OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 19993–20002
« Show journal navigation

Application of cavity ring-down spectroscopy to the Boltzmann constant determination

Y. R. Sun, H. Pan, C.-F. Cheng, A.-W. Liu, J.-T. Zhang, and S.-M. Hu  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 19993-20002 (2011)
http://dx.doi.org/10.1364/OE.19.019993


View Full Text Article

Acrobat PDF (1043 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The Boltzmann constant can be optically determined by measuring the Doppler width of an absorption line of molecules at gas phase. We propose to apply a near infrared cavity ring-down (CRD) spectrometer for this purpose. The superior sensitivity of CRD spectroscopy and the good performance of the near-ir lasers can provide ppm (part-per-million) accuracy which will be competitive to present most accurate result obtained from the speed of sound in argon measurement. The possible influence to the uncertainty of the determined Doppler width from different causes are investigated, which includes the signal-to-noise level, laser frequency stability, detecting nonlinearity, and pressure broadening effect. The analysis shows that the CRD spectroscopy has some remarkable advantages over the direct absorption method proposed before. The design of the experimental setup is presented and the measurement of C2H2 line near 0.8 μm at room temperature has been carried out as a test of the instrument.

© 2011 OSA

1. Introduction

The group in Université Paris 13 (France) has obtained kB with uncertainty of 2 × 10−4 using a stabilized CO2 laser to measure an absorption line of NH3 at λ ≈ 10 μm [2

2. C. Daussy, M. Guinet, A. Amy-Klein, K. Djerroud, Y. Hermier, S. Briaudeau, C. J. Bordé, and C. Chardonnet, “Direct determination of the boltzmann constant by an optical method,” Phys. Rev. Lett. 98, 250801 (2007). [CrossRef] [PubMed]

]. They have improved the accuracy to 3.8 × 10−5 using a multi-pass cell to increase the signal-to-noise ratio (SNR) at lower sample gas pressure (below 1 Pa) [6

6. K. Djerroud, C. Lemarchand, A. Gauguet, C. Daussy, S. Briaudeau, B. Darquie, O. Lopez, A. Amy-Klein, C. Chardonnet, and C. J. Borde, “Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8 × 10−5 accuracy level,” C. R. Physique 10, 883–893 (2009). [CrossRef]

] and approached to several ppm (part per million) level very recently [7

7. C. Lemarchand, M. Triki, B. Darquié, Ch. J. Bordé, C. Chardonnet, and C. Daussy, “Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy,” New J. Phys.13, 073028 (2011). [CrossRef]

]. The Italian group at Caserta applied a distributed feed back (DFB) diode laser to measure the absorption line of CO2 at 2 μm and determined kB with uncertainty of 1.6 × 10−4 [5

5. G. Casa, A. Castrillo, G. Galzerano, R. Wehr, A. Merlone, D. Di Serafino, P. Laporta, and L. Gianfrani, “Primary gas thermometry by means of laser-absorption spectroscopy: Determination of the boltzmann constant,” Phys. Rev. Lett. 100, 200801 (2008). [CrossRef] [PubMed]

]. They proposed to improve the accuracy by measuring the water absorption lines at the 1.4 μm region [8

8. A. Castrillo, G. Casa, A. Merlone, G. Galzerano, P. Laporta, and L. Gianfrani, “On the determination of the Boltzmann constant by means of precision molecular spectroscopy in the near-infrared,” C. R. Physique 10, 894–906 (2009). [CrossRef]

]. Yamada et al. proposed to measure a line of 13C2H2 in the near-ir region using a comb-stabilized diode laser [9

9. K. M. T. Yamada, A. Onae, F. L. Hong, H. Inaba, H. Matsumoto, Y. Nakajima, F. Ito, and T. Shimizu, “High precision line profile measurements on C-13 acetylene using a near infrared frequency comb spectrometer,” J. Mol. Spectorsc. 249, 95–99 (2008). [CrossRef]

, 10

10. K. M. T. Yamada, A. Onae, F.-L. Hong, H. Inaba, and T. Shimizu, “Precise determination of the Doppler width of a rovibrational absorption line using a comb-locked diode laser,” C. R. Physique 10, 907–915 (2009). [CrossRef]

].

