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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 3401–3407
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Modulation cancellation method for isotope 18O/16O ratio measurements in water

Vincenzo Spagnolo, Lei Dong, Anatoliy A. Kosterev, and Frank K. Tittel  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 3401-3407 (2012)
http://dx.doi.org/10.1364/OE.20.003401


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Abstract

The application of an innovative spectroscopic balancing technique to measure the isotope 18O/16O ratio in water vapor is reported. Quartz enhanced photoacoustic spectroscopy has been employed as the absorption sensing technique. Two isotope absorption lines with the same quantum numbers, with very close lower energy levels, have been selected to limit the sensitivity to temperature variations and guarantee identical broadening as well as relaxation properties. The sensitivity in measuring the deviation from a standard sample δ18O is 1.4‰, in 200 sec of integration time.

© 2012 OSA

1. Introduction

δ[]=RRstRst×1000
(1)

For isotopic characterization of samples, practically important values of δ range from ~0.1‰ to 1‰. Making such precise measurements is difficult due to the small variations in pressure, laser power and other external factors. The most common instrument for this type of measurements is a mass-spectrometer (MS). A MS provides the required precision and accuracy, but there are a number of shortcomings associated with this technology. Mass spectrometers are expensive, bulky and in general cannot be used in field applications. Moreover, a MS cannot discriminate between molecules or molecular fragments with identical masses. In addition, a MS is not compatible with condensable gases, such as water, due to instrumental limitations. Thus isotopic analysis of water requires sample pretreatment that can potentially affect the isotopic composition. Infrared molecular absorption spectroscopy is considered as a viable alternative to MS. Current optical instrumentation for determination of isotopic composition is based on precise measurements of the peak absorption or the integrated absorbance signals of lines corresponding to two isotopes with a subsequent numerical comparison [7

7. D. D. Nelson, J. B. Mcmanus, S. C. Herndon, M. S. Zahniser, B. Tuzson, and L. Emmenegger, “New method for isotopic ratio measurements of atmospheric carbon dioxide using a 4.3 μm pulsed quantum cascade laser,” Appl. Phys. B 90(2), 301–309 (2008). [CrossRef]

9

9. D. A. Long, M. Okumura, C. E. Miller, and J. T. Hodges, “Frequency-stabilized cavity ring-down spectroscopy measurements of carbon dioxide isotopic ratios,” Appl. Phys. B 105(2), 471–477 (2011). [CrossRef]

]. Hence, a small difference between isotopic compositions of the analyzed sample and the reference sample is determined as a small difference between two large numbers (concentration ratios). Sources of errors of such an approach are: the temperature and pressure dependence of the absorption line strength; non-linearity of laser tuning; baseline distortions caused by spurious interference fringes and far wings of the irrelevant strong absorption lines; and isotopic fractionation in the sampling procedure. To address these issues, we have developed a novel spectroscopic technique, the modulation cancellation method (MOCAM) that relies on the physical cancellation of the measured sensor response if R = Rst [10

10. A. A. Kosterev and R. F. Curl, “Modulation cancellation method in laser spectroscopy,” International Patent WO 2007/056772 A2 (2007).

12

12. V. Spagnolo, L. Dong, A. A. Kosterev, D. Thomazy, J. H. Doty III, and F. K. Tittel, “Modulation cancellation method in laser spectroscopy,” Appl. Phys. B 103(3), 735–742 (2011). [CrossRef]

]. In this case, the signal from the analyzed sample will be directly proportional to the deviation of the absorption line strength ratio from the reference ratio.

2. Experimental setup

For proof of concept of the use of MOCAM for isotopologue abundance quantification, we employed quartz enhanced photoacoustic spectroscopy (QEPAS) in a 2f wavelength modulation mode [13

13. A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of Quartz Tuning Forks in Spectroscopic Gas Sensing,” Rev. Sci. Instrum. 76(4), 043105 (2005). [CrossRef]

] as an absorption sensing technique and water vapor as a test analyte. There is a strong interest in water isotopic ratio measurement, since the stable isotopes of water are effective tracers to investigate the hydrological cycle, ecological processes or paleoclimatic archives. The natural abundance ratio of isotopic water is 99.756: 0.039: 0.205 for H216O, H217O and H218O [14

