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We propose a new methodology to measure gas concentration by light-absorption spectroscopy when the light source spectrum is larger than the spectral width of one or several molecular gas absorption lines. We named it optical similitude absorption spectroscopy (OSAS), as the gas concentration is derived from a similitude between the light source and the target gas spectra. The main OSAS-novelty lies in the development of a robust inversion methodology, based on the Newton-Raphson algorithm, which allows retrieving the target gas concentration from spectrally-integrated differential light-absorption measurements. As a proof, OSAS is applied in laboratory to the 2ν3 methane absorption band at 1.66 µm with uncertainties revealed by the Allan variance. OSAS has also been applied to non-dispersive infra-red and the optical correlation spectroscopy arrangements. This all-optics gas concentration retrieval does not require the use of a gas calibration cell and opens new tracks to atmospheric gas pollution and greenhouse gases sources monitoring.
© 2016 Optical Society of America
1. Introduction
Light absorption spectroscopy in the Earth’s atmosphere has largely contributed to understanding the impact of anthropogenic gas emissions to air pollution and consequently to human health [1] and global warming [2]. However, large uncertainties still remain, which mainly originate from inaccurate evaluations of gas emission sources [2]. Monitoring the emission of gases is indeed difficult to achieve in industrial and urban sites but also in environments presenting poor infrastructures. This concern underscores the need for developing robust and accurate methodologies to assess gas concentrations, which is the context of this work.
A comprehensive review, providing the state-of-the-art techniques on optical gas sensing, can be found in [3]. To monitor atmospheric gases, several monitoring devices have been proposed, based on high resolution spectroscopy [4–8] or non-dispersive absorption spectroscopy [9], either with point source measurement [10] or laser-based stand-off arrangements [11,12], often by applying effective cross-sections for low optical depths [9]. In non-dispersive absorption spectroscopy, the target gas (TG) concentration is evaluated from absorbance measurements which require an absolute calibration of gas concentration. It uses a light source whose spectral width is larger than the TG-absorption spectral linewidths. The optical correlation spectroscopy technique [13,14] is a particular arrangement of non-dispersive absorption spectroscopy in which a reference cell, filled with the TG, acts as a spectral filter. For field or airborne applications, it should then be limited to non-explosive gases, different from methane for example. However, non-dispersive absorption spectroscopy measurements interestingly remain accurate even for large variations of atmospheric pressure (1000-100 hPa) and temperature (230-500 K) [15], as required for identifying TG emitters from combustion or explosive sources.
To retrieve gas concentration from non-dispersive differential absorption measurements without the use of a standard gas calibration procedure, we here introduce a new concentration retrieval methodology. We have named it Optical Similitude Absorption Spectroscopy (OSAS), as the gas concentration is derived by achieving a similitude between the light source and the target gas spectra. Basically, OSAS can be described in the statistical theory as a non-zero similitude or covariance operator between the emitted power spectrum of the light source and the TG-absorption spectrum. Since OSAS deals with spectrally-integrated measurements, the standard inversion of the monochromatic Beer-Lambert law cannot be applied. Hence, a quantitative evaluation of the TG-concentration from OSAS-measurements is a priori not straightforward. However, TG-concentration is here determined by applying a new robust inversion methodology, based on the Newton-Raphson iterative algorithm. In this study, the OSAS-methodology is proved in laboratory by determining methane gas concentration from non-dispersive light absorption, by using only optical compounds, which is new to our knowledge. Hence we here show that, starting from the spectrum of the OSAS opto-electronic detection efficiency, the iterative Newton-Raphson algorithm can be applied to such differential light absorption measurements.