CRDS has been introduced by O’Keefe and Deacon in 1988 [13

13. A. O’Keefe and D. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–51 (1988). [CrossRef]

] and a historic review of CRDS can be found in Ref. [14

14. B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys. 83, 975–999 (2005). [CrossRef]

]. The main idea of CRDS is to measure the decay rate of the laser light inside a resonant cavity composed of two high-reflectivity mirrors. The absorption coefficient of the sample gas can be obtained by measuring the “ring-down time” of a single frequency laser pulse injected into the cavity. Using an optimized cw-CRDS setup [12

12. B. Gao, W. Jiang, A.-W. Liu, Y. Lu, C.-F. Cheng, G.-S. Cheng, and S.-M. Hu, “Ultra sensitive near-infrared cavity ring down spectrometer for precise line profile measurement,” Rev. Sci. Instrum. 81, 043105 (2010). [CrossRef] [PubMed]

], we has shown that the minimal detectable absorption coefficient αmin can be as low as 7 × 10−11/cm. Consequently, for an absorption line with α ≃ 10−6/cm (typical intensity of a strong molecular line in the near-ir), it is possible to determine the α value with uncertainty below 10−5. Meanwhile, in order to determine the Doppler width of a molecular absorption line with ppm accuracy, it is also necessary to achieve sufficient frequency precision in the spectral scanning. This can be accomplished by using CRDS based on a frequency-locked laser. As will be shown in the Experimental Section, by locking the laser frequency to a thermo-stabilized etalon and using a scanning sideband as the light source of the CRDS, sub-kHz frequency accuracy can be achieved. A different approach of the frequency-stabilized CRDS has been established by Hodges et al. by locking the length of the ring-down cavity to a stabilized reference laser [15

15. J. T. Hodges, H. P. Layer, W. W. Miller, and G. E. Scace, “Frequency-stabilized single-mode cavity ring-down apparatus for high-resolution absorption spectroscopy,” Rev. Sci. Instrum. 75, 849–863 (2004). [CrossRef]

, 16

16. J. T. Hodges and R. Ciurylo, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum. 76, 023112 (2005). [CrossRef]

]. The spectrometer has been applied for various quantitative measurements including the sub-Doppler hyperfine structure measurements of O2 molecule [17

17. D. A. Long, D. K. Havey, M. Okumura, C. E. Miller, and J. T. Hodges, “Cavity ring-down spectroscopy measurements of sub-doppler hyperfine structure,” Phys. Rev. A 81, 064502 (2010). [CrossRef]

]. Very recently, they also locked the laser frequency to the stabilized ring-down cavity to increase the ring-down event acquisition rates and a minimal detectable absorption coefficient αmin of 2 × 10−10/cm has been achieved [18

18. A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-drever-hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011). [CrossRef] [PubMed]

]. They also mentioned the possibility to apply the frequency-stabilized CRDS for the determination of the Boltzmann constant.

In the following sections, the error budget in determining the γD value in a CRDS measurement will be discussed and the experimental method toward ppm level accuracy kB determination will be presented. Measurements of the C2H2 788 nm line at room temperature will be given as a demonstration of the present CRD spectrometer.

2. CRDS measurement error analysis

In CRDS, the decay rate 1/τ of the emitted light is proportional to the total optical losses inside the cavity, where τ is the “ring-down time” [19

19. P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995). [CrossRef]

]:
τ=L/clnR+αL
(2)
L is the length of the cavity, c is the speed of light, R is the reflectivity of a cavity mirror, and α is the sample absorption coefficient. α can be determined using Eq. (2):
α=1cτ+lnRL
(3)

Typically, using a pair of mirrors with reflectivity higher than 99.99% and a cavity of about 1 m long, the ring-down time τ will be of several tens micro-seconds. Since the lnRL term can be treated in the baseline, the absorption line profile can be obtained by fitting the measured curve 1cτ.

The accuracy of the CRDS measurement is mainly limited by the noise level and frequency jitters during scanning. The causes contribute to the deviation in the Doppler line width are given below.

Frequency uncertainty: The line width derived from the fitting of experimental spectrum is perturbed by the experimental noise resulting from the measurements of the absorbance and frequency. The frequency measurement contributes directly an uncertainty to the determination of line width. A simulation of the uncertainty contribution by frequency measurement is illustrated in Fig. 1. The deviation in the line width is presented as the relative value: γD/γD°1, where γD is the Doppler width derived from the fitting of the simulation spectra, γD° is the physical true value of γD. Apparently, to achieve an accuracy of 10−6 level in the line width, comparative frequency accuracy is necessary. For an absorption line in the near infrared region, the Doppler width of a light molecule like C2H2 is about 1 GHz. In this case, it is necessary to apply a laser source with frequency stability better than 10 kHz, which is moderate for a frequency-stabilized diode laser.

Fig. 1 Relative deviations in γD resulting from the noise level and frequency uncertainty.

