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Journal of Quantitative Spectroscopy &Radiative Transfer

Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 670–674

0022-40http://d

n CorrEnginee316-851

E-m

journal homepage: www.elsevier.com/locate/jqsrt

Detection of stable carbon isotopes of methane with a 2.4-μmdistributed feedback laser

Kotaro Tanaka a,n, Kenshi Takahashi b, Kenichi Tonokura a, Hiroaki Sugiyama c,Nobuo Nakano c, Yukio Nakano d

a Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8563, Japanb Research Institute for Sustainable Humanosphere, Kyoto University, Gokasyo, Uji, Kyoto 611-0011, Japanc RIKEN KEIKI Co., Ltd., 2-7-6 Azusawa, Itabashi, Tokyo 174-8744, Japand Department of Environmental Science, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei, Tokyo 184-8501, Japan

a r t i c l e i n f o

Article history:Received 16 July 2013Received in revised form7 October 2013Accepted 15 October 2013Available online 23 October 2013

Keywords:MethaneStable carbon isotopesNear-infrared laserPressure-broadening parameters

73/$ - see front matter & 2013 Elsevier Ltd.x.doi.org/10.1016/j.jqsrt.2013.10.004

esponding author. Present address: Departring, Ibaraki University, 4-12-1 Nakanarusa1, Japan. Tel.: þ81294385080.ail address: k_tanaka@mx.ibaraki.ac.jp (K. Ta

a b s t r a c t

Direct absorption spectra of methane (12CH4 and 13CH4) at room temperature have beenrecorded using a 2.4-μm distributed feedback laser. Integrated cross-sections of 13CH4 weremeasured and compared with those listed in the HITRAN 2008 and 2012 databases,indicating that there are some discrepancies between our results and both editions of theHITRAN database. The pressure-broadening parameters of those 13CH4 lines in synthetic airwere also examined experimentally. For the purpose of determining the carbon isotoperatio (13CH4/12CH4) through the spectral measurements, candidate line pairs of 12CH4 and13CH4 within the range 4147–4154 cm�1 were explored. Resultantly, the well-isolated linepair of 12CH4 at 4151.843 cm�1 and 13CH4 at 4151.966 cm�1 was suggested to be a candidatefor determining the carbon isotope ratio of CH4 in this wavenumber region.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The application of tunable diode-lasers in trace gasdetection systems brings a compelling combination ofhigh sensitivity, specificity, and self-calibration. Dependingon which types of lasers are used [1], the sensitivity oftrace gas detection systems depends on several factors,including the wavelength, the optical path through thesample, photodetector sensitivity, and low-noise detectiontechniques. Early systems based on lead-salt lasersachieved high sensitivity but required liquid nitrogen tooperate. In contrast, InGaAsP lasers developed for fiber-optic communications in the 1.3–1.65 μm wavelengthrange have proven to be especially easy to use, and thedemands of the communications marketplace have led to

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ment of Mechanicalwa, Hitachi, Ibaraki

naka).

highly engineered devices at increasingly lower costs.Distributed feedback (DFB) architectures enable reprodu-cible operation at a single frequency determined by thelaser temperature and injection current. Although theselasers and associated photodetectors operate at roomtemperature, most gases have only relatively weak over-tone transitions in the 1.3–1.65 μm wavelength range,which is not optimal for the sensitivity required in tracegas detection.

A type I antimonide laser with metal-grating DFBstructures emits continuous, single frequency light in the2.0–2.8 μm range at room temperature [2,3], where gases ofenvironmental interest (CH4, NH3, CO, and N2O) haverelatively strong absorption lines and can thus be efficientlydetected. Furthermore, the 2.0–2.5 μm region has theadvantage that it is located in an atmospheric transmissionwindow where absorption by water vapor and carbondioxide is weak and where standard glass optical elements(windows, lenses) present acceptable losses. When com-pared with the 1.3–1.65 μmwavelength range, the strongest

Fig. 1. (a) Experimental direct absorption spectrum of 2.5% CH4 in11.5 kPa of air (sample A); and (b) simulated spectrum at a total pressureof 11.5 kPa using spectroscopic parameters in the HITRAN 2012 database.

K. Tanaka et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 670–674 671

absorption lines in the ν1þν4 band of CH4 at 2.37 μm havean intensity twice that of the 2ν3 band at 1.65 μm.