14. J. R. de Laeter, J. K. Bohlke, P. De Bievre, H. Hidaka, H. S. Peiser, K. J. R. Rosman, and P. D. P. Taylor, “Atomic weights of the elements. Review 2000 (IUPAC Technical Report),” Pure Appl. Chem. 75(6), 683–799 (2003). [CrossRef]

]. For our investigation, we selected the H216O and H218O isotopologues, because in geochemistry, paleoclimatology and paleoceanography δ18O, defined as a measure of the ratio of stable isotopes 18O:16O, is commonly used as a measure of the temperature of precipitation as well as a measure of groundwater/mineral interactions and as indicator of processes that show isotopic fractionation, such as methanogenesis [15

15. M. Barbour, “Stable oxygen isotope composition of plant tissue: a review,” Funct. Plant Biol. 34(2), 83–94 (2007). [CrossRef]

,16

16. K. K. Andersen, N. Azuma, J. M. Barnola, M. Bigler, P. Biscaye, N. Caillon, J. Chappellaz, H. B. Clausen, D. Dahl-Jensen, H. Fischer, J. Flückiger, D. Fritzsche, Y. Fujii, K. Goto-Azuma, K. Grønvold, N. S. Gundestrup, M. Hansson, C. Huber, C. S. Hvidberg, S. J. Johnsen, U. Jonsell, J. Jouzel, S. Kipfstuhl, A. Landais, M. Leuenberger, R. Lorrain, V. Masson-Delmotte, H. Miller, H. Motoyama, H. Narita, T. Popp, S. O. Rasmussen, D. Raynaud, R. Rothlisberger, U. Ruth, D. Samyn, J. Schwander, H. Shoji, M. L. Siggard-Andersen, J. P. Steffensen, T. Stocker, A. E. Sveinbjörnsdóttir, A. Svensson, M. Takata, J. L. Tison, T. Thorsteinsson, O. Watanabe, F. Wilhelms, and J. W. White, “High-resolution record of Northern Hemisphere climate extending into the last interglacial period,” Nature 431(7005), 147–151 (2004). [CrossRef] [PubMed]

].

The simplified architecture of the MOCAM-based QEPAS setup is shown in Fig. 1
Fig. 1 Schematic of the QEPAS-based MOCAM setup. QTF – quartz tuning fork; FC1, 2 – 50:50 optical fiber couplers; CEU-control electronics unit. f – synchronization signal from CEU.
. A 3f technique with two 99:1 fiber beam couplers and two reference tubes, each equipped with a photo-detector, are employed to lock two diode lasers, DL1 and DL2, to absorption lines belonging to two different water isotopologues, i.e., H218O and H216O, as described in [13

13. A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of Quartz Tuning Forks in Spectroscopic Gas Sensing,” Rev. Sci. Instrum. 76(4), 043105 (2005). [CrossRef]

]; We used standard water vapor to fill the reference tubes. Therefore, we employed a 10 cm-long tube for H216O (99.756%) and a 50 cm-long one for H218O (0.205%). Line locking feedback loops are not shown in Fig. 1.

Both lasers are modulated via a sinusoidal current dither at the same frequency. We select a frequency f ≈(fR+ fA)/4, where fR and fA are resonant frequencies of the two spectrophones, labeled as “Reference” (R) and “Analyzer” (A). The DL2 is mounted inside the control electronics unit (CEU) and driven by it. The CEU triggered the phase lock loop (PLL) function generator, which produces the modulation signal for DL1. The two laser beams were combined using 50:50 optical fiber couplers (FC1 OZ Optics model Fused-12-1300/1550-9/125-50/50-3A3A3A-1-0.5). Half of the optical power was used to monitor the lasers operation and check that the optical power fluctuations remain negligible for all the measurement time. Subsequently the optical emission was directed to a second 50:50 optical coupler (FC2), and the two final beams were focused into the reference and analyzer QEPAS cells. The modulation phase φ and amplitude Am are set in such a way that the QEPAS signals at 2f produced in the reference cell by the two lasers are opposite in phase and cancel each other. The detected signal UR from the reference sample is used as the error signal in a computer controlled feedback loop, which continuously adjusts modulation amplitude Am for DL1 to keep UR constant (ideally, zero).

MOCAM measurements do not require exact 50:50 power split at FC2. However, for ideal experimental conditions it is necessary that FC2 divides radiation of DL1 and DL2 between R and A channels identically. Unfortunately, the evanescent wave fiber coupler used in our experiments was wavelength selective and did not fully satisfy that requirement. The consequences of that will be described and discussed in the following sections.

3. Isotopic composition calculation

The signal produced by the reference cell under balanced conditions will be:
UR=kR(P1[H2O18]RP2[H2O16]R)=0±σR
(2)
where σR is the QTF thermal noise in the reference channel and kR describes the responsivity of the spectrophone. P1,2 is the optical power of DL1,2. [H218O]R and [H216O]R are two water isotopologue concentrations in the reference cell, The following equation is derived from Eq. (2):
P2=P1[H2O18]R[H2O16]R±σRkR[H2O16]R=P1RR±σRkR[H2O16]R
(3)
where RR = [H218O]R/[H216O]R is the isotopologue concentration ratio in the reference cell.

Assuming that the QEPAS spectrophones are similar (kRkA = k and σR≈σA = σ) and considering a small variation of H216O concentration ([H216O]A≈[H216O]R = [H216O]), we obtain:
UA=kP1[H2O16]RRδ18O11000±σR±σA==UA1RRδ18O11000±2σ
(5)
where UA1 = kP1[H216O] is the signal generated by the DL2 (resonant with H216O absorption line) when DL1 is inactive (for example, its modulation disabled). RR is known because the reference cell is filled with a calibrated sample. The 21/2 coefficient reflects the fact that the noise of the two spectrophones is uncorrelated and therefore adds up in quadrature. Thus the deviation of the sample isotopic composition from reference δ18O is expressed by the following equation:

δ18O=UAUA11000RR
(6)

In case of a natural 18O abundance RR≈1/500, it can be seen that for perfect balancing and with small δ18O, errors in δ18O are primarily determined by a weak signal UA. In case of QEPAS, fluctuations of UA are determined by thermal noise of the QTF. The unbalanced signal UA1 is much stronger, and its instability is primarily determined by the laser power fluctuations. However, these fluctuations are transferred to δ18O as its relative error. In contrast, for the traditional approach of separate measurements of two absorption lines power fluctuations impact the absolute error. For example, if δ = 10‰ which must be known to a 0.1‰ precision (1% relative error), MOCAM requires 1% UA1 error, which means 1% laser power stability. Traditional approach requires 0.1‰ = 10−4 stability for the same conditions.

If balancing is not perfect (as is the case in our experiments), then Eq. (6) changes to
δ18O=UA+UoffUA11000RR.
(7)
where Uoff is an unbalanced offset proportional to the laser power. This offset decreases the theoretical MOCAM sensitivity.

4. Results and discussion

To determine the best achievable detection sensitivity of the MOCAM-based QEPAS isotope concentration sensor we performed an Allan variance analysis [21

21. P. Werle, “Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence,” Appl. Phys. B 102(2), 313–329 (2011). [CrossRef]

], measuring and averaging sensor response under balanced conditions. The Allan plot is shown in Fig. 2
Fig. 2 Allan deviation of the δ18O as a function of integration time.
. For a 200s averaging time we achieved a minimum detection error of ~1.5 ‰ for δ18O.

The theoretically achievable sensitivity for isotopic measurements is determined from the SNR for the UA signal, since the error derived from UA1 measurements results negligible with respect to that determined by UA, being the UA1 signal much larger than UA. The technical limit of SNR/21/2 for the used control electronic unit (CEU) is ~104 Hz-1/2, corresponding to an error in δ = 0.1 ‰ for a 1 Hz bandwidth. Possible ways to improve the achievable sensitivity is to employ lasers capable of higher laser output power. Furthermore, due to not perfectly matching between the laser and the 99:1 fiber splitter, we lose half of the lasers power. Hence, by improving the laser-fiber coupling in our setup we can reach a 1 ‰ δ-value. An additional improvement can be obtained by using spectrophones employing QTFs equipped with MR. We previously demonstrated up to a factor of 30 improvement of the SNR with respect to spectrophones using bare tuning forks [19

19. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

], however, great care has to be taken to match the resonance frequencies of the two R and A cells within the resonance curves of both QTFs.

Acknowledgments

The Rice University Laser Science Group acknowledges financial support from a National Science Foundation ERC MIRTHE award and a grant C-0586 from The Welch Foundation. V. Spagnolo acknowledges financial support from the Regione Puglia “Intervento Cod. DM01, Progetti di ricerca industriale connessi con la strategia realizzativa elaborata dal Distretto Tecnologico della Meccatronica” and the II Faculty of Engineering of the Politecnico di Bari.

References and links

1.

L. Gianfrani, G. Gagliardi, M. van Burgel, and E. Kerstel, “Isotope analysis of water by means of near infrared dual-wavelength diode laser spectroscopy,” Opt. Express 11(13), 1566–1576 (2003). [CrossRef] [PubMed]

2.

E. Kerstel, G. Gagliardi, L. Gianfrani, H. Meijer, R. van Trigt, and R. Ramaker, “Determination of the 2H/1H, 17O/16O, and 18O/16O isotope ratios in water by means of tunable diode laser spectroscopy at 1.39 μm,” Spectrochim. Acta [A] 58(11), 2389–2396 (2002). [CrossRef]

3.

J. B. McManus, D. D. Nelson, J. H. Shorter, R. Jimenez, S. Herndon, S. Saleska, and M. Zahniser, “A high precision pulsed quantum cascade laser spectrometer for measurements of stable isotopes of carbon dioxide,” J. Mod. Opt. 52(16), 2309–2321 (2005). [CrossRef]

4.

D. R. Bowling, S. D. Sargent, B. D. Tanner, and J. R. Ehleringer, “Tunable diode laser absorption spectroscopy for stable isotope studies of ecosystem-atmosphere CO2 exchange,” Agric. For. Meteorol. 118(1-2), 1–19 (2003). [CrossRef]

5.

T. J. Griffis, J. M. Baker, S. D. Sargent, B. D. Tanner, and J. Zhang, “Measuring field-scale isotopic CO2 fluxes with tunable diode laser absorption spectroscopy and micrometeorological techniques,” Agric. For. Meteorol. 124(1-2), 15–29 (2004). [CrossRef]

6.

F. K. Tittel, D. Weidmann, C. Oppenheimer, and L. Gianfrani, “Laser absorption spectroscopy for volcano monitoring,” Opt. Photon. News 17(5), 24–31 (2006). [CrossRef]

7.

D. D. Nelson, J. B. Mcmanus, S. C. Herndon, M. S. Zahniser, B. Tuzson, and L. Emmenegger, “New method for isotopic ratio measurements of atmospheric carbon dioxide using a 4.3 μm pulsed quantum cascade laser,” Appl. Phys. B 90(2), 301–309 (2008). [CrossRef]

8.

L. Croizé, D. Mondelain, C. Camy-Peyret, C. Janssen, M. Lopez, M. Delmotte, and M. Schmidt, “Isotopic composition and concentration measurements of atmospheric CO2 with a diode laser making use of correlations between non-equivalent absorption cells,” Appl. Phys. B 101(1-2), 411–421 (2010). [CrossRef]

9.

D. A. Long, M. Okumura, C. E. Miller, and J. T. Hodges, “Frequency-stabilized cavity ring-down spectroscopy measurements of carbon dioxide isotopic ratios,” Appl. Phys. B 105(2), 471–477 (2011). [CrossRef]

10.

A. A. Kosterev and R. F. Curl, “Modulation cancellation method in laser spectroscopy,” International Patent WO 2007/056772 A2 (2007).

11.

V. Spagnolo, L. Dong, A. A. Kosterev, D. Thomazy, J. H. Doty 3rd, and F. K. Tittel, “Modulation cancellation method for measurements of small temperature differences in a gas,” Opt. Lett. 36(4), 460–462 (2011). [CrossRef] [PubMed]

12.

V. Spagnolo, L. Dong, A. A. Kosterev, D. Thomazy, J. H. Doty III, and F. K. Tittel, “Modulation cancellation method in laser spectroscopy,” Appl. Phys. B 103(3), 735–742 (2011). [CrossRef]

13.

A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of Quartz Tuning Forks in Spectroscopic Gas Sensing,” Rev. Sci. Instrum. 76(4), 043105 (2005). [CrossRef]

14.

J. R. de Laeter, J. K. Bohlke, P. De Bievre, H. Hidaka, H. S. Peiser, K. J. R. Rosman, and P. D. P. Taylor, “Atomic weights of the elements. Review 2000 (IUPAC Technical Report),” Pure Appl. Chem. 75(6), 683–799 (2003). [CrossRef]

15.

M. Barbour, “Stable oxygen isotope composition of plant tissue: a review,” Funct. Plant Biol. 34(2), 83–94 (2007). [CrossRef]

16.