Absorbance uncertainty, signal-to-noise ratio: For a direct absorption measurement, the vertical noise mainly results from the laser power instability, which is typically at a level of 0.01% – 0.1% [20

20. M. D. De Vizia, F. Rohart, ccedil ois, A. Castrillo, E. Fasci, L. Moretti, and L. Gianfrani, “Speed-dependent effects in the near-infrared spectrum of self-colliding h2o18 molecules,” Phys. Rev. A 83, 052506 (2011). [CrossRef]

, 21

21. R. Wehr, J. R. Drummond, and A. D. May, “Design of a difference-frequency infrared laser spectrometer for absorption line-shape studies,” Applied Optics 46, 978–985 (2007). [CrossRef] [PubMed]

]. Such noise will directly contribute to an uncertainty to the determination of line width. To illustrate the influence by the experimental noise, we simulated a group of spectra with random noise at different SNR level, and the relative deviation in γD are presented in Fig. 1. As shown in the figure, only when SNR is better than 30,000, the γD accuracy can possibly reach the 1 ppm level, thus to determine the Boltzmann constant with a competitive accuracy by the optical Doppler width measurement. Since the cavity ring down spectroscopy is immune to the power fluctuation of the light source and has very large dynamic region, it is ideal for this application. In CRDS measurement, the SNR level is mainly governed by the stability of the cavity loss. As shown in Eq. (2), it results from the fluctuations in the cavity length, the mirror reflectivity, and the speed of light (change of the refractive index). In a CRDS measurement with sample pressure below 10 Pa, drift of the refractive index can be well below 10−8. We have achieved noise equivalent absorption coefficient of 7 × 10−11/cm using a ring-down cavity with temperature fluctuation about 1 K [12

12. B. Gao, W. Jiang, A.-W. Liu, Y. Lu, C.-F. Cheng, G.-S. Cheng, and S.-M. Hu, “Ultra sensitive near-infrared cavity ring down spectrometer for precise line profile measurement,” Rev. Sci. Instrum. 81, 043105 (2010). [CrossRef] [PubMed]

]. According to Eq. (2), the drift of the cavity length L due to temperature fluctuation will result in the drift of the measured decay time τ. In other word, it is possible to significantly improve the SNR if the whole ring-down cavity can be thermo-stabilized to 1 mK. In this case, a SNR at the 105 level will be achievable for an absorption line with strength over 1 × 10−6/cm which is moderate for a near-ir molecular line.

Pressure dependence: A detailed theory of the absorption line shape of low-pressure gases has been presented recently by Bordé [22

22. C. J. Borde, “On the theory of linear absorption line shapes in gases,” C. R. Physique 10, 866–882 (2009). [CrossRef]

]. Cygan et al. pointed out that the collisional line width can introduce systematic error when pursuing Doppler limited line width even at very low pressure [11

11. A. Cygan, D. Lisak, R. S. Trawiński, and R. Ciuryło, “Influence of the line-shape model on the spectroscopic determination of the boltzmann constant,” Phys. Rev. A 82, 032515 (2010). [CrossRef]

]. The measurement of NH3 line at the 10.3 μm region carried out by Daussy et al. [2

2. C. Daussy, M. Guinet, A. Amy-Klein, K. Djerroud, Y. Hermier, S. Briaudeau, C. J. Bordé, and C. Chardonnet, “Direct determination of the boltzmann constant by an optical method,” Phys. Rev. Lett. 98, 250801 (2007). [CrossRef] [PubMed]

] with 1 – 10 Pa sample gas will include a systematic error of a few ppm. The use of a near-ir line can help to reduce this error, partly because the Doppler width increases linearly with the line frequency while the collisional line width does not. Regardless of the adopted model of the collisional line profile, linear extrapolation of the fitted Doppler width values to zero pressure can give good Doppler width value with accuracy better than 10−6 [11

11. A. Cygan, D. Lisak, R. S. Trawiński, and R. Ciuryło, “Influence of the line-shape model on the spectroscopic determination of the boltzmann constant,” Phys. Rev. A 82, 032515 (2010). [CrossRef]

]. To investigate this effect in proposed CRDS measurements, spectra of C2H2 at 788 nm with sample pressure varying from 0.1 Pa to 60 Pa have been simulated with Voigt line profile. When fitting the spectra with pure Gaussian profile, the deviations of the retrieved line width γD to the true value γD° are plotted in Fig. 2. Note that the relative deviation is at the level of 10−4 at a sample pressure of 10 Pa. After extrapolation of the line width values to zero pressure, the relative deviation of the Doppler width at zero pressure is well below 2 × 10−7.

