Precise wavelength calibration in continuous-wavecavity ringdown spectroscopy based
on the HITRAN database
Zhongqi Tan,* Xingwu Long, Jie Yuan, Yun Huang, and Bin ZhangDepartment of Optoelectronic Engineering, College of Optoelectronic Science and Engineering,
National University of Defense Technology, Changsha 410073, China
As a high-sensitivity absorption technique, cavityringdown spectroscopy (CRDS) has been successfullyused in analytical chemistry and physical chemistry[1], especially to detect the concentration of trace gas[2,3] and measurement of the absorption spectrum ofgaseous species [4,5]. Unlike conventional absorp-tion spectroscopy [6], CRDSmeasures the absorptionrate rather than the absorption magnitude of laserlight confined in a high-finesse optical cavity, so itis insensitive to the fluctuations of laser intensityand can achieve long absorption paths (many kilo-meters) in a short cavity [7]. Although both a pulsedlaser and a continuous-wave (CW) laser can be usedas the light source of CRDS, the CW CRDS [8] hashigher spectral resolution and absorption sensitivitythan pulsed CRDS [9]. Furthermore, with the use ofa compact and inexpensive laser diode as the lightsource [10], the volume and expense of CW CRDS ap-paratus can obviously be reduced. Therefore, CW
CRDS is more attractive, especially for portable spec-trummeasurement and trace gas detection at remotelocations.
As is known, accurate determination of wave-length is a central problem in laser spectroscopybecause it allows the determination of molecular en-ergy levels and molecular structure [11]. Some tech-niques have been developed to solve this problem inconventional absorption spectroscopy. For example,some equipment, such as different kinds of inter-ferometer, has been applied to calibrate laser wave-lengths, and the absolute wavelength determinationwith an uncertainty that is less than 10−3 cm−1 can beachieved. In CW CRDS, when a laser diode is used asthe light source, the laser wavelength can be continu-ously scanned in a small wavelength region by tun-ing its injection current or operating temperature[12,13]. Then the laser wavelength can also be cali-brated by the traditional method as follows. Thelaser diode wavelength–current relation can firstbe characterized at each operating temperature witha high precision wavemeter and then checked andrefined with those known spectral positions [14].
In this case, a wavelength precision of∼2 × 10−3 cm−1
was reported [15].Here we present a compact CWCRDS and use it to
study the wavelength calibration method. By record-ing the absorption spectrum of N2O in the range of6594:3 − 6595:5 cm−1, the measured spectral posi-tions will be compared to the HITRAN 2004 database[16], which is recognized as the international stan-dard of fundamental spectroscopic parameters. Sub-sequently, to improve the precision of wavelengthcalibration, a developed method of wavelength cali-bration will be proposed and experimentally tested.In this method, the measured spectral lines are usedas wavelength markers to calibrate the DFB laserwavelength, and their reference positions are takendirectly from the HITRAN 2004 database.