The paper is organized as follows. In Section 2, the formalism of the OSAS-methodology is presented, by starting from the spectrally-integrated Beer-Lambert law. To achieve a spectral similitude with the TG-absorption spectrum, amplitude modulations of a broadband spectral light source and the methane 2ν3 ro-vibrational absorption band [16] are considered. A study on the amplitude modulation spectral characteristics (central wavelength and spectral width) and their consequences on the OSAS-sensitivity is then presented. Section 3 is dedicated to the experimental proof of the OSAS-methodology in laboratory by evaluating methane gas concentrations in a 1-meter gas cell. To show that the OSAS-methodology can be applied with different amplitude modulation techniques, three different optical arrangements (Acousto-Optic Programmable Dispersive Filter (AOPDF), interference filters as in NDIR, gas absorption cell as in Optical Correlation Spectroscopy (OCS)), are then considered to perform the light source amplitude modulation. By applying our OSAS-inversion algorithm, all three arrangements provide consistent methane gas concentrations within respective error bars. This new methodology hence appears as a robust TG-concentration retrieval procedure when dealing with non-dispersive absorption spectroscopy. The paper ends with a conclusion and proposes outlooks of this work, emphasizing possible applications of the OSAS-methodology coupled with point source measurements and laser remote sensing, to monitor air pollution and to identify greenhouse gas emission sources.
2. OSAS methodology
2.1 Principle
In the OSAS-methodology, the power spectral density (PSD) of a broadband light source (i.e. broader than the spectral width of one or several molecular absorption lines), is tuned or spectrally shaped to be similar with the TG-gas absorption spectrum (the active channel), while a second PSD is set or shaped in a less absorbing spectral region (the reference channel). Ideally, both PSD must be carefully set to ensure that no interfering species absorbs in their respective spectral ranges [3]. The OSAS-principle is shown in more details in Fig. 1 when considering methane in its 2ν3 absorption band. The active channel P0;1(λ), which overlaps a high density of absorption lines, undergoes light absorption along the optical path, while the reference channel P0;2(λ) experiences a lower light extinction. Hence, two different signals, S1 and S2, are detected after light absorption. In Fig. 1, η(λ) is the spectrum of the opto-electronic efficiency of the detection part of the set-up. This figure is derived from laboratory measurements to be detailed and discussed in Section 3.
Fig. 1 The OSAS-principle applied to the methane gas. The power spectral density (PSD, black curve) of a broadband light source is spectrally shaped to enfold (red curve) or not (blue curve) the methane absorption cross-section spectrum σCH4(λ). The 2ν3 absorption band is here considered (green lines), calculated from HITRAN 2012 database [16] for T = 294 K, p = 1013.25 mbar and air-broadening; a Voigt profile is used to model the line-shape. η(λ) is the spectrum of the opto-electronic efficiency of the OSAS detection part (orange curve).
Following the Beer-Lambert law, the detected optical signals Si (i = 1, 2) can be expressed as follows in the absence of interfering species:
where ΤTG(λ) = exp(−σTG(λ)Nℓ) is the optical transmission of the TG, N is the gas concentration, σTG(λ) the TG absorption cross-section at wavelength λ and ℓ is the optical path length. The integral is considered to be taken over the wavelength range Δλ, extending over P0;1(λ) and P0;2(λ). K is an opto-electronic conversion factor assumed to be achromatic and constant during the measurements. The spectral shape or the position of P0;i(λ) can be modified by tuning the light source or by applying several modulation techniques, such as a gas correlation cell with pressure modulation [17] or a Fabry-Perot interferometer [14]. In the present work, a broadband light source P0(λ) is spectrally shaped by applying active or passive optical filters or by using a gas absorption cell. In these cases, the expression of P0;i(λ) can be decomposed as follows:where the amplitude modulation (AM) functions Mi(λ) depend on the amplitude modulator device, as detailed in Section 3.2.2 Target gas concentration retrieval