Fig. 2 Relative deviation on the Doppler line width from spectrum recorded with different sample pressure. The linear fit gives the extrapolation to the zero pressure limit.

Nonlinearity: Note that any nonlinearity in the detecting scheme will distort the experimental spectrum and bring direct influence on the accuracy of the retrieved linewidth. Moreover, such nonlinearity may introduce a systematic deviation which does not decrease after averaging. In this case, it is necessary to make sure that the instrumental nonlinearity is either negligible (for instance, below the noise level) or can be compensated. The cw-CRDS spectrometer also has the advantage of excellent linearity over a very large dynamic region of the absorption coefficient since the variation of the ring-down time instead of the absorption depth is measured in the CRDS experiment. Simulation of the CRDS result has been carried out assuming that the detector (or the amplifier) has a fixed nonlinearity,
I=I0+δI02
(4)
where I0 is the true signal while I′ is the detected (distorted) signal, δ is the nonlinearity coefficient. The ring-down signal was normalized to the one at the beginning of the ring-down (t = 0) for simplicity. The nonlinearity brings distortion on the measured ring-down curve. It imposes critical influence on the signal height. But the ring-down time τ′ derived from the single-exponential fitting of the ring-down curve is still proportional to the true τ value with an almost fixed factor with a given nonlinear coefficient. In this case, the “measured” absorption line will has a line profile almost same as the true one, except that the line intensity is distorted. So the derived line width value is only perturbed with a much smaller amount. The relative deviation on the line width with a given nonlinear coefficient is plotted in Fig. 3. As a comparison, we also simulated direct absorption measurement with nonlinearity similar to the one given in Eq. (4). In the simulation, the transmission signal was normalized to the one without absorption and the absorbance at the line center was assumed to be 10%. In a direct absorption measurement, the nonlinearity in the detection brings direct influence to the line profile and the line width value derived from the fitting to the profile. For illusion, the relative deviation in the line width due to nonlinearity in direct absorption measurements is also plotted in Fig. 3. As shown in the figure, under the same nonlinearity in the detection, the influence to the CRDS measurement can be about two orders of magnitude smaller than the influence to a standard direct absorption measurement. However, because fast detection with bandwidth over several MHz is necessary in CRDS, which is usually much faster than that in the direct absorption measurement, the nonlinear effect is still need to be carefully investigated in quantitative CRDS measurement. Nevertheless, 1 ppm accuracy in line width determination is achievable when the nonlinearity is below 1% in CRDS.

Fig. 3 Relative deviations in the determined line width with different nonlinearity coefficients in the detection, for direct absorption measurement (upper) and for cavity ring-down measurement (lower).

3. Experimental

3.1. Optical layout

Fig. 4 Schematics of a frequency-stabilized CRDS setup. AOM: acousto-optic modulator; EOM: electro-optic modulator. DAQ: Data acquisition card.

3.2. Ring-down cavity: temperature control

According to Eq. (1), the measurement for the temperature of gas sample in the cavity contributes an uncertainty to the redetermination of kB. The ring-down cavity comprises a cylinder of stainless steel in a diameter of about 25 mm and a length 600 mm. The uncertainty by temperature measurement is produced by the following causes. The first is the fluctuation and the non-uniformity of the temperature on the cylinder during the period probing the Doppler width. This uncertainty contribution is governed by the thermal environment around the cylinder. The temperature non-uniformity appears a cause deserving a careful treatment. The cylindrical cavity has an optical path through both ends for the admitting laser beam. There are a gas fill duct on the cavity, and three thermometry wells in the cavity to house the capsule standard platinum thermometers (CSPRTs). These components comprise the paths of heat leak and yield disturbances to the temperature uniformity.

One of the authors has practical experience of using high stable thermostat of a stability of 0.05 mK per 24 hours [23

23. J. T. Zhang, H. Lin, J. P. Sun, X. J. Feng, K. A. Gillis, and M. R. Moldover, “Cylindrical acoustic resonator for the re-determination of the boltzmann constant,” Int. J. Thermophys. 31, 1273–1293 (2010). [CrossRef]