2. Experimental Theory
The operating principle of CW CRDS was describedby Anderson et al.[17] in 1984. The interested readercan find the necessary background in the cited litera-ture. Here we cite only the theoretical result. In ty-pical CW CRDS, the narrowband light from a DFBlaser is coupled into a high-finesse optical cavity.When the laser frequency overlaps with one of thecavity modes, the laser light switches off in ultra-short time, and the intensity of the light that exitsthe cavity decays as a single-exponential functionof time. The 1=e fall time of the decay signal is de-fined as ringdown time τ, which can be expressedas a function of the loss of empty optical cavity δ0ðδ0 ≈
1 − RÞ and absorption coefficient αðvÞ of the gaseousspecies placed in the cavity and is given by
τðvÞ ¼ Lc · ½δ0 þ αðvÞ · L� ; ð1Þ
where L is the cavity length, c is the speed of light,and τðvÞ is the ringdown time of the cavity at laserfrequency v. According to Eq. (1), the loss spectrumof mirror δ0ðvÞ, which is referred to as the baselinespectrum, can be obtained from ringdown timeτ0ðvÞ of the empty cavity. Then αðvÞ is given as
αðvÞ ¼ 1c · τðvÞ −
1c · τ0ðvÞ
:
αðvÞ obviously changes with laser frequency v, and itsprofile yields the absorption spectrum of the species.As we know, when the optical cavity is at a low pres-sure, the absorption intensity of the gaseous speciesis a Gaussian function of laser frequency v [18] andthen αðvÞ can also be expressed as
αðvÞ ¼ NSγ
ffiffiffiffiffiffiffiffiln 2π
rexp
�−
ðv − v0Þ2 ln 2
γ2�;
whereN is the absorbing molecule density, γ is half ofthe Doppler width, and S is the absorption intensity.v0 is the spectral position, which is stable and
independent of the temperature, that can be deter-mined only by the energy levels of the molecular sys-tem. Therefore, the known spectral lines are oftenused as a reference to calibrate the laser wavelength,for example, the I2 spectral lines in the range of14800 − 20000 cm−1. Similarly, in CW CRDS, whenwe record the known spectral lines by scanningthe laser diode current and then determine their cur-rent values at each spectral position with the fittingmethod, we can also calibrate the laser wavelengthaccurately based on the characteristics of the laserdiode (the laser wavelength is a function of its injec-tion current).
3. Experimental Apparatus
The experimental CW CRDS apparatus of this workis shown in Fig. 1. Here we describe the operation ofthe apparatus and the parameters of its components.The DFB laser diode (NLK1556STB, NEL) wascontrolled by a temperature controller (WTC3343,Wavelength Electronics) and a laser diode driver(LDD-1P, Wavelength Electronics). Its short-term(1h) stability of temperature and current was∼5mK and ∼0:05mA, respectively. The emitting la-ser of 1:517 μm (∼6594 cm−1) passed through an op-tical isolator (PIS-155-A-025, Accelink) and a fibercollimator (F240-1550, Thorlabs) and was thentransformed into a Gaussian beam in free space witha waist radius of ∼0:75mm and a full-angle diver-gence of ∼0:0750. Unlike the traditional method,no mode-matching lens was used. The collimated la-ser beam was directed into an ∼25 cm optical cavitythat consists of two 2:5 cm diameter spherical mir-rors. These mirrors were especially made in our la-boratory to have reflectivities greater than 99.95%at 1:517 μm (Lambda 950, Perkin-Elmer). And the ra-dius of curvature of both mirrors was 8m. Based onthe mode-coupling theory [19], the in-coupling effi-ciency between the incident beam and a TEM00 modeof the optical cavity can be calculated, which is∼99%at 1:517 μm if we ignore misadjustment. Because sta-bility of the cavity is critical to the precision of theCW CRDS system, an ultralow-thermal expansionglass ceramic was chosen for the cavity. Its inner dia-meter was 1:0 cm, so the diffraction loss can beignored. Furthermore, two faces of the cavity werepolished and the mirrors were all cemented opticallyon the faces of the cavity.
Fig. 1. Schematic of the experimental setup for CW CRDS: 1, op-tical isolator; 2, fiber collimator; 3, piezoelectric transducer; 4, lowloss cavity; 5, detector; 6, DFB laser; 7, driver circuit; 8, compara-tor and trigger circuit; 9, peak detector; 10, ADC and computer; 11,wavemeter.