We here propose a new TG-concentration retrieval procedure from non-dispersive differential absorption signal. As Eq. (1) is non-linear with N, the traditional approach is to linearize this equation [9] and to consider the S1/S2-ratio between the measured signals [3]. In this paper, we still retrieve the concentration from the S1/S2-ratio but we propose a new TG-concentration retrieval procedure, which is valid whatever the optical depth. It is based on a root-finding algorithm, such as the iterative Newton-Raphson algorithm, which is adequate for solving non-linear problems [18]. We therefore introduce the following function g defined by the cross-product:
whose x-variable is related to the TG-concentration while fi is a function modeling the detected signal defined as:Compared with Eq. (1), K does not appear in the expression of fi since, as explained above, K is achromatic over Δλ and constant during signal measurement. Interestingly, the x-variable corresponds to N when the S1/S2-ratio is equal to the f1/f2-ratio. As a result, the gas concentration N appears as the first zero of the g-function which can be retrieved by applying a root-finding algorithm, such as the iterative Newton-Raphson algorithm. At the nth-iteration, starting from x0 = 0, the solution of this algorithm is given by xn + 1 = xn - g(xn)/g’(xn). A unique solution is ensured when g’ < 0, g” > 0 and N belongs to [0; xmax], where xmax is the first zero of the f1/f2 first derivative. These mathematical conditions reflect the non-linearity of the measured signals Si when increasing the gas concentration N, as a result of the Beer-Lambert law. The xmax-value depends on the experimental set-up but is very high, above 1028 #.m−3 for the three experimental configurations presented in Section 3. To highlight the convergence of the inversion algorithm in the case of a high methane optical depth, the g-function is displayed in Fig. 2(a). The numerical relative error is below 10−12 after only n = 5 iterations and reaches the computation limit (about 10−16) after only 7 iterations (see Fig. 2(b)).As a result, the gas concentration can be retrieved if the fi-function can be calculated, which requires knowledge of the spectral dependence of Eq. (1) variables, and assuming that they remain stable over time. Hence, OSAS-methodology does not require the use of a gas calibration procedure, as usually presented in the literature.Fig. 2 a) The iterative Newton-Raphson algorithm applied to a methane concentration of N = 2.5.1024 #.m−3 (black line). Its convergence is shown with successive iterations (labeled by the iteration number n) while the grey area represents the variation of g when considering ± 2% statistical errors on Si. b) Relative numerical error on N as a function of the iteration number n.
When considering the uncertainties affecting the measured signals Si, the root-finding algorithm converges to the target gas concentration with an uncertainty that depends on the statistical uncertainties and biases on the measured signals Si as displayed in grey in Fig. 2(a). To provide an order of magnitude on the knowledge and stability requirements on P0 and η, we considered the rather pessimistic case where a 2%-uncertainty is affecting the measured signals. Such a 2%-relative error on Si corresponds to a 3.9 nm shift in the central wavelength (CWL) of the PSD (1.3 nm in its spectral width), or a 1.8 nm shift in the opto-electronic efficiency spectrum, or a 0.4 nm shift in the CWL of the M1-modulation (6.1 nm for the M2-modulation). The corresponding relative error on the gas concentration for a path-integrated concentration of 105 ppm.m is 23% for the CWL of the PSD (5.10-3% for its spectral width, 0.8% for a shift in η and 16% for the two modulation functions). Therefore, CWL shifts in P0 and Mi in the nanometre range are acceptable. When the 2%-relative error on Si are of statistical origin, the relative error on the gas concentration is 24%. Moreover, from an experimental point of view, the stability of the measurements with time can be indirectly verified by evaluating the Allan variance, as explained by Werle et al. [21].