]. Base on the experience, We has designed a thermostat consisting of a vacuum jacket for the cavity. The outer cylindrical container is cooled by the methanol to hold the temperature 2.5 °C below the objective triple point of water for the ring-down cavity. The inner wall of the container is gold plated to diminish thermal radiation. An active radiation shield is set between the cavity and the out container. Both sides of the shield are gold plated to increase their reflection to thermal radiations from both the cavity and the inner wall of the container. A line heater is installed on the outside of the shield. The shield is heated to track the temperature of the cavity. The wire of the heater shall have an optimal distribution based on a heat transfer simulation to achieve satisfied temperature uniformity. The temperature difference between the shield and the cavity is controlled within 1 mK. The leads of thermometers and the gas duct for the cavity are thermally anchored on the shield to diminish heat leak from those paths. The outside wall of the cavity is also gold plated to reduce the thermal radiation. The space housing the cavity and the shield is filled with pure argon at beginning to let the cavity and the shield quickly approximate the objective temperature. Once the triple point of water is approximated, the space is evacuated. Therefore, the left paths for heat leaks are thermal radiation and conduction. Both paths are controlled to their minimum by tracking the temperature of the shield to that of the cavity.

3.3. 12C2H2 788 nm line measured at room temperature

To demonstrate the viability of CRDS for precise Doppler width measurement, we performed CRDS measurement of an absorption line of acetylene near 788 nm at room temperature. The line at 12696.4 cm−1 is the R(9) line of the ν1 + 3ν3 band of 12C2H2. This band has been reported by Zhan and Halenon using photoacoustic spectroscopy [24

24. X. Zhan and L. Halonen, “High-resolution photoacoustic study of the ν1 + 3ν3 band system of acetylene with a titanium:sapphire ring laser,” J. Mol. Spectorsc. 160, 464 (1993). [CrossRef]

]. The C2H2 line near 788 nm is over 10 times stronger than the O2 line near 687 nm proposed by Cygan et al. [11

11. A. Cygan, D. Lisak, R. S. Trawiński, and R. Ciuryło, “Influence of the line-shape model on the spectroscopic determination of the boltzmann constant,” Phys. Rev. A 82, 032515 (2010). [CrossRef]

] In this case, measurement with lower sample pressure is possible. In addition, because the atmospheric absorption is negligible in this spectral region, it avoids any possible interference from air in the open optical path or trace water vapor in the ring-down cavity. Our simulation shows that SNR of about 105 is achievable with C2H2 sample gas pressure of 0.1 – 10 Pa.

The ring-down cavity was directly placed on an optical table and the spectra with acetylene sample gas pressure ranging from 0.5 Pa to 3 Pa were recorded. The spectrum with 0.5 Pa sample is presented in Fig. 5 (left panel). The spectrum can be well fitted by a Gaussian profile and the fitting residual is also shown in Fig. 5. The line width (FWHM) γD obtained from the fitting was used to retrieve the sample gas temperature following Eq. (1). The temperature values obtained from each recorded spectrum are also shown in Fig. 5 (right panel). The determined sample temperature is 298.7 ± 0.6 K which agrees with the readout from a thermometer used to monitor the room temperature. The present accuracy 2 × 10−3 is limited by the temperature fluctuation of the sample cell during the measurement since no temperature-stabilizing has been applied in present experiment. That is why the present accuracy is lower than those reported in Refs. [2

2. C. Daussy, M. Guinet, A. Amy-Klein, K. Djerroud, Y. Hermier, S. Briaudeau, C. J. Bordé, and C. Chardonnet, “Direct determination of the boltzmann constant by an optical method,” Phys. Rev. Lett. 98, 250801 (2007). [CrossRef] [PubMed]

, 5

5. G. Casa, A. Castrillo, G. Galzerano, R. Wehr, A. Merlone, D. Di Serafino, P. Laporta, and L. Gianfrani, “Primary gas thermometry by means of laser-absorption spectroscopy: Determination of the boltzmann constant,” Phys. Rev. Lett. 100, 200801 (2008). [CrossRef] [PubMed]

, 6

6. K. Djerroud, C. Lemarchand, A. Gauguet, C. Daussy, S. Briaudeau, B. Darquie, O. Lopez, A. Amy-Klein, C. Chardonnet, and C. J. Borde, “Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8 × 10−5 accuracy level,” C. R. Physique 10, 883–893 (2009). [CrossRef]

, 8

8. A. Castrillo, G. Casa, A. Merlone, G. Galzerano, P. Laporta, and L. Gianfrani, “On the determination of the Boltzmann constant by means of precision molecular spectroscopy in the near-infrared,” C. R. Physique 10, 894–906 (2009). [CrossRef]

] where temperature stabilized sample cells were used. A chamber with temperature stabilized within 1 mK at the triple point of water is under construction and a dramatic improvement of the accuracy is expected when the ring-down cell is installed in the temperature-stabilized chamber. The residual shown in Fig. 5 also implies the Gaussian profile adopted in the fitting may be oversimplified. As discussed in Refs. [22

22. C. J. Borde, “On the theory of linear absorption line shapes in gases,” C. R. Physique 10, 866–882 (2009). [CrossRef]

, 11

11. A. Cygan, D. Lisak, R. S. Trawiński, and R. Ciuryło, “Influence of the line-shape model on the spectroscopic determination of the boltzmann constant,” Phys. Rev. A 82, 032515 (2010). [CrossRef]

], more proper treating of the line profile can further improve the accuracy for spectrum with higher SNR.