Both the linewidth of the laser and the cavitymodes were very narrow (∼2:0MHz and∼15:0kHz). To record the decay time of the intracav-ity intensity, the cavity length was scanned with apiezoelectric transducer that was driven by a100Hz triangle wave signal. Then the laser fre-quency and the cavity modes were periodically inresonance. The light leaking from the cavity was fo-cused by a lens and sensed by an InGaAs detector(PDA400, Thorlabs). Following this, the detector out-put was divided into three: one was fed into a peakdetector, the second was connected to a high-speedanalog–digital converter card, and the third was sentto the negative input terminal of a high-speed com-parator. Approximately 90% of the peak detector out-put was used as the threshold for the ringdowntransient and was connected to the positive inputterminal of the comparator. When the laser was inresonance with one of the TEM00 longitudinal modesof the cavity, the light intensity sensed by the detec-tor increased quickly. After it exceeded threshold, thelaser diode driver was triggered by a trailing edgefrom the comparator to switch off the injection cur-rent in ∼40ns. In the following ∼1:0ms, the DFB la-ser was maintained at the off status until a completeringdown transient was recorded. The decay signalwas digitized by a 12 bit gauge 1250 CompuScopecard mounted in a personal computer. We then usedthe Levenberg–Marquardt method [20] to obtain the1=e fall time. Finally, the loss of the cavity was deter-mined by Eq. (1). To stabilize the operating tempera-ture, the driver switched on the DFB laser for ∼0:1 sbefore taking the next measurement.When the apparatus was applied to measure the
absorption spectrum of the gaseous species, weplaced the species in the optical cavity. The DFB la-ser wavelength was scanned in small-wavelength re-gions (∼1 cm−1) by tuning its injection current, andits values were calibrated with a high precisionwavemeter (WA-1500-NIR, EXEO Burleigh) and alaser spectrum analyzer (WA-650, EXEO Burleigh).The CW CRDS spectrum was then obtained by re-cording the cavity loss as a function of laser wave-length. When the baseline spectrum of the cavitywas measured beforehand, the absorption spectrumwas determined by subtracting the baseline from themeasured spectrum. In addition, a set of vacuum sys-tems, which is not shown in Fig. 1, was installed inour apparatus to pump the closed optical cavity. Thevacuum system was composed of three level pumpsand a vacuum gauge (CMR264, Pfeiffer).
4. Results and Analyses
We first characterized the wavelength-current rela-tion of the DFB laser with the wavemeter. In this ex-periment, the driver of the laser diode was controlledby a microcomputer, and the laser injection currentwas changed by ∼0:154mA in the range of20 − 80mA. The light from the DFB laser passedthrough an optical attenuator and was then directedinto the wavemeter that was set at the average mode
of two points. Limited by updating the speed of thewavemeter, the stepping rate of the laser diode cur-rent was set at 1Hz, and the measured wavelengthdata were transferred at the same frequency by a la-ser spectrum analyzer to a computer for further pro-cessing. As a result, an example of measured data ata laser temperature of 15 °C is shown in Fig. 2(a).From the profile of the measured curve in Fig. 2(a)we found that the laser wavenumber could be ex-pressed as a multinomial function of its injection cur-rent. Then a second-order polynomial was chosen asthe target function to fit the curve, and the fittedrelation between laser wavenumber and its currentis given by
λ¼6595:69965−0:010544× i−0:000080619× i2; ð2Þ
where the deviation of ∼0:8 × 10−3 cm−1 betweenmeasured data and fitted results was obtained. Toverify the influence of the stepping rate on the cali-bration result, we reduced the stepping rate of theinjection current to 0:5Hz. We then determinedthe deviation of ∼0:78 × 10−3 cm−1 between the twocalibrations.
When the optical cavity was pumped to ∼10−3 Torrwith the vacuum system, we measured its baselinespectrum in ∼90 s. In fact, to improve the spectralresolution, the scanning step of the injection currentwas reduced to ∼0:046mA. Under the condition ofenvironmental fluctuations caused by the pumpingsystem, the measured baseline spectrum is shownin Fig. 2(b), in which the laser wavelength was deter-mined by Eq. (2). Because water vapor existed in thecavity, we could observe an absorption spectral line ofH2O at 6595:078 cm−1 [21] in Fig. 2(b). Furthermore,a baseline ripple can also be observed, which is
Fig. 2. Wavelength–current relation of the DFB laser calibratedby a wavemeter and CW CRDS spectrum of the empty cavityobtained at ∼10−3 Torr. (a) Laser wavelength at an operating tem-perature of 15 °C versus DFB laser currents. The points representthe data; the dotted curve represents the results of a second poly-nomial function to fit the data. (b) CW CRDS spectrum of theempty cavity obtained at 6594:3 − 6595:5 cm−1, and a spectral lineof H2O at 6595:078 cm−1 is clearly visible.
caused by etalon effects and adversely limits the de-tection sensitivity of the CW CRDS system. In thiscase, the minimum detectable sensitivity (noiseequivalent levels) of ∼7:6 × 10−9 cm−1 was achieved,and it could be improved to ∼3:2 × 10−9 cm−1 by elim-inating the etalon effects. As we know, loss of theempty cavity comes mainly from the mirror (trans-mission plus scatter and absorption), therefore weobtained a mirror reflectivity of ∼99:9915% fromthe baseline.To demonstrate the calibration precision of Eq. (2),
we recorded the absorption lines of the N2O mole-cule, which were embodied by the HITRAN 2004database. As shown in Fig. 3(a), separate spectrallines could be clearly observed by subtracting thebaseline from the measured spectrum. The pressurein our sample was 7:5 × 10−2 Torr. In this case, thecollisional broadening, ∼2:0 × 10−5 cm−1 FWHM ofN2O, is negligible compared with its Doppler widthof ∼1:22 × 10−2 cm−1 FWHM, so the measured spec-tral line shape of N2O is mostly Gaussian. We fittedthemeasured spectral lines with a Gaussian functionto obtain their positions and compared the fitted re-sult with the HITRAN 2004 database (the results arelisted in Table. 2). We then obtained a wavelengthshift of 2:95 × 10−2 cm−1 and a nonlinear error of3:1 × 10−3 cm−1. To test the repeatability of the CRDSsystem, the spectrum measurement was repeated.Deviation of the single spectral position and thespace between different lines were obtained as∼2:0 × 10−3 and ∼0:9 × 10−3 cm−1, respectively. Inour controller circuit, the operating temperatureand injection current of the DFB laser were set bya digital–analog converter (DAC) (two 16 bit chan-nels), and wavelength scanning was set by tuningthe laser diode current. Therefore, we believe thatthe wavelength shift resulted from the laser diodetemperature or current drift caused by the voltage
drift of the DAC, and the nonlinear deviation mighttake root in the laser diode temperature fluctuationsat different wavelength scanning rates.
Compared with the nonlinear deviation, the wave-length drift is not essential for wavelength calibra-tion, because it can be easily corrected by referringto the known spectral positions. To reduce thenonlinear deviation of the conventional method, wepropose our developed method. As we know, the equi-distant transmission peaks of a long Fabry–Perot in-terferometer are often used as frequency markers tocalibrate laser wavelength. Analogously, we can alsomeasure those absorption lines that are embodied bythe HITRAN 2004 database and use their positionsas wavelength markers to calibrate the wavelength–current relation of DFB lasers.
Fig. 3. CW CRDS spectrum of different gaseous species versusthe laser wavelength calibrated by a wavemeter. (a) Measuredspectrum of N2O at a pressure of 0:075Torr and (b) a mixtureof gases at a pressure of 5:4Torr. Also plotted are their positionsthat were obtained from the HITRAN 2004 database.
a Their reference positions were provided by the HITRAN 2004database and the relevant laser currents at individual lines wereobtained by Gaussian fitting.
Fig. 4. Wavelength–current relation of the DFB laser calibratedby the developed method and its calibration precision evaluatedwith the measured spectral lines of N2O. (a) The points representthe data and the solid curve represents the result of a multinomialfunction to fit the data. (b) CW CRDS spectrum of the N2O mole-cule plotted at different wavelength calibration methods. Alsoplotted are the spectral positions provided by the HITRAN 2004database.