2.3 Normalized weighted transmission
OSAS-measurements depend on the TG-absorption spectrum as well as on the chosen spectral properties of the AM functions. In the absence of interfering species, these dependencies can be studied by evaluating the normalized weighted transmission Tw(λi) of a TG-sample cell, which is defined as follows:
where the spectra P0(λ) and η(λ) are presented in Fig. 1. The AM-function Μ(λi,λ) simulates a modulation function centered at wavelength λi, with a Lorentzian shape function that carefully fits with the AM-experimental spectra presented in Fig. 1 (R2 = 0.98). The methane transmission TTG(λ) is computed from the TG-cross section spectrum σTG(λ) by using a path-integrated concentration Nl set to 1.104 ppm.m, using the HITRAN 2012 database [16] in the same spectral range as in Fig. 1. For that, air-broadening at laboratory temperature and pressure (T = 294 K, P = 1013.25 mbar) is considered in the individual Voigt’s line profiles. The normalized transmission Tw(λi) is shown in Fig. 3 for methane in the 1630-1680 nm range. Tw(λi) reaches a minimum at 1665.6 nm in the Q-branch. Local maxima are obtained at a central wavelength (CWL) of λi = 1660.0 nm, 1630 nm and 1672.3 nm due to the decreasing number of strong methane absorption lines. The influence of the spectral width δλ of the modulation on Tw(λi) is also shown in Fig. 3 by considering δλ = 2.5 nm and δλ = 5 nm. As expected, the transmission is increasing in the center of the Q-branch when δλ is increased. Moreover, Tw(λi) extrema positions are slightly shifted. In complement, the role of interfering gas molecules has been addressed by considering water vapor, carbon dioxide or ethane whose absorption lines lie in the same spectral range as methane. Such calculations however show that these molecules barely affect the normalized transmission Tw(λi) in the ‰ range even at high methane concentrations, as considered in this study. These results will be used in Section 3 to set the AM-functions which are required to apply the OSAS-methodology. The position of the M2-modulation function will affect the relative error on the TG-concentration, as shown below.Fig. 3 Normalized weighted transmission Tw(λi) as a function of the central wavelength λi and the amplitude modulation function M(λi, λ), as defined in Eq. (5). Two different modulation spectral widths are considered (δλ = 2.5 nm, blue curve; δλ = 5 nm, red curve) in the case study of a path-integrated concentration of 104 ppm.m of methane.
3. Experimental set-up
The experimental set-up for applying the OSAS-methodology is shown in Fig. 4. A Superluminescent Light Emitting Diode (SLED, DL-BZ1-CS65M5A from Denselight), emitting at 1650 nm wavelength, is used as the broadband light source with a spectral width of 65 nm (FWHM), to cover a large part of the methane gas absorption spectrum in its 2ν3 absorption band. This light source is pulsed at a 1 kHz pulse repetition rate (20 µs pulse duration) to carry out experiments with an AOPDF in Section 3.1. Light coupling is ensured with a SMF-28 fiber having a 10 µm mode field diameter whose output is collimated with a 10x-microscope objective. The SLED broadband PSD is shown in Fig. 1 between 1630 and 1680 nm. Spectral ripples are related to the SLED coupling with the single mode fiber. A broadband polarizing beam splitter cube sets the p-polarization of the light. Amplitude modulations are applied through three different modulation techniques (I, II and III) to be detailed below. The measurement gas cell (1 meter long) is positioned after the amplitude modulator, but could have been set before [12], since the spectral transmission of the gas cell is constant over the considered spectral range. The gas cell is filled with a mixture of CH4-clean air and N2 buffer gas and the gas partial pressures are monitored with a Capacitron (DM21). Gas fluxes are not considered here because it is beyond the scope of this study to achieve a field instrument. The Si-signals, measured with an Avalanche Photo-Diode (Laser Components, LCIA-200-10) are sampled with a transient recorder (Licel, 14 bits, 20 MHz sample rate), averaged over 1 second and the electronic offset is corrected. The measurement of P0;i(λ) is achieved with an intensity and frequency-calibrated spectrograph (ANDOR Shamerock SR-750) using the removable mirror shown in Fig. 4. In this way, any supplementary modulation induced by semi-transparent mirror or polarizing beam splitter is avoided. To ensure that Eq. (1) can be applied, we also verified that the detector and the spectrograph operated in the linear regime, by using calibrated grey filters. For each method, the weighted transmission are: for setup-I, TW(λ1) = 0.964 and TW(λ2) = 0.996; for setup-II, TW(λ1) = 0.986 and TW(λ2) = 0.994; for setup-III: TW(λ1) = 0.975 and TW(λ2) = 0.997.
Fig. 4 Scheme of the experimental set-up. The SLED broadband PSD is shaped by an amplitude modulator generating the Mi(λ) function, either I or II or III. The Si-signals are measured with an Avalanche Photo-Diode (APD) after passing through a 1-meter-long gas cell. A removable mirror is added on the optical path for spectral characterizations. A quarter waveplate is used to avoid biases induced by the polarization dependent spectrograph grating efficiency. Each amplitude modulator is described in subsection 3.1, 3.2 and 3.3.