K. K. Andersen, N. Azuma, J. M. Barnola, M. Bigler, P. Biscaye, N. Caillon, J. Chappellaz, H. B. Clausen, D. Dahl-Jensen, H. Fischer, J. Flückiger, D. Fritzsche, Y. Fujii, K. Goto-Azuma, K. Grønvold, N. S. Gundestrup, M. Hansson, C. Huber, C. S. Hvidberg, S. J. Johnsen, U. Jonsell, J. Jouzel, S. Kipfstuhl, A. Landais, M. Leuenberger, R. Lorrain, V. Masson-Delmotte, H. Miller, H. Motoyama, H. Narita, T. Popp, S. O. Rasmussen, D. Raynaud, R. Rothlisberger, U. Ruth, D. Samyn, J. Schwander, H. Shoji, M. L. Siggard-Andersen, J. P. Steffensen, T. Stocker, A. E. Sveinbjörnsdóttir, A. Svensson, M. Takata, J. L. Tison, T. Thorsteinsson, O. Watanabe, F. Wilhelms, and J. W. White, “High-resolution record of Northern Hemisphere climate extending into the last interglacial period,” Nature 431(7005), 147–151 (2004). [CrossRef] [PubMed]

17.

P. Bergamaschi, M. Schupp, and G. W. Harris, “High-precision direct measurements of 13CH4/12CH4 and 12CH3D/12CH4 ratios in atmospheric methane sources by means of a long-path tunable diode laser absorption spectrometer,” Appl. Opt. 33(33), 7704–7716 (1994). [CrossRef] [PubMed]

18.

L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf. 110(9-10), 533–572 (2009). [CrossRef]

19.

L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B 100(3), 627–635 (2010). [CrossRef]

20.

N. Petra, J. Zweck, A. A. Kosterev, S. E. Minkoff, and D. Thomazy, “Theoretical analysis of a quartz-enhanced photoacoustic spectroscopy sensor,” Appl. Phys. B 94(4), 673–680 (2009). [CrossRef]

21.

P. Werle, “Accuracy and precision of laser spectrometers for trace gas sensing in the presence of optical fringes and atmospheric turbulence,” Appl. Phys. B 102(2), 313–329 (2011). [CrossRef]

OCIS Codes
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(280.3420) Remote sensing and sensors : Laser sensors

ToC Category:
Sensors

History
Original Manuscript: October 17, 2011
Revised Manuscript: November 21, 2011
Manuscript Accepted: December 5, 2011
Published: January 30, 2012

Citation
Vincenzo Spagnolo, Lei Dong, Anatoliy A. Kosterev, and Frank K. Tittel, "Modulation cancellation method for isotope 18O/16O ratio measurements in water," Opt. Express 20, 3401-3407 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3401