A few months after the first wavelength calibra-tion, we experimented with the developed method.We filled the cavity with an ∼5:4Torr of mixturegases, including N2O, H2O, and CH4 molecules atpressures of∼0:05,∼0:2, and∼5:2Torr, respectively.We then measured the CW CRDS spectrum in the6594:3 − 6595:5 cm−1 range. As shown in Fig. 3(b),some absorption lines are clearly visible after sub-tracting the baseline from the measured spectrum.Since the positions of these measured spectral linescan be found in the HITRAN 2004 database, the lasercurrents that correspond to the individual linescan be used to check and correct the wavelength–current relation of the DFB laser. Taking into consid-eration that the laser current with its wavenumberin the small wavelength region is an approximate lin-ear function, we used a Gaussian fit to determine thelaser current values at individual lines. The fitted re-sults of 12 spectral lines and their wavelengths fromthe HITRAN 2004 database are listed in Table. 1.With these data we were able to fit the wave-
length–current relation of the DFB laser again asbefore. The fitting result is shown in Fig. 4(a); the re-lated expression between the laser wavelength andits injection current must be corrected to
where the fitting deviation of ∼1:1 × 10−3 cm−1 wasdetermined, which was worse than the previous re-sult of 0:8 × 10−3 cm−1. Comparison of Eq. (3) withEq. (2) yielded the wavelength shift of ∼5:4 ×10−2 cm−1 and the deviation of ∼2:3 × 10−3 cm−1. Toestimate the wavelength precision of the developedmethod, we still used the measured spectral linesof the N2O molecule in 6594:3 − 6595:5 cm−1 as a re-ference and compared them with the HITRAN 2004database. The new calibration result for the laserwavelength also has a parallel shift as in the conven-tional wavelength calibration method. In Fig. 4(b) weeliminated the parallel shift by referencing theknown spectral lines of N2O, which were taken fromthe HITRAN 2004 database, to the redrawn mea-sured spectra of N2O. As mentioned above, we per-formed a least-squares fit to the line shape byusing a Gaussian function and obtained their posi-tions as listed in Table 2. For comparison, the spec-tral positions calibrated by the wavemeter and theirreference wavelengths provided by the HITRAN2004 database are also listed in Table 2. From ananalysis of Table 2, the wavelength precision (thedeviation in Table 2) of the developed method was
obtained as ∼0:8 × 10−3 cm−1, which is four timesmore precise than that of the conventional method.
5. Conclusions
Based on a compact continuous-wave cavity ring-down spectroscopy apparatus and the HITRAN2004 database, we have described and experimentedwith two wavelength calibration methods of a nar-rowband laser diode. Compared with the traditionalmethod, the developed method has proved to havehigher calibration precision (compared with the HI-TRAN 2004 database) and less demand of wave-meter precision. With this method, the absoluteaccuracy of wavelength calibration is decided bythe number and accuracy of wavelength markers.Presumably, the calibration accuracy can be furtherimproved if the reference number is increased andthe reference accuracy is enhanced. This developedmethod is suitable for calibration of the wavelengthof the new spectral lines that are not embodied by theHITRAN database, such as the weak absorptionspectrum of CH4 near 6594 cm−1, and maintainingself-consistent positions with other spectral linesincluded by the HITRAN 2004 database.
References1. C. Ramos and P. J. Dagdigian, “Detection of vapors of explo-
sives and explosive-related compounds by ultraviolet cavityringdown spectroscopy,” Appl. Opt. 46, 620–627 (2007).
2. D. Romanini, A. A. Kachanov, J. Morville, and M. Chenevier,“Measurement of trace gases by diode laser cavity ringdownspectroscopy,” Proc. SPIE 3821, 94–104 (1999).
3. E. R. Crosson, “A cavity ring-down analyzer for measuringatmospheric levels of methane, carbon dioxide, and watervapor,” Appl. Phys. B 92, 403–408 (2008).
4. P. Macko, D. Romanini, S. N. Mikhailenko, O. V. Naumenko,S. Kassi, A. Jenouvrier, Vl. G. Tyuterev, and A. Campargue,“High sensitivity CW-cavity ring down spectroscopy of waterin the region of the 1:5 μm atmospheric window,” J. Mol. Spec-trosc. 227, 90–108 (2004).
5. S. N. Mikhailenko, W. Le, S. Kassi, and A. Campargue, “Weakwater absorption lines around 1.455 and 1:66 μm byCW-CRDS,” J. Mol. Spectrosc. 244, 170–178 (2007).