3.1 AOPDF
As shown in the insert I of Fig. 4, the amplitude modulation of the broadband light source can be achieved by using the AOPDF as an active modulator (Dazzler-HR-1000-1650 from Fastlite) to generate versatile Mi(λ) functions on the 1°-diffracted beam as presented in Fig. 4(I). AOPDF is frequently used with chirped femtosecond laser [19]. Its maximal transmission and spectral rejection respectively reach 0.6 and 2.10−4. To match the AOPDF polarization specification, a half wave-plate (see Fig. 4) is inserted on the optical pathway. Using the 1 kHz repetition rate of the light source, each light pulse can be alternately - without dead time - adjusted to the active M1(λ1, λ) or to the reference M2(λ2, λ) AM-function. The remaining 3.6°-beam outgoing from the AOPDF is not used here. Examples of the resulting P0;1(λ) and P0;2(λ) spectra are presented in Fig. 1, for λ1 = 1666 nm, λ2 = 1660 nm, with δλ = 2.5 nm for both modulations. This spectral width of 2.5 nm was the smallest experimental value that could be achieved with our apparatus. The broadband PSD P0;1(λ) obtained in Fig. 1 corresponds to an AM-function that effectively overlaps the Q-branch of the methane 2ν3 absorption band, hence addressing the similitude between the P0;1(λ) and the TG-absorption spectra. OSAS-measurements are performed in Section 4.3 by using these spectral settings.
3.2 Passive filters
The second modulation technique relies on passive filters as shown in Fig. 4(II) with its related modulation function Mi(λ). The two interference filters were designed, in agreement with Section 2.3, to exhibit a transmission FWHM bandwidth of 5.07 nm (respectively 4.04 nm) centered at a CWL of 1666.31 nm (respectively 1660.99 nm). The half waveplate, set before the amplitude modulator, balances the energy between the active (λ1 = 1666.31 nm) and the reference (λ2 = 1660.99 nm) channel. For selecting one channel at a time, a mechanical chopper is implemented and rotated at a 500 Hz frequency which then triggers the SLED pulse. Delays are adjusted so that the SLED alternately emits pulses to the active channel and to the reference channel without cross-talk. Afterwards, the two optical paths are recombined with a polarizing beam splitter cube. For experimental versatility, a chopper is used instead of a conventional filter wheel [20] that may simplify the set-up.
3.3 Absorption cell
The third amplitude modulation technique relies on a gas absorption cell, as presented in Fig. 4(III). The AM-function is here achieved by inserting a 10 cm-sealed methane gas cell, filled with 1500 Torr of pure methane on the optical pathway of the reference channel. It is shown in Fig. 4(III). As the light propagates through this absorption cell, it undergoes the characteristic TG-absorption spectrum, in contrary to the other light pathway, corresponding to the active channel, where no gas cell or optical compound is inserted. Both pathways are recombined with a polarizing beam splitter cube, before entering the 1 m-measurement gas cell. To increase the relative transmission between both channels, the bandwidth of the broadband light source is reduced by inserting an optical filter (Filter 3) before the polarizing beam splitter cube. The AM-functions defined in Eq. (2) then express as: M1(λ) = TIF3(λ) and M2(λ) = TIF3(λ) × Tcell(λ) where TIF3 is the transmission of the interference filter 3 and Tcell is the transmission of the absorption cell, calculated from the HITRAN database by considering self-broadening and Voigt line profiles at the laboratory temperature of 294 K and using the methane pressure of 1500 Torr. The interference filter 3 is centered at a CWL of 1667.62 nm with a FWHM spectral bandwidth δλ = 11.46 nm.
4. Methane concentration measurements using OSAS-methodology
In this section, methane concentration measurements are reported by applying OSAS based on the novel inversion formalism introduced in Section 2.2. The spectral behavior of the opto-electronic efficiency η is first measured by using the AOPDF. An OSAS verification is then proposed to indirectly check the validity of the measured spectral parameters (i.e. P0;i(λ) and η(λ)). Moreover, four different methane concentrations, corresponding to increasing light absorptions, are then evaluated by applying the OSAS-methodology, for each of the above three amplitude modulators. The obtained results are then compared and discussed.
