Modulation cancellation method for isotope O/O ratio measurements in water

The application of an innovative spectroscopic balancing technique to measure the isotope O/O 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 δO is 1.4‰, in 200 sec of integration time. ©2012 Optical Society of America OCIS codes: (280.3420) Laser sensors; (140.3070) Infrared and far-infrared lasers. 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). 2. E. Kerstel, G. Gagliardi, L. Gianfrani, H. Meijer, R. van Trigt, and R. Ramaker, “Determination of the H/H, O/O, and O/O isotope ratios in water by means of tunable diode laser spectroscopy at 1.39 μm,” Spectrochim. Acta [A] 58(11), 2389–2396 (2002). 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). 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). 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). 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). 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). 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). 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). 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). 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). 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). 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). #156447 $15.00 USD Received 17 Oct 2011; revised 21 Nov 2011; accepted 5 Dec 2011; published 30 Jan 2012 (C) 2012 OSA 13 February 2012 / Vol. 20, No. 4 / OPTICS EXPRESS 3401 15. M. Barbour, “Stable oxygen isotope composition of plant tissue: a review,” Funct. Plant Biol. 34(2), 83–94 (2007). 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). 17. P. Bergamaschi, M. Schupp, and G. W. Harris, “High-precision direct measurements of CH4/ CH4 and CH3D/ CH4 ratios in atmospheric methane sources by means of a long-path tunable diode laser absorption spectrometer,” Appl. Opt. 33(33), 7704–7716 (1994). 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). 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). 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). 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).


Introduction
Isotopic composition measurements of a chemical species require determining deviation of the concentration ratio R of two related isotopes from the ratio in a reference sample R st . The most common application where such measurements are required is isotopologue abundance quantification. These measurements provide information about the sample origin, can be used for process identification or as a tracer. This is especially important in atmospheric climate and ecosystem research, volcanic emission studies and medical diagnostics [1][2][3][4][5][6][7][8][9]. For isotopologue abundance quantification, the isotopic ratio is expressed in a δ-notation as a deviation from the reference ratio: 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][8][9]. 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; nonlinearity 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 = R st [10][11][12]. 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.

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] 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.  16 O, 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 [15,16].
The simplified architecture of the MOCAM-based QEPAS setup is shown in Fig. 1. 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., H 2 18 O and H 2 16 O, as described in [13]; We used standard water vapor to fill the reference tubes. Therefore, we employed a 10 cmlong tube for H 2 16 O (99.756%) and a 50 cm-long one for H 2 18 O (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 ≈(f R + f A )/4, where f R and f A 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 A m 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 U R from the reference sample is used as the error signal in a computer controlled feedback loop, which continuously adjusts modulation amplitude A m for DL1 to keep U R 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.

Isotopic composition calculation
The signal produced by the reference cell under balanced conditions will be: where σ R is the QTF thermal noise in the reference channel and k R describes the responsivity of the spectrophone. P 1,2 is the optical power of DL where where U A1 = kP 1 [H 2 16 O] is the signal generated by the DL2 (resonant with H 2 16 O absorption line) when DL1 is inactive (for example, its modulation disabled). R R is known because the reference cell is filled with a calibrated sample. The 2 1/2 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 δ 18 O is expressed by the following equation: In case of a natural 18 O abundance R R ≈1/500, it can be seen that for perfect balancing and with small δ 18 O, errors in δ 18 O are primarily determined by a weak signal U A . In case of QEPAS, fluctuations of U A are determined by thermal noise of the QTF. The unbalanced signal U A1 is much stronger, and its instability is primarily determined by the laser power fluctuations. However, these fluctuations are transferred to δ 18 O 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% U A1 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 18 1

.
A off where U off is an unbalanced offset proportional to the laser power. This offset decreases the theoretical MOCAM sensitivity.