6. G. Durry and G. Megie, “In situ measurements of H2O from astratospheric balloon by diode laser direct-differential absorp-tion spectroscopy at 1:39 μm,” Appl. Opt. 39, 5601–5608 (2000)
7. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spec-troscopy: experimental schemes and applications,” Int. Rev.Phys. Chem. 19, 565–607 (2000).
8. D. Romanini, A. A. Kachanov, N. Sadeghi, and F. Stoeckel,“CW cavity ring down spectroscopy,” Chem. Phys. Lett. 264,316–322 (1997).
9. A. O’Keefe and D. A. G. Deacon, “Cavity ring-down opticalspectrometer for absorption measurements using pulsed lasersources,” Rev. Sci. Instrum. 59, 2544–2552 (1988).
Table 2. Spectral Positions of Four Lines of N2O Calibrated by Different Methodsa
10. D. Romanini, A. A. Kachanov, and F. Stoeckel, “Diode lasercavity ring down spectroscopy,” Chem. Phys. Lett. 270, 538–545 (1997).
11. W. Demtröder, Laser Spectroscopy: Basic Concepts and Instru-mentation, 3rd ed. (Springer-Verlag, 2003).
12. W. Zhao, X. Gao, L. Deng, T. Huang, T. Wu, and W. Zhang, “Ab-sorption spectroscopy of formaldehyde at 1:573 μm,” J. Quant.Spectrosc. Radiat. Transfer 107, 331–339 (2007).
13. Y. He andB. J. Orr, “Continuous-wave cavity ringdown absorp-tion spectroscopy with a swept-frequency laser: rapid spectralsensing of gas-phase molecules,” Appl. Opt. 44, 6752–6761 (2005).
14. A. W. Liu, S. Kassi, and A. Campargue, “High sensitivity CW-cavity ring down spectroscopy of CH4 in the 1:55 μm transpar-ency window,” Chem. Phys. Lett. 447, 16–20 (2007).
15. W. Zhao, X. Gao, L. Hao, M. Huang, T. Huang, T.Wu,W. Zhang,andW. Chen, “Use of integrated cavity output spectroscopy forstudying gas phase chemistry in a smog chamber: character-izing the photolysis of methyl nitrite (CH3ONO),” Vib. Spec-trosc. 44, 388–393 (2007).
16. L. S. Rothman, D. Jacquemart, A. Barbe, D. C. Benner,M. Birk, L. R. Brown, M. R. Carleer, C. Chackerian, Jr.,K. Chance, L. H. Coudert, V. Dana, V. M. Devi, J. -M. Flaud,R. R. Gamache, A. Goldman, J. M. Hartmann, K. W. Jucks,
A. G. Maki, J. -Y. Mandin, S. T. Massie, J. Orphal,A. Perrin, C. P. Rinsland, M. A. H. Smith, J. Tennyson,R. N. Tolchenov, R. A. Toth, J. Vander Auwera, P. Varanasi,and G. Wagner, “The HITRAN 2004 molecular spectroscopicdatabase,” J. Quant. Spectrosc. Radiat. Transfer 96, 139–204 (2005).
17. D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflec-tometer based on optical cavity decay time,” Appl. Opt. 23,1238–1245 (1984).
18. A. W. Liu, S. Kassi, P. Malara, D. Romanini, V. I. Perevalov,S. A. Tashkun, S. M. Hu, and A. Campargue, “High sensitivityCW-cavity ring down spectroscopy of N2O near 1:5 μm (I),” J.Mol. Spectrosc. 244, 33–47 (2007).
19. H. Kogelnik, “Coupling and conversion coefficients foroptical modes,” in Proceedings of the Symposium on Quasi-Optics, Vol. 14 of the Microwave Research Institute SymposiaSeries (Polytechnic Press, 1964), pp. 333–345.
20. P. D. Nation, A. Q. Howard, and L. J. Webb, “Modelingbiological fluorescence emission spectra using Lorentz lineshapes and nonlinear optimization,” Appl. Opt. 46, 6192–6195 (2007).
21. R. A. Toth, “Extensive measurements of H216O line frequen-
cies and strengths: 5750 to 7965 cm−1,” Appl. Opt. 33, 4851–4867 (1994).