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References

  1. L. Gianfrani, G. Gagliardi, M. van Burgel, and E. Kerstel, “Isotope analysis of water by means of near infrared dual-wavelength diode laser spectroscopy,” Opt. Express11(13), 1566–1576 (2003). [CrossRef] [PubMed]
  2. E. Kerstel, G. Gagliardi, L. Gianfrani, H. Meijer, R. van Trigt, and R. Ramaker, “Determination of the 2H/1H, 17O/16O, and 18O/16O isotope ratios in water by means of tunable diode laser spectroscopy at 1.39 μm,” Spectrochim. Acta [A]58(11), 2389–2396 (2002). [CrossRef]
  3. J. B. McManus, D. D. Nelson, J. H. Shorter, R. Jimenez, S. Herndon, S. Saleska, and M. Zahniser, “A high precision pulsed quantum cascade laser spectrometer for measurements of stable isotopes of carbon dioxide,” J. Mod. Opt.52(16), 2309–2321 (2005). [CrossRef]
  4. D. R. Bowling, S. D. Sargent, B. D. Tanner, and J. R. Ehleringer, “Tunable diode laser absorption spectroscopy for stable isotope studies of ecosystem-atmosphere CO2 exchange,” Agric. For. Meteorol.118(1-2), 1–19 (2003). [CrossRef]
  5. T. J. Griffis, J. M. Baker, S. D. Sargent, B. D. Tanner, and J. Zhang, “Measuring field-scale isotopic CO2 fluxes with tunable diode laser absorption spectroscopy and micrometeorological techniques,” Agric. For. Meteorol.124(1-2), 15–29 (2004). [CrossRef]
  6. F. K. Tittel, D. Weidmann, C. Oppenheimer, and L. Gianfrani, “Laser absorption spectroscopy for volcano monitoring,” Opt. Photon. News17(5), 24–31 (2006). [CrossRef]
  7. D. D. Nelson, J. B. Mcmanus, S. C. Herndon, M. S. Zahniser, B. Tuzson, and L. Emmenegger, “New method for isotopic ratio measurements of atmospheric carbon dioxide using a 4.3 μm pulsed quantum cascade laser,” Appl. Phys. B90(2), 301–309 (2008). [CrossRef]
  8. L. Croizé, D. Mondelain, C. Camy-Peyret, C. Janssen, M. Lopez, M. Delmotte, and M. Schmidt, “Isotopic composition and concentration measurements of atmospheric CO2 with a diode laser making use of correlations between non-equivalent absorption cells,” Appl. Phys. B101(1-2), 411–421 (2010). [CrossRef]
  9. D. A. Long, M. Okumura, C. E. Miller, and J. T. Hodges, “Frequency-stabilized cavity ring-down spectroscopy measurements of carbon dioxide isotopic ratios,” Appl. Phys. B105(2), 471–477 (2011). [CrossRef]
  10. A. A. Kosterev and R. F. Curl, “Modulation cancellation method in laser spectroscopy,” International Patent WO 2007/056772 A2 (2007).
  11. V. Spagnolo, L. Dong, A. A. Kosterev, D. Thomazy, J. H. Doty, and F. K. Tittel, “Modulation cancellation method for measurements of small temperature differences in a gas,” Opt. Lett.36(4), 460–462 (2011). [CrossRef] [PubMed]
  12. V. Spagnolo, L. Dong, A. A. Kosterev, D. Thomazy, J. H. Doty, and F. K. Tittel, “Modulation cancellation method in laser spectroscopy,” Appl. Phys. B103(3), 735–742 (2011). [CrossRef]
  13. A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of Quartz Tuning Forks in Spectroscopic Gas Sensing,” Rev. Sci. Instrum.76(4), 043105 (2005). [CrossRef]
  14. J. R. de Laeter, J. K. Bohlke, P. De Bievre, H. Hidaka, H. S. Peiser, K. J. R. Rosman, and P. D. P. Taylor, “Atomic weights of the elements. Review 2000 (IUPAC Technical Report),” Pure Appl. Chem.75(6), 683–799 (2003). [CrossRef]
  15. M. Barbour, “Stable oxygen isotope composition of plant tissue: a review,” Funct. Plant Biol.34(2), 83–94 (2007). [CrossRef]
  16. K. K. Andersen, N. Azuma, J. M. Barnola, M. Bigler, P. Biscaye, N. Caillon, J. Chappellaz, H. B. Clausen, D. Dahl-Jensen, H. Fischer, J. Flückiger, D. Fritzsche, Y. Fujii, K. Goto-Azuma, K. Grønvold, N. S. Gundestrup, M. Hansson, C. Huber, C. S. Hvidberg, S. J. Johnsen, U. Jonsell, J. Jouzel, S. Kipfstuhl, A. Landais, M. Leuenberger, R. Lorrain, V. Masson-Delmotte, H. Miller, H. Motoyama, H. Narita, T. Popp, S. O. Rasmussen, D. Raynaud, R. Rothlisberger, U. Ruth, D. Samyn, J. Schwander, H. Shoji, M. L. Siggard-Andersen, J. P. Steffensen, T. Stocker, A. E. Sveinbjörnsdóttir, A. Svensson, M. Takata, J. L. Tison, T. Thorsteinsson, O. Watanabe, F. Wilhelms, and J. W. White, “High-resolution record of Northern Hemisphere climate extending into the last interglacial period,” Nature431(7005), 147–151 (2004). [CrossRef] [PubMed]
  17. P. Bergamaschi, M. Schupp, and G. W. Harris, “High-precision direct measurements of 13CH4/12CH4 and 12CH3D/12CH4 ratios in atmospheric methane sources by means of a long-path tunable diode laser absorption spectrometer,” Appl. Opt.33(33), 7704–7716 (1994). [CrossRef] [PubMed]
  18. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transf.110(9-10), 533–572 (2009). [CrossRef]
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