Results and discussion
The temperature dependence of δ 18 O is proportional to the difference of ground-state energies ∆E of the selected isotope transitions [17]: where k is the Boltzmann constant and T is the absolute temperature. Thus, the selection of absorption lines for a pair of isotopes require that the related lower energy levels are as close as possible, to limit the sensitivity of the measurement to temperature variations, and also that they have the same quantum numbers, so as to guarantee identical broadening and relaxation properties. The concentration ratio 16  The optical powers of DL1 and DL2 passing through the two spectrophones were 5.6 mW and 1 mW, respectively. We employed sealed QEPAS cells with a volume of ~1.3 cm 3 . Before each measurements we evacuated the two cells to remove any residual water. Next we filled the cells with water vapor samples, sealed them and performed the measurements at room temperature at a corresponding saturated vapor pressure of 20 Torr. The resonance frequencies for the two QTFs must be as close as possible, since the two lasers must be modulated at the same frequency and this frequency must fall within the resonance curves of both QTFs. Since the resonance curves of QTFs are very narrow (< 1 Hz) at 20 torr, spectrophones with a bare tuning fork, i.e. without micro-resonator (MR) tubes were used, since adding a MR to a QTF can result in a shift of several Hz of the QTF resonant frequency [19]. The resonance frequency of the reference spectrophone was 32.763,80 Hz, while that of the sample spectrophone was 32.763,17 Hz. The FWHM of the two resonance curves [20] was ~0.65 Hz, so that the two bandwidths overlapped. Therefore we chose to drive the lasers at half of the average resonant frequency of 32.763,48 Hz (f=16381.74 Hz), because the laser frequency crosses the absorption lines twice per cycle.
Initially, both R and A spectrophones contain the same reference water sample, and the signal from R was balanced out. However, it was observed that the signal measured from the lock-in amplifier from A was not zero for these conditions, because of the wavelength selectivity of FC2. The unbalance was ~12 µV corresponding of ~4% of the full DL1-induced signal. Therefore, we re-adjusted A m to set the signal in the A channel equal to zero. This procedure resulted in a non-zero U R signal, and a computer-controlled feedback loop was set to maintain this signal at constant level. In this way Eq. (6) remains valid, although sensitive to variations of laser power in the reference channel. Next we filled the A cell with calibrated water samples and compared the estimated δ 18 O with that obtained using Eq. (6) 2 18 O, that is not completely removed by the evacuation procedure. For the second sample we obtained a good correlation between the expected and measured values for δ 18 O. We measured δ 18 O = 52900±260 ‰, with a relative deviation of 0.3% from the expected value of 53068 ‰. Besides random errors related to the laser power and balancing fluctuations, our result contains systematic error because of dilution of the isotopically enriched water vapor sample by residual moisture in the gas system.
To determine the best achievable detection sensitivity of the MOCAM-based QEPAS isotope concentration sensor we performed an Allan variance analysis [21], measuring and averaging sensor response under balanced conditions. The Allan plot is shown in Fig. 2. For a 200s averaging time we achieved a minimum detection error of ~1.5 ‰ for δ 18 O. The main sources of error result from laser power fluctuations. The feedback loop for balancing is based on a Labview control program with ~1 Hz bandwidth. The initial growth from 1 to 4s reflects delay and the related oscillations in the feedback loop when balancing the signal of the reference channel. The program will set a small limit window. When the error signal is outside of the limit window, the modulation voltage will be automatically adjusted by sending a command signal to the CEU to either increase or decrease the minimum step size of 0.01 V in order to adjust the error signal within the limit window and maintain the reference channel balanced. The resolution of the 0.01 V for modulation voltage and 1 Hz correction frequency limit the feedback loop performance. If a faster, continuous PID realtime control feedback loop is available instead of a digital correction method with a limited window setting, it will compensate the temporal variation of the laser power and further lower the noise level. Another source of error results from the non-optimal configuration since the signal in the R channel is not zero but exceeds the thermal noise of by a factor 2 (the thermal noise is 6.4µV) in a 0.785 Hz detection bandwidth, which is set by the internal CEU digital filters and is applicable when the data are read every 1 s without additional averaging.
The theoretically achievable sensitivity for isotopic measurements is determined from the SNR for the U A signal, since the error derived from U A1 measurements results negligible with respect to that determined by U A , being the U A1 signal much larger than U A. The technical limit of SNR/2 1/2 for the used control electronic unit (CEU) is ~10 4 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], 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.