Fig. 5 Spectrum of a 12C2H2 line near 788 nm at the room temperature. Left panel: observed and simulated spectrum (upper) and the fitting residual (lower). Right panel: temperature values derived from the Gaussian widths of a series of spectrum obtained with different sample gas pressure.

4. Summary

We have explored the possibility to apply a near infrared cavity ring-down spectrometer to the determination of the Boltzmann constant by measuring the Doppler width of a molecular absorption line. Compared with the direct absorption measurement in the mid-infrared region, the signal-to-noise level can be raised to the 10−5 level, the influence from detecting nonlinearity will be negligible, and the enhanced sensitivity will compensate the loss in the molecular absorption strength due to switching from the mid-infrared to the near infrared. Using a diode laser with frequency stabilized to sub-10 kHz level and a ring-down cavity with temperature stabilized to 1 mK, measuring the Doppler width of the absorption line of C2H2 near 0.8 um, we expect an optical determination of the Boltzmann constant to the ppm accuracy. Since compact near infrared diode laser can be applied, the instrument can be developed as a portable universal gas thermometry if the Boltzmann constant is fixed.

Acknowledgments

This work is jointly supported by NSFC ( 90921006, 20903085 & 20873132), by NKBRSF ( 2007CB815203) and by the Fundamental Research Funds for the Central Universities.

References and links

1.

I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor, and E. R. Williams, “Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing cipm recommendation 1 (ci-2005),” Metrologia 43, 227–246 (2006). [CrossRef]

2.

C. Daussy, M. Guinet, A. Amy-Klein, K. Djerroud, Y. Hermier, S. Briaudeau, C. J. Bordé, and C. Chardonnet, “Direct determination of the boltzmann constant by an optical method,” Phys. Rev. Lett. 98, 250801 (2007). [CrossRef] [PubMed]

3.

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]

4.

P. J. Mohr, B. N. Taylor, and D. B. Neweo, “CODATA recommended values of the fundamental physical constants: 2006,” J. Phys. Chem. Ref. Data 37, 1187–1284 (2008). [CrossRef]

5.

G. Casa, A. Castrillo, G. Galzerano, R. Wehr, A. Merlone, D. Di Serafino, P. Laporta, and L. Gianfrani, “Primary gas thermometry by means of laser-absorption spectroscopy: Determination of the boltzmann constant,” Phys. Rev. Lett. 100, 200801 (2008). [CrossRef] [PubMed]

6.

K. Djerroud, C. Lemarchand, A. Gauguet, C. Daussy, S. Briaudeau, B. Darquie, O. Lopez, A. Amy-Klein, C. Chardonnet, and C. J. Borde, “Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8 × 10−5 accuracy level,” C. R. Physique 10, 883–893 (2009). [CrossRef]

7.

C. Lemarchand, M. Triki, B. Darquié, Ch. J. Bordé, C. Chardonnet, and C. Daussy, “Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy,” New J. Phys.13, 073028 (2011). [CrossRef]

8.

A. Castrillo, G. Casa, A. Merlone, G. Galzerano, P. Laporta, and L. Gianfrani, “On the determination of the Boltzmann constant by means of precision molecular spectroscopy in the near-infrared,” C. R. Physique 10, 894–906 (2009). [CrossRef]

9.

K. M. T. Yamada, A. Onae, F. L. Hong, H. Inaba, H. Matsumoto, Y. Nakajima, F. Ito, and T. Shimizu, “High precision line profile measurements on C-13 acetylene using a near infrared frequency comb spectrometer,” J. Mol. Spectorsc. 249, 95–99 (2008). [CrossRef]

10.

K. M. T. Yamada, A. Onae, F.-L. Hong, H. Inaba, and T. Shimizu, “Precise determination of the Doppler width of a rovibrational absorption line using a comb-locked diode laser,” C. R. Physique 10, 907–915 (2009). [CrossRef]

11.