4.1 Opto-electronic efficiency measurement
To evaluate the opto-electronic efficiency η(λ) introduced in Section 2.1, we used the AOPDF that operates as a monochromator having a spectral resolution of δλ = 2.5 nm (see Fig. 4(I)). η(λ) is hence obtained by interpolating η(λi) measurements characterized between 1.6 and 1.7 µm, assuming η is constant over δλ. Hence, we get:
where S(λi) is the detected signal in the absence of absorbing species, when the CWL is set to λi. P0;i(λi,λ) is the corresponding spectrum simultaneously recorded with the spectrograph by placing a spectrally-calibrated polarizing cube instead of the removable mirror. The CWL λi is swept with the AOPDF from 1.6 µm to 1.7 µm with 1 nm steps. The η(λi)-values are normalized and shown in Fig. 1. Absolute measurements are not mandatory since the concentration is retrieved from the ratio S1/S2 and the calibration constant K does not appear in the retrieved equations. The decrease of η(λ) in the high wavelength range is in agreement with our InGaAs APD spectral cut-off. Uncertainties on η(λ) come from the detector shot-noise (see section 4.3). The uncertainty on λi is lower than 0.1 nm and hence not reported in Fig. 1. In the following sections, we assume that this spectral specification of our optical set-up remains stable over time.4.2 OSAS-verification
In this section, the OSAS-methodology is verified over a broad spectral range of the TG-absorption spectrum based on the measured spectra P0;i(λ) and η(λ) presented in Fig. 1. The OSAS-methodology has been applied by filling the measurement gas cell with a commercial gas mixture of CH4 and air (1.8% vol. concentration ± 1% relative error), corresponding to a methane gas path-integrated concentration (PIC) of 18000 ppm.m. The AM-function of the active channel M1(λ1, λ) is set at λ1 = 1666 nm (Section 2.3, Fig. 3). The CWL λ2 of the reference channel M2(λ2, λ) is swept from 1630 nm to 1680 nm with 1 nm step to retrieve methane PIC as a function of λ2. Each methane PIC is retrieved by applying the Newton-Raphson inversion algorithm to the differential absorption measurements using the measured value of η(λ), that of both power spectral densities P0;i, and the calculated methane absorption cross section. Figure 5 presents the OSAS-retrieved methane PIC. Errors bars are evaluated by considering statistical errors on S1 and S2. Interestingly, on average over all measurements, the relative error remains below 10% (when considering the median). Within error bars, the retrieved PIC are compatible with the expected value of 18000 ppm.m, except when λ2 is set too close to λ1 (between 1665 and 1667 nm), as discussed in Section 2.3. The increase in the error bars in Fig. 5 is due to the SNR on Si and to the CWL of M2(λ), as expected. Indeed, when considering a 1%-relative error on the S1/S2-ratio, a 10%-relative error on N is obtained for every λ2-value of our numerical spectral range (1630-1680 nm), apart from the spectral interval between 1664.5 and 1667 nm, in agreement with the observed strong increase in the error bars. As expected, the OSAS-methodology is not applicable at λ2 = 1666 nm since Μ1(λ) = Μ2(λ).
Fig. 5 Methane path-integrated concentrations retrieved from the OSAS-methodology depending on the reference channel AM function central wavelength λ2. The expected methane PIC is represented in dashed-lines.
4.3 OSAS-measurements
OSAS-measurements are here performed for four different methane PIC (4500, 9000, 13500, 18000 ppm.m), corresponding to increasing light absorptions, by using the three modulation techniques presented in Section 3. The retrieved OSAS PIC are presented in Fig. 6. PIC and error bars are evaluated by considering the mean value and the standard deviation of the measurements acquired over 20 minutes. In each four methane case study, the measured PIC are comparable within error bars of the respective modulation techniques.
Fig. 6 Methane PIC retrieved by applying different AM-techniques. The expected PIC-values are indicated with the dotted lines for comparison.
The largest standard deviations are obtained with the absorption cell set-up (Fig. 4(III)) for which the differential absorption is the lowest. These error bars can be further reduced by increasing the absorption in the gas cell or by decreasing the IF3 spectral width (see Fig. 4(III) and Section 3.3). Error bars when using the AOPDF-amplitude modulation (Fig. 4(I)) are larger than those obtained with the IF-amplitude modulation (Fig. 4(II)). This seems contradictory because set-up I provides a greater differential absorption (see Fig. 3) that should induce smaller error on PIC. This loss in sensitivity originates from the AOPDF fast jittering during the AM-generation and from the temperature variation of the SLED PSD. These temperature variations affect all OSAS-measurements causing a detuning of the SLED CWL in the range of ± 0.2 nm. Its consequence on OSAS PIC is highlighted in Fig. 7 by the observed slow oscillation on the retrieved PIC-values (314 ppm.m, with a period of about 103 s). The standard deviation of S1/S2 as a function of the averaging time τ is shown in the Allan deviation plot in Fig. 7 [21]. As expected, for short signal averaging times, the measurement precision is limited by white noise (following a τ−1/2 trend). It is attributed to statistical AOPDF AM-function jitter and to the detector shot noise. Moreover, the Allan deviation plot exhibits the optimal averaging time around τ = 30 s. At larger τ-values, the standard deviation is increasing, which is related to the previous remark on the SLED temperature change. The abrupt change in the standard deviation at τ = 400 s can be related to inherent - non-strictly periodical - temperature change. Other error contributions from changes in SLED spectral density (e.g. ripples involved in fiber coupling) or variations in opto-electronic efficiency are lower than the previously discussed error sources. When comparing the retrieved methane PIC elaborated from the different amplitude modulators, the OSAS-methodology is found consistent, even if the light and the AOPDF stability affect the precision and the sensitivity of the methodology.
Fig. 7 a) Temporal evolution of methane PIC retrieved with OSAS by using the AOPDF-modulator over 6000 seconds. At time t = 2000 s, the 1-meter-long measurement gas cell buffered with N2 is filled with a methane-air mixture (1.8% of methane). Then, methane is removed from the gas cell by flushing it with N2. The stability over time of P(λ) and η(λ) has been directly checked before and after the measurements. b) Allan deviation of the signal ratio S1/S2 between t = 2050 s and t = 5050 s.
5. Conclusion and outlooks
In this paper, we present the OSAS, which is a new methodology to evaluate TG-concentrations from spectrally integrated (or non-dispersive) differential absorption measurements. We verify OSAS in laboratory by retrieving methane path integrated concentration. We show that methane PIC is retrieved by applying the Newton-Raphson inversion algorithm on the differential absorption measurements after measuring the optical set-up efficiency and both power spectral densities P0;i(λ) and calculating the target gas absorption cross-section. It is also shown that OSAS-methodology can be applied to different light source amplitude modulation techniques (AOPDF, interference filters and absorption gas cell). The spectral fluctuations of the broadband light source should be in the nanometre range, while its amplitude fluctuations will barely affect the TG-concentration retrieval as long as the detected signals are shot-noise limited. Reaching a high sensitivity and a high precision on these measurements was beyond the scope of this work but improvements can be achieved by using a temperature stabilized PSD light source. Moreover, a higher sensitivity can be obtained by considering stronger TG-absorption cross sections as for example for methane, in the ν3 band at 3.2 µm. Interfering species may be an issue at ambient methane concentrations, but a methane concentration measurement in their presence was beyond of the scope of this study. OSAS could however be considered to carry out several AM-functions covering several TG-absorption bands as a in the standard NDIR [20]. Hence, OSAS appears promising. This work also settles the basements towards the use of the OSAS-methodology to improve DIAL (DIfferential Absorption Lidar) retrievals using broadband laser sources. The remote sensing methodologies relying on effective cross section formalism [22] may also take benefit from the OSAS-concentration inversion methodology to avoid biases related to the light source bandwidth. Moreover, determining quantitative TG-concentrations by applying OSAS can avoid the traditional use of gas calibration concentration procedure but assuming that the spectral specification of the set-up remains stable over time and taking advantage of a comprehensive study on the TG-spectroscopy.
Acknowledgments
The authors thank CIFRE for partly funding this work. We also thank the team of the ILM mechanic workshop for performing precise experimental hardware.
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