In spite of these attractive aspects, few groups havereported laser development and spectroscopic applica-tions in the 2.0–2.5 μm region. Recent reports havedescribed the detection of methane [4–6], ammonia [7,8]and formaldehyde [9] with wavelength modulation spec-troscopy (WMS) and photoacoustic spectroscopy. Ourgroup has used WMS at 2.008 μm to measure carbonisotope ratios of CO2 [10,11].

This paper describes the use of a 2.4-μm DFB laser fordetecting CH4 molecules by direct optical absorptionspectroscopy. In addition, we have examined the use ofpairs of 12CH4 and 13CH4 absorption lines for isotopomerratio measurements. These measurements have been per-formed in the 8.1 μm [12] and 3.3 μm [13] regions. Mostrecently, 13CH4 spectrum from 0.8 μm to 9 μm at tempera-tures ranging from 80 K to 300 K measured by highresolution Fourier transform infrared (FTIR) spectroscopyhas been reported [14]. However, no study to date hasbeen reported on the use of a DFB laser at 2.4-μm for 12CH4

and 13CH4 detection.

2. Experimental

The experimental setup was similar to that used pre-viously, except that a 2.4-μm DFB laser was used as a lightsource [10,11,15]. The 5-mW, 2.4-μm DFB laser (Nanoplus,Wurzburg, Germany) is in a TO-5 can that includes athermo-electric cooler and a thermistor. It was mountedin an aluminum housing having thermal contact with thebottom (lead side) of the laser package. The injectioncurrent and the temperature of the laser chip were bothmaintained by an ILX LDC 3724C controller (Lightwave,Bozeman, MT, USA). Laser light was collimated with ananti-reflection (AR) coated 4-mm aspheric lens and intro-duced into a wedged-window Herriott-type multi-passcell (TOPTICA CMP-30, Munich, Germany) consisting oftwo concave mirrors. The cell had a path length of 29.91 mand a volume of 0.9 L. The beam was focused at the centerof the multi-pass cell with an external 500-mm AR-coatedCaF2 lens. The transmitted laser beam was focused with a50-mm AR-coated CaF2 lens onto an InGaAs photodiodedetector (THORLABS PDA10DT, Newton, NJ, USA).

The laser was scanned at 10 Hz by ramping the injec-tion current with a triangle voltage wave (Agilent 33220A,Santa Clara, CA, USA). The photodetector signal wasdigitized with a 16-bit AD PCMCA card (CONTEC ADA16-8/2(CB)L, Osaka, Japan) and analyzed in LabVIEW (NationalInstruments, Austin, TX, USA). The signals were averagedover 10 cycles.

The multi-pass cell was evacuated with a rotary pumpthat had a liquid-nitrogen trap. The pressure in the cell waskept at 1 kPa or 11.5 kPa (70.01 kPa), as monitored by acapacitance manometer (MKS Baratron 722B, Andover, MA,USA). The sample gas mass flow rate was controlled by amass flow controller (Kofloc 3660, Kyoto, Japan) duringmeasurements. Standard gas samples were CH4/air (TaiyoNippon Sanso Corp, Tokyo, Japan, 2.5%, hereafter sample A),12CH4 (Cambridge Isotope Laboratories, MA, USA, 499.95%,sample B), 13CH4 (Isotec, OH, USA, 499%, sample C) and

synthetic air (Taiyo Nippon Sanso Corp, 499.999%). Thecell was kept at room temperature (29573 K).

3. Results and discussion

3.1. 12CH4 detection

Fig. 1 shows a comparison of the experimental andsimulated absorption spectra of CH4 in the 4147–4154 cm�1

region. The experimental spectrum was obtained by directabsorption spectroscopy of sample A at a total pressure of11.5 kPa, and the simulated spectrum was calculated withparameters in the HITRAN 2012 database [16] at 295 K. Asshown in Fig. 1, most of the intense absorption lines wereassigned to 12CH4 since the ratio of 13CH4/12CH4 in sample Acould be as low as that in ambient air.