A. Cygan, D. Lisak, R. S. Trawiński, and R. Ciuryło, “Influence of the line-shape model on the spectroscopic determination of the boltzmann constant,” Phys. Rev. A 82, 032515 (2010). [CrossRef]

12.

B. Gao, W. Jiang, A.-W. Liu, Y. Lu, C.-F. Cheng, G.-S. Cheng, and S.-M. Hu, “Ultra sensitive near-infrared cavity ring down spectrometer for precise line profile measurement,” Rev. Sci. Instrum. 81, 043105 (2010). [CrossRef] [PubMed]

13.

A. O’Keefe and D. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544–51 (1988). [CrossRef]

14.

B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys. 83, 975–999 (2005). [CrossRef]

15.

J. T. Hodges, H. P. Layer, W. W. Miller, and G. E. Scace, “Frequency-stabilized single-mode cavity ring-down apparatus for high-resolution absorption spectroscopy,” Rev. Sci. Instrum. 75, 849–863 (2004). [CrossRef]

16.

J. T. Hodges and R. Ciurylo, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum. 76, 023112 (2005). [CrossRef]

17.

D. A. Long, D. K. Havey, M. Okumura, C. E. Miller, and J. T. Hodges, “Cavity ring-down spectroscopy measurements of sub-doppler hyperfine structure,” Phys. Rev. A 81, 064502 (2010). [CrossRef]

18.

A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-drever-hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum. 82, 063107 (2011). [CrossRef] [PubMed]

19.

P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995). [CrossRef]

20.

M. D. De Vizia, F. Rohart, ccedil ois, A. Castrillo, E. Fasci, L. Moretti, and L. Gianfrani, “Speed-dependent effects in the near-infrared spectrum of self-colliding h2o18 molecules,” Phys. Rev. A 83, 052506 (2011). [CrossRef]

21.

R. Wehr, J. R. Drummond, and A. D. May, “Design of a difference-frequency infrared laser spectrometer for absorption line-shape studies,” Applied Optics 46, 978–985 (2007). [CrossRef] [PubMed]

22.

C. J. Borde, “On the theory of linear absorption line shapes in gases,” C. R. Physique 10, 866–882 (2009). [CrossRef]

23.

J. T. Zhang, H. Lin, J. P. Sun, X. J. Feng, K. A. Gillis, and M. R. Moldover, “Cylindrical acoustic resonator for the re-determination of the boltzmann constant,” Int. J. Thermophys. 31, 1273–1293 (2010). [CrossRef]

24.

X. Zhan and L. Halonen, “High-resolution photoacoustic study of the ν1 + 3ν3 band system of acetylene with a titanium:sapphire ring laser,” J. Mol. Spectorsc. 160, 464 (1993). [CrossRef]

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(120.3940) Instrumentation, measurement, and metrology : Metrology
(300.6360) Spectroscopy : Spectroscopy, laser

ToC Category:
Spectroscopy

History
Original Manuscript: June 27, 2011
Revised Manuscript: August 16, 2011
Manuscript Accepted: September 12, 2011
Published: September 28, 2011

Citation
Y. R. Sun, H. Pan, C.-F. Cheng, A.-W. Liu, J.-T. Zhang, and S.-M. Hu, "Application of cavity ring-down spectroscopy to the Boltzmann constant determination," Opt. Express 19, 19993-20002 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-19993


