetector) to perform real-time calibrations. The reference measurement can provide an accurate evaluation of the zero-path 1f-PA signal, which can be used for calibration as indicated in Eq. (8). The maximum measurement range of the absorption path length is inversely proportion to the modulation frequency, which can reach up to 3 km for 50 kHz modulation frequency in this work. Such a measurement range could be enough for most open-path applications.
3.3 Gas concentration retrieval
The open-path absorption signal measured with the near-range reflective sheet (NO.1), zero-path signal, and background subtracted absorption open-path signal are shown in Fig. 5(a). Although the 1f-PA signal has obvious baseline (Fig. 2(b)), which changes with the demodulation phase, its waveform is independent of the demodulation phase [19]. Besides, the differential of the 1f-PA signal (Fig. 5(a)) is also baseline-free. The SNR of the open-path absorption signal ($\partial {\theta _{1f}}$) was about 50, where the noise level was evaluated from the background signal. The root-sum-square 2f/1f signal has also been evaluated for comparison studies, as shown in Fig. 5(b). As can be seen, the background of the root-sum-square 2f/1f signal is much more conspicuous and its SNR is only about 12, which was much worse than $\partial {\theta _{1f}}$. Meanwhile, the 1f-PA differential signal is nearly background-free and independent of the demodulation phase, comparing with the traditional 2f/1f method.
Fig. 5. The open-path, zero-path and zero-path subtracted signals of (a) the 1f-PA differential signal and (b) root-sum-square 2f/1f.
As shown in Fig. 6, there are three absorption lines in the laser wavelength tuning range, CO2 absorption line at 6358.64 cm−1, H2O absorption line at 6357.87 cm−1, and CO2 absorption line at 6357.31 cm−1. To measure the carbon diode concentration, the calibration-free method based on spectrum fitting has been utilized [21]. The frequency modulation response is measured by the etalon reference signal. The environmental parameters such as temperature, pressure and dew point were acquired by a conspicuous mini weather station (AIRMAR, 200WX). The product of the CO2 concentration and the absorption path length can then be obtained by performing minimum least square fitting on the retrieved differential 1f-PA signal ($\partial {\theta _{1f - \textrm{open}}}$). The CO2 concentrations were 426.1 ppm and 389.7 ppm for measurements shown in Fig. 6(a) and Fig. 6(b), respectively. The measurement sensitivity was about 2 ppm with 700 m absorption path length and 1 second average time.
Fig. 6. Calibration-free spectral fitting result (upper panel) and the residual (lower panel) of the 1f-PA differential signals (${\theta _{1f - \textrm{open}}}$) measured for (a) the near-range reflective sheet (NO.1) and (b) the far-range reflective sheet (NO.2).
The temporal variation of the CO2 average concentration between the host and the far-range reflective sheet (NO.2) has be obtained by utilizing the measured absorption path length, as shown in Fig. 7. As the measurement path crossed the top of the woods, the respiration and photosynthesis of the woods imposed a daily variation on the CO2 concentration. The CO2 peak concentration appeared between 4 am and 6 am before sunrise. The occurrence time for the valley of the CO2 concentration was mainly affected by weather and emissions of ambient vehicles, etc. Nevertheless, the daily evolution of the CO2 concentration conformed to the rule of the local summer CO2 variance.
Fig. 7. Temporal evolution of the CO2 average concentration between the host and the far-range reflective sheet (NO.2) during a seven-day continuous measurement.
4. Conclusion
In this paper, the 1f-PA signal of the WMS has been utilized to measure the gas absorption and the absorption path length simultaneously. The absorption path length was obtained from the non-absorption region of the 1f-PA. The differential of the 1f-PA signal, which is nearly background-free and independent with the demodulation phase, has been utilized for the calibration-free retrieval of gas concentration. The principle of the proposed approach has been investigated theoretically, which was also validated by measuring carbon dioxide (CO2) concentration in open path environment. The CO2 concentration was evaluated by measuring the reflectance signal from a distant object with hundreds of meters away from the system. The measurement accuracy of the absorption path length can reach up to 1% through 7-day continuous measurements. This approach, which is of low-cost and highly integrated, would be suitable for open path measurements with unknown absorption path length in sophisticated field environments.
Funding
National Key R&D Program of China, Chinese Ministry of Science and Technology (2016YFC0200600, 2016YFC0302302, 2016YFC1400604, 2018YFC0213103); Instrument Developing Project of the Chinese Academy of Sciences (YJKYYQ20170062).
Disclosures
The authors declare no conflicts of interest.
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