3.2. 13CH4 detection

We prepared the 13CH4 cylinder (sample C) andacquired direct absorption spectra. Fig. 2(a) shows a directabsorption spectrum of 13CH4 diluted (4.0%) in 1 kPa ofsynthetic air over 4147–4154 cm�1. To our knowledge, thisis the first reported absorption spectrum of 13CH4 by diodelaser spectroscopy in this wavenumber region. For com-parison, the direct absorption spectrum of 12CH4 (sampleB) diluted (4.6%) in 1 kPa of synthetic air is shown in Fig. 2(b). We note that six strong 13CH4 absorption lines labeledby asterisks in Fig. 2(a) were listed as 12CH4 in the HITRAN2008 database [17] with no definitive assignment of thequantum state and are now listed as 13CH4 in the HITRAN2012 database with their assignments [16]. From compara-tive intensities of the direct absorption spectra of 12CH4

(sample B) and 13CH4 (sample C), the aspect ratio of the

K. Tanaka et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 670–674672

absorption line at 4150.670 cm�1 (13CH4) to that at 4152.611 cm�1 (12CH4) was measured to be 1.0870.17, allowingus to estimate the integrated cross-section at 4150.670 cm�1

to be (2.6870.50)�10�23 cm2 molecule�1 cm�1 using theintegrated cross-section and the air-broadening coefficientat 4152.611 cm�1 in the HITRAN 2012 database. The errorbar was due to uncertainties in the aspect ratio measure-ment and the partial pressure. In the same manner, theintegrated cross-sections of the other strong 13CH4 absorp-tion lines were also estimated and were compared withthose in the HITRAN 2008 and 2012 databases (Table 1).

Fig. 2. Direct absorption spectra of (a) 4% 13CH4 (sample C) in 1 kPa ofsynthetic air and (b) 4.6% 12CH4 (sample B) in 1 kPa of synthetic air.Asterisks in the 13CH4 spectrum indicate the lines whose integratedcross-sections are measured experimentally in this work (see text). Thewell-isolated absorption lines pairs of 12CH4 and 13CH4 in the markedregion were examined for use in determining isotope ratios.

Table 1Absorption lines for 13CH4 and 12CH4 investigated in this work.

Line center/cm�1 a Assignment Int

This work HITRAN Th

2008 2012 20

4148.918 13CH412CH4 – 2.7

4149.300 13CH412CH4

13CH4 1.84149.763 13CH4

12CH413CH4 2.1

4150.670 13CH412CH4

13CH4 2.74150.700 12CH4

12CH412CH4

c

4150.846 12CH412CH4

12CH4c

4151.042 12CH412CH4

12CH4c

4151.966 13CH412CH4

13CH4 2.04152.091 13CH4

12CH412CH4 1.5

4153.721 12CH412CH4

12CH4c

a Reported in the HITRAN 2012 database except for the line at 4148.918 cmb Estimated from the absorption spectrum measured in 1 kPa of synthetic ac Not measured in this work because of interference from neighboring abso

The integrated cross-sections of four absorption lines(4148.918 cm�1, 4149.763 cm�1, 4150.670 cm�1, and 4151.966 cm�1) were in fair agreement with those in the 2008edition than the 2012 edition of the HITRAN database. Theother two lines (4149.300 cm�1 and 4152.091 cm�1) weredifferent from both editions of the HITRAN database. Toinvestigate the discrepancy, we experimentally acquiredtheir absolute absorption cross-sections at 4149.300 cm�1

and 4152.091 cm�1. For the measurements, the total pres-sure in the cell was varied over the range 0.4–7.0 kPa. The13CH4 partial pressure was kept at 0.02 kPa and the totalpressure was adjusted by adding synthetic air. The depen-dence of the peak absorption cross-section on the totalpressure is given by Eq. (1), which was derived from ananalytical solution of the Voigt function [18]

ssD

¼ 2ffiffiffiπ

p expðy2ÞZ 1

yexpð�t2Þdt ð1Þ

In Eq. (1), s is the absorption cross-section at each pressure,sD is the Doppler absorption cross-section at zero totalpressure, and y is the normalized pressure-broadeningparameter given by

y¼ wL

wD

� � ffiffiffiffiffiffiffiffiffiln 2

pð2Þ

where wL is the Lorentz half-width at half-maximum(HWHM), and wD is the Doppler HWHM. The absoluteabsorption cross-sections of the absorption peaks at4149.300 cm�1 and 4152.091 cm�1 were obtained as fittingparameters for Eq. 1 and are (1.7170.26)�10�21 cm2

molecule�1 and (1.0570.16)�10�21 cm2 molecule�1 (two-standard deviations), respectively, based on the HITRAN2012 database. These determinations are altered to(1.7670.26)�10�21 cm2 molecule�1 and (1.0970.16)�10�21 cm2 molecule�1, when referring to the 2008 editionof the HITRAN. In addition, we determined the air-broadening coefficients for the two absorption lines as wellas the other four lines. Pressure-dependent Voigt profileswere fit to the experimental spectra via nonlinear least-squares. The Gaussian HWHM of the absorption lines were

egrated cross-section/10�23 cm2 molecule�1 cm�1

is work b HITRAN

08 2012 2008 2012

070.40 2.6270.40 2.94 –

870.36 1.8270.36 4.25 1.04770.46 2.1170.46 1.52 1.07570.50 2.6870.50 2.05 1.96

c 2.64 2.75c 2.28 1.58c 1.76 0.97

870.40 2.0270.40 1.61 1.07970.32 1.5570.32 3.04 3.20

c 1.34 1.25

�1 which was reported in the HITRAN 2008 database.ir and the parameters in the HITRAN 2008 or 2012 database.rption lines (see text).

K. Tanaka et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 670–674 673

fixed to the Doppler HWHM at 295 K. Pressure-dependentLorentz HWHM as a function of air pressure was plotted andtheir slopes were obtained. Representative results (absorp-tion line at 4152.091 cm�1) are shown in Fig. 3. The air-broadening coefficients for the six absorption lines and thevalues reported in the HITRAN 2008 and 2012 databases aresummarized in Table 2, showing discrepancies in the air-broadening coefficients for the lines at 4148.918 cm�1

between our determination and both editions of the HITRANdatabase; we see agreement for the other five absorptionlines within experimental error. In the HITRAN 2012 data-base, the absorption lines at 4149.300 cm�1, 4149.763 cm�1,4150.670 cm�1 and 4151.966 cm�1 are assigned to 13CH4,which are consistent with our experimental observations.The absorption line at 4152.091 cm�1 is assigned to 12CH4 inthe HITRAN 2012 database, although our experimentalresults show that it is originated from 13CH4. Our broadeningcoefficient for the line at 4152.091 cm�1 shows a closeagreement with that in the HITRAN 2008 database but notwith that in the HITRAN 2012 database. The broadening

Fig. 3. Lorentz half-width at half-maximum (HWHM) in cm�1 for the13CH4 absorption line at 4152.091 cm�1 as a function of total gaspressure. The buffer gas was synthetic air. The straight line is the least-squares fit, from which the pressure-broadening parameter 0.05070.008 cm�1 atm�1 is derived (1 atm¼1.013�102 kPa).

Table 2Air-broadening coefficients of absorption lines labeled by asterisks inFig. 2.

Line center a/cm�1 Air-broadening coefficient/cm�1 atm�1 b

This work HITRAN

2008 2012

4148.918 0.04170.006 0.055 –

4149.300 0.05370.008 0.055 0.0564149.763 0.05670.008 0.055 0.0564150.670 0.05270.008 0.055 0.0534151.966 0.05070.007 0.055 0.0564152.091 0.05070.008 0.055 0.041

a Reported in the HITRAN 2012 database except for the line at4148.918 cm�1 which was reported in the HITRAN 2008 database.

b 1 atm¼1.013�102 kPa.

coefficient for the line at 4148.918 cm�1 is not in agreementwith that in the HITRAN 2008 database. The reason for thediscrepancies is unclear.

Furthermore, in Table 1 there are the other fourabsorption lines in which their quantum states wereuncertain in the HITRAN 2008 database (4150.700,4150.846, 4151.042, and 4153.721 cm�1) and becomeavailable in the HITRAN 2012 database. We did observethem in the 12CH4 spectrum (Fig. 2(b)), though it wasdifficult to precisely determine the center of the absorp-tion lines because of overlap with strong neighboringabsorption lines. We roughly estimated their absorptionintensities approximately 10�23 cm2 molecule�1 cm�1,which are in reasonable agreement with those in theHITRAN 2008 and 2012 databases.

High-sensitivity laser spectroscopic detection of stableisotopomers of atmospheric molecules such as CH4 isbecoming more important as their concentrations can beused to investigate atmospheric and biological processes[19]. Here we examined well-isolated absorption line pairsof 12CH4 and 13CH4 (with an appropriate aspect ratio) withthe goal of measuring stable isotope ratios. We focused onthe two absorption lines of 13CH4 at 4151.966 cm�1 and4152.091 cm�1, as shown in Fig. 2(a) (marked region).To investigate whether these lines are well isolated fromneighboring 12CH4 lines, the aspect ratio of the line at4151.966 cm�1 to that at 4152.091 cm�1 was measured bydirect absorption spectroscopy at a total pressure of 1 kPaand as a function of the 13CH4 concentration ratio r¼{[13CH4]/([12CH4]þ[13CH4])} (Fig. 4). The aspect ratio wasfound to be almost unity within experimental error forr¼0.1–1, which suggests, at least at 1 kPa total pressure,that neighboring 12CH4 lines do not interfere significantlywith the two 13CH4 lines at 4151.966 cm�1 and 4152.091 cm�1. Accordingly, the line pair of 12CH4 at 4151.843 cm�1 and 13CH4 at 4151.966 cm�1 is a candidate fordetermining 13CH4/12CH4 ratios through spectral measure-ments using our 2.4 μm laser.

For better accuracy and precision in molecular isotoperatios using the spectroscopic approach, two additionalcriteria dictate the choice of suitable 12CH4 and 13CH4

absorption lines. First, the signals for each isotope shouldbe of similar intensity to limit non-linearities both in Beer'slaw and in the photodetectors. Thus the overall absorptions

Fig. 4. Ratios of the absorption line intensity at 4151.966 cm�1 to that at4152.091 cm�1 as a function of r¼[13CH4]/([12CH4]þ[13CH4]). The errorbars show the two-standard-deviation scatter of the experimental data.

K. Tanaka et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 133 (2014) 670–674674

of 12CH4 and 13CH4 must be similar. Second, the lowerenergy levels of the 12CH4 and 13CH4 transitions must be asclose as possible to limit temperature sensitivity. Thistemperature dependence is approximately given by

ΔT=ΔE¼Δδ=kT2 ð3Þwhere ΔT is the temperature variation, ΔE is the differencebetween the lower-state energies of the 12CH4 and 13CH4

transitions, Δδ is the corresponding precision of the deltavalue (that is a parameter to describe isotopic composition[19]), k is Boltzmann's constant, and T is the temperature[20]. According to the spectroscopic information of the linepair of 12CH4 at 4151.843 cm�1 and 13CH4 at 4151.966 cm�1

in the HITRAN 2012 database, when the temperaturechanges by þ1 K from 296 K, Δδ is estimated to be11.6‰. This result indicates that the precise control of gastemperature is necessary for determining 13CH4/12CH4

ratios. The selected line pairs have their resonance frequen-cies close enough to detect within a single scan of the laser,and the spectral window is free of atmospheric interferenceby water vapor and carbon dioxide; fortunately, both ofthese gases are relatively weak in the 2.0–2.5 μm region.

4. Conclusions

We acquired spectra of CH4 by direct absorption spectro-scopy using a Herriott-type multi-pass cell and a 2.4-μmDFBlaser. We reported the first diode laser high-resolutionabsorption spectra of 13CH4 in the 2.4 μm region. We foundthat the 13CH4 peaks observed in this work were attributedto 12CH4 in the HITRAN 2008 database with no assignedquantum states, but in the 2012 edition they were attributedto 13CH4 with assigned quantum states. There are somediscrepancies in the integrated cross-sections of observed13CH4 between our measurements and both editions of theHITRAN database, implying that detailed spectroscopicstudy (absorption line positions, ro-vibrational assignments,temperature- and pressure-dependence of absorption cross-sections) for 13CH4 is needed more. In the wavelength rangewhich our laser could cover by a current scan at a fixedtemperature, line-pairs appropriate for measuring stablecarbon isotope ratio (13CH4/12CH4) were explored. Althoughthe line-pair we found is quite sensitive to gas temperature,our study shows that in the 2.4 μm region there would beline-pairs more appropriate for isotope ratio measurementsand thus diode laser spectroscopy in this region could be atool for isotope ratio determinations.

Acknowledgments

This study was supported in part by the Japan Scienceand Technology Agency “Development of Systems andTechnology for Advanced Measurement and Analysis”

program. This work was also supported in part byGrants-in-Aid from the Ministry of Education, Culture,Sports, Science and Technology of Japan.

References

[1] Werle PW. In: Hering P, Lay JP, Stry S, editors. Laser in environ-mental and life sciences. Berlin: Springer; 2006.

[2] Seufert J, Fischer M, Legge M, Koeth J, Werner R, Kamp M, et al. DFBlaser diodes in the wavelength range from 760 nm to 2.5 μm.Spectrochim Acta A Mol Biomol Spectrosc 2004;60:3243–7.

[3] Joullié A, Christol P, Baranov AN, Vicet A. In: Sorokina IT, Vodopya-nov KL, editors. Solid-state mid infrared laser sources. Berlin:Springer; 2003.

[4] Schilt S, Vicet A, Werner R, Mattiello M, Thevenaz L, Salhi A, et al.Application of antimonide diode lasers in photoacoustic spectro-scopy. Spectrochim Acta A Mol Biomol Spectrosc 2004;60:3431–6.

[5] Salhi A, Barat D, Romanini D, Rouillard Y, Ouvrard A, Werner R, et al.Single-frequency Sb-based distributed-feedback lasers emitting at2.3 μm above room temperature for application in tunable diodelaser absorption spectroscopy. Appl Opt 2006;45:4957–65.

[6] Werle P, Maurer K, Kormann R, Mucke R, D’Amato F, Lancia T, et al.Spectroscopic gas analyzes based on indium-phosphide, antimonideand lead-salt diode-lasers. Spectrochim Acta A Mol Biomol Spectrosc2002;58:2361–72.

[7] Mattiello M, Nikles M, Schilt S, Thevenaz L, Salhi A, Barat D, et al.Novel Helmholtz-based photoacoustic sensor for trace gas detectionat ppm level using GaInSb/GaAlAsSb DFB lasers. Spectrochim Acta AMol Biomol Spectrosc 2006;63:952–8.

[8] McKellar AR. Spectroscopic tests of a 2.3 μm tunable diode laser.Spectrochim Acta A Mol Biomol Spectrosc 2006;63:959–62.

[9] Civis S, Cihelka J, Matulkova I. Infrared diode laser spectroscopy.Opto-Electron Rev 2010;18:408–20.

[10] Tanaka K, Tonokura K. Sensitive measurements of stable carbonisotopes of CO2 with wavelength modulation spectroscopy near2 μm. Appl Phys B 2011;105:463–9.

[11] Tanaka K, Kojima R, Takahashi K, Tonokura K. Continuous measure-ments of stable carbon isotopes in CO2 with a near-IR laser absorp-tion spectrometer. Infrared Phys Technol 2013;60:81–7.

[12] Kosterev AA, Curl RF, Tittel FK, Gmachl C, Capasso F, Sivco DL, et al.Methane concentration and isotopic composition measurementswith a mid-infrared quantum-cascade laser. Opt Lett 1999;24:1762–4.

[13] Anzai K, Sasada H, Yoshida N. Best pair of 3.3-μm-band transitionsfor isotopomer abundance ratio measurements of 13CH4/12CH4. Jpn JAppl Phys 2007;46:1717–21.

[14] Niederer H-M, Wang X-G, Carrington Jr T, Albert S, Bauerecker S,Boudon V, et al. Analysis of the rovibrational spectrum of 13CH4 inthe Octad range. J Mol Spectrosc 2013 (in press).

[15] Asakawa T, Kanno N, Tonokura K. Diode laser detection of green-house gases in the near-infrared region by wavelength modulationspectroscopy: pressure dependence of the detection sensitivity.Sensors 2010;10:4686–99.

[16] Rothman LS, Gordon IE, Babikov Y, Barbe A, Chris Benner D, BernathPF, et al. The HITRAN 2012 molecular spectroscopic database. JQuant Spectrosc Radiat Transfer 2013;130:4–50.

[17] Rothman LS, Gordon IE, Barbe A, Chris Benner D, Bernath PF, Birk M,et al. The HITRAN 2008 molecular spectroscopic database. J QuantSpectrosc Radiat Transfer 2009;110:533–72.

[18] Zaghloul MR. On the calculation of the Voigt line profiles: a singleproper integral with a damped sine integrated. Mon Not R AstronSoc 2007;375:1043–8.

[19] Michener R, Lajtha K, editors. Stable isotopes in ecology andenvironmental science. 2nd ed. Blackwell Publishing; 2007.

[20] Bergamaschi P, Schupp M, Harris GW. High-precision direct mea-surements of 13CH4/12CH4 and 12CH3D/12CH4 ratio in atmosphericmethane sources by means of a long-path tunable diode laserabsorption spectrometer. Appl Opt 1994;33:7704–10.