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor, and E. R. Williams, “Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing cipm recommendation 1 (ci-2005),” Metrologia43, 227–246 (2006). [CrossRef]
  2. C. Daussy, M. Guinet, A. Amy-Klein, K. Djerroud, Y. Hermier, S. Briaudeau, C. J. Bordé, and C. Chardonnet, “Direct determination of the boltzmann constant by an optical method,” Phys. Rev. Lett.98, 250801 (2007). [CrossRef] [PubMed]
  3. T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature416, 233–237 (2002). [CrossRef] [PubMed]
  4. P. J. Mohr, B. N. Taylor, and D. B. Neweo, “CODATA recommended values of the fundamental physical constants: 2006,” J. Phys. Chem. Ref. Data37, 1187–1284 (2008). [CrossRef]
  5. G. Casa, A. Castrillo, G. Galzerano, R. Wehr, A. Merlone, D. Di Serafino, P. Laporta, and L. Gianfrani, “Primary gas thermometry by means of laser-absorption spectroscopy: Determination of the boltzmann constant,” Phys. Rev. Lett.100, 200801 (2008). [CrossRef] [PubMed]
  6. K. Djerroud, C. Lemarchand, A. Gauguet, C. Daussy, S. Briaudeau, B. Darquie, O. Lopez, A. Amy-Klein, C. Chardonnet, and C. J. Borde, “Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8 × 10−5 accuracy level,” C. R. Physique10, 883–893 (2009). [CrossRef]
  7. C. Lemarchand, M. Triki, B. Darquié, Ch. J. Bordé, C. Chardonnet, and C. Daussy, “Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy,” New J. Phys.13, 073028 (2011). [CrossRef]
  8. A. Castrillo, G. Casa, A. Merlone, G. Galzerano, P. Laporta, and L. Gianfrani, “On the determination of the Boltzmann constant by means of precision molecular spectroscopy in the near-infrared,” C. R. Physique10, 894–906 (2009). [CrossRef]
  9. K. M. T. Yamada, A. Onae, F. L. Hong, H. Inaba, H. Matsumoto, Y. Nakajima, F. Ito, and T. Shimizu, “High precision line profile measurements on C-13 acetylene using a near infrared frequency comb spectrometer,” J. Mol. Spectorsc.249, 95–99 (2008). [CrossRef]
  10. K. M. T. Yamada, A. Onae, F.-L. Hong, H. Inaba, and T. Shimizu, “Precise determination of the Doppler width of a rovibrational absorption line using a comb-locked diode laser,” C. R. Physique10, 907–915 (2009). [CrossRef]
  11. A. Cygan, D. Lisak, R. S. Trawiński, and R. Ciuryło, “Influence of the line-shape model on the spectroscopic determination of the boltzmann constant,” Phys. Rev. A82, 032515 (2010). [CrossRef]
  12. B. Gao, W. Jiang, A.-W. Liu, Y. Lu, C.-F. Cheng, G.-S. Cheng, and S.-M. Hu, “Ultra sensitive near-infrared cavity ring down spectrometer for precise line profile measurement,” Rev. Sci. Instrum.81, 043105 (2010). [CrossRef] [PubMed]
  13. A. O’Keefe and D. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum.59, 2544–51 (1988). [CrossRef]
  14. B. A. Paldus and A. A. Kachanov, “An historical overview of cavity-enhanced methods,” Can. J. Phys.83, 975–999 (2005). [CrossRef]
  15. J. T. Hodges, H. P. Layer, W. W. Miller, and G. E. Scace, “Frequency-stabilized single-mode cavity ring-down apparatus for high-resolution absorption spectroscopy,” Rev. Sci. Instrum.75, 849–863 (2004). [CrossRef]
  16. J. T. Hodges and R. Ciurylo, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum.76, 023112 (2005). [CrossRef]
  17. D. A. Long, D. K. Havey, M. Okumura, C. E. Miller, and J. T. Hodges, “Cavity ring-down spectroscopy measurements of sub-doppler hyperfine structure,” Phys. Rev. A81, 064502 (2010). [CrossRef]
  18. A. Cygan, D. Lisak, P. Maslowski, K. Bielska, S. Wojtewicz, J. Domyslawska, R. S. Trawinski, R. Ciurylo, H. Abe, and J. T. Hodges, “Pound-drever-hall-locked, frequency-stabilized cavity ring-down spectrometer,” Rev. Sci. Instrum.82, 063107 (2011). [CrossRef] [PubMed]
  19. P. Zalicki and R. N. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys.102, 2708–2717 (1995). [CrossRef]
  20. M. D. De Vizia, F. Rohart, ccedil ois, A. Castrillo, E. Fasci, L. Moretti, and L. Gianfrani, “Speed-dependent effects in the near-infrared spectrum of self-colliding h2o18 molecules,” Phys. Rev. A83, 052506 (2011). [CrossRef]
  21. R. Wehr, J. R. Drummond, and A. D. May, “Design of a difference-frequency infrared laser spectrometer for absorption line-shape studies,” Applied Optics46, 978–985 (2007). [CrossRef] [PubMed]
  22. C. J. Borde, “On the theory of linear absorption line shapes in gases,” C. R. Physique10, 866–882 (2009). [CrossRef]
  23. J. T. Zhang, H. Lin, J. P. Sun, X. J. Feng, K. A. Gillis, and M. R. Moldover, “Cylindrical acoustic resonator for the re-determination of the boltzmann constant,” Int. J. Thermophys.31, 1273–1293 (2010). [CrossRef]
  24. X. Zhan and L. Halonen, “High-resolution photoacoustic study of the ν1 + 3ν3 band system of acetylene with a titanium:sapphire ring laser,” J. Mol. Spectorsc.160, 464 (1993). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited