Madiematical and Physical Sci., 2014, Vol. 59, No. 7, pp. 157-164 This paper is available online at http://stdb.hnue.edu.vn
TUNABLE D I O D E LASER S P E C T R O S C O P Y AND L I N E P A R A M E T E R S O F WATER VAPOR IN T H E N E A R - I N F R A R E D
N g o N g o c H o a a n d N g u y e n M a n l i N g h i a Faculty of Physics, Hanoi National University of Education
Abstract. In this study, we present the technique of tunable diode laser specttoscopy and the specttoscopic parameters of 13 lines of H2O in the 11980 -12260 cm" ^ spectral region. Spectta were recorded at room temperature for a wide range of pressures (2- 15TorrforpureH2Oand50-760TorrforH2Oinair). Line parameters were adjusted from experiments using the least square method, Fortran and three line-shape models; the Voigt profile (VF), the (hard collision) Rautian profile (RP) and the speed dependent Voigt profde (SDVP). A comparison between our results with the HITRAN database 2012 shows good agreement.
Keywords: Water vapor, line-shape, tunable diode laser specttoscopy.
1. Introduction
Water vapor is a key molecule in the Earth's atmosphere, its distribution the object of several remote sensing experiments. The latter provide recordings of atmospheric absorption spectta whose inversion yields the atmospheric humidity vertical profile. For such applications, precise knowledge of the specttoscopic parameters of the H2O lines is needed. In this work, hne parameters (position, integrated intensity and broadening coefficient) are deduced from laboratory" spectta assuming a specific line-shape. For this, the Voigt profile [1] is used in most of the available studies. Within this model, two colhsional parameters are used, i.e. the Lorentz broadening and shifting coefficients, the Doppler width being fixed to its theoretical value. As is well known, [2-4], the Voigt model can lead to discrepancies with measured spectta since it does not take into account two velocity effects: (a) collision-induced velocity changes, leading to the so-called Dicke narrowing and (b) tiie speed dependence of the pressiu:e-induced width and shift. Using more refmed models diat take into account such effects, several studies showed that the line broadening determined by the Voigt profile can be underestimated up to 10% [2, 4]
while the error for integrated intensity is from 0.3 to 2% [5, 6].
Received August 12, 2014. Accepted October 13, 2014.
Contact Ngo Ngoc Hoa, e-mail address: [email protected]
Ngo Ngoc Hoa and Nguyen Manh Nghia
Three specttal shape models have been used: the Voigt, the Rautian (to take into account the Dicke narrowing effect) and the speed dependent Voigt models (to take into account the speed dependence of the colhsional parameters). The corresponding absorption coefficients for a single line are given by [7];
a^(a) = ^^^Re{Wio^ao,rr„A,r)}, (1.1)
S.PH.
[ " ('^ - <70) - ^ - t - Zit) J
where PH^O is the partial pressure of H2O and S is the integrated intensity of the line, CTQ and Vx) are the unperturbed spectral position of the transition, and the Doppler width F, A and B are the coUisional half-width (HWHM), the pressure induced hne-shift, and the narrowing parameter, respectively. The complex probability function W is given by:
W(c7-C7o,rD,A,r) = i T "-^ T=dt. (1.4)
(cr - (To - A) — t + iT—r- 1 D I D The function Z(t) and its derivative Z'(t) in equation (3) are given by:
zit) = \-[A{vt) + rivt)\,
(1.5)z' (t) = « ^ [A' ivt) + r' («()], (1.6)
where v is the most probable speed, A (yt) and T(vt) being the speed dependent lineshifting and broadening parameters. The speed dependence of the line broadening is modeled using a quadratic function (8].
2. Content 2.1. Experimental setup
The experimental setup used for the measurements of spectroscopic parameters of water vapor in the near-infrared spectral region is shown in Figure 1. An external-cavitv
158
diode laser [9] provides a wide tuning range of about 850 nm at room temperature. The diode laser wavelength can be continuously scanned by means of a voltage-ramp signal that simidtaneously drives the laser injection current and the piezoelecttic ttansducer that sets the angle of the external-cavity grating. The emission hne width of die diode laser is about 1 MHz. In this specttal region, we investigated tines of the 2:/i + V2 + v^ bands of H2 ^^O by scaiming intervals about 0.8 cm~^.
Figure 1. Experimental setup used for the measurements of line parameters in the near-infrared region
A White blood cell with a total optical path of 40 m was used. The experiments were carried out as follows: a specttum was first recorded with the empty cell, providing the 100% ttansmission reference. The cell was then filled with H2O vapor at pressures ranging from 2 to 15 Torr, well below the saturated vapor pressure (about 18 Torr at room temperature) and self-broadening spectta were recorded. For air-broadening spectta, the cell was first filled with pure H2O (from 4 to 7 Torr) before ambient air was added up to total pressures of 50 to 760 Torr. Partial pressures of H2O in the mixtures were 159
then calculated using the integrated intensity determined from the pure H2O spectta. All measurements in this study are reahzed by diode laser system al Paris East University.
A Fabry-Perot cavity was used for the calibration of the wavenumber scale. Two spherical mirrors have a curvature radius of 75 mm, resulting in a fi"ee specttal range of I GHz (Figure 2). The finesse is 1000 leading to a resolution of 1 MHz. The peak positions of this Fabry-Perot etalon allow a determination of the relative frequency scale with a precision of better than 1 MHz (or 3.3.10"^ cm~^) while scarming the diode laser. The peak positions of the Fabry Perot cavity were calibrated to relative wave numbers by using a third degree polynomial function.
Number of acquisition
Figure 2. An example of the signal by recording simultaneously the detector signal, the current ramp and the Fabry-Perot signal
2.2. R e s u l t s a n d d i s c u s s i o n s
The measured spectta were least-squares fitted with the three profiles described above and Doppler widths fixed to theoretical values. The integrated intensity the effective hne position, and the hne-shape parameters (F, B, r 2 ) , together with two parameters describing the zero absorption level, are adjusted in the fits. As expected and exemplified by Figure 3, the VP leads to significant residuals, and the Rp and SDVP are in better agreement with measured spectta.
The three lowest panels show the differences between measured absorptions and tiiose adjusted using tiie VP, RP and SDVP.
160
Relative wavenumber (cm')
Figure 3. Room temperature measured absorptions of the 6o6 ^ 5o5 (12249.3895 cm'^) transition
of pure water vapor (left) and ofH20 in air (right) at different pressures
2.2.1. Integrate intensities
For the integrated intensity, only the results from pure H2O spectra were used. As can be seen from this table and Figure 4, the RP and the SDVP lead to very close values, both slightly larger (typically by 0.8%) than those determined with the VP. This result is fully consistent with those obtained in other spectral regions [5, 6].
Intensity (IO'Neill molec' cm )
Figure 4. Ratios of the intensities of the 13 considered transitions obtained by the RP (o) and SDVP (U) to those obtained by the VP
2.2.2. Broadening coe^cients
The self-broadening coefficients were determined from fits of pure H2O spectta, shown in Figure 5a, display the colhsional tine-widths of the ttansition at 12249.3895 cm~^, which shows that they have the expected Hnear variation with the H2O pressure.
The slopes give broadening coefficients. For example with the ttansition at 12249.3895 cm~^, the corresponding broadening coefficients obtained with the VP, RP and SDVP are 161
Ngo Ngoc Hoa and Nguyen Manh Nghia
0.429, 0.446 and 0.452 cm"^atm~\ respectively. The smaller value obtained with the VP shows the effect of the hne narrowing, observed in Figure 3. For spectta of H2O diluted in ambient air, the total line-width of a ttansition is written as:
r = lself-PH,0 + lair. {P " PH,O) ,
where 7seif and 7air are the self and air-broadening coefficients, respectively. P is the total pressure in the celle. In order to determine 7air, the partial pressure P//20 in the cell was for each specttum first determined from the ratio of the integrated area under the measured spectrum (obtained from fits) to the line intensity determined from the specttum of pure H2O. A hnear fit of (F — TsdfPffzo) versus Pa,r = (P - P^ao) gives 7air. As exemplified in Figure 5b, the values obtained vary linearly with Pair. The slopes from Figure 5b (0.0763, 0.0792 and 0.0799 cm'^atm^^ obtained witii the VP, RP and SDVP, respectively) again demonsttate die consistency of the RP and SDVP determinations and the underestimation of the broadening by the VP of about 5% as presented in Figure 6.
(a)
y
• VP
• RP
> SDVP
0 000 0.005 0 010
Figure 5. Line widths of the transition at 12249.3895 cm~^ as functions of (a) the H2O pressure and (b) air pressure,
obtained using the VP, RP and SDVP
Figure 6. Ratios of (a) the self and (b) the air-broadening coefficients of the 13 considered transitions obtained
using the SDVP (U) and the RP(o) to those obtained using the VP
162
The H2O vapor self- and air-broadening coefficients from this study obtained using tiie VP are compared witii data firom ttie hterattne HITRANOS [10] and HTTRANU [11].
Note that our results are in good agreement with all previous studies as shown in Table 1 and Figure 7. The self-broadening coefficients from this smdy are slightly lower than the values in the databases with a mean deviation of 2% and 7%. However, the air-broadening coefficients are about 4% higher tiian tiie values in the databases.
Table 1. H2O self and air-broadening coefficients at 296 K
(To, cm ^ 11988.4939 11988.7257 12226.1012 12236.5601 12244.7186 12244.7881 12248.5787 12249.3895 12259.4776 12259.6033 12268.9969 12280.4387 12280.6634
S, 10-23 cm-i
VP 1.0626 0.3422 4.8473 4.0128 3.5084 1.0197 0.9492 2.6468 0.5645 1.6060 1.0111 0.2820 0.9262
7seif, cm ' atm ' VP
0.369 0.314 0.526 0.475 0.467 0.392 0.362 0.429 0.354 0.358 0.300 0.389 0.374
[10]
0.353 0.364 0.461 0.416 0.424 0.299 0.352 0.376 0.323 0.330 0.258 0.429 0.329
[11]
0.352 0.352 0.483 0.412 0.398 0.402 0.391 0.391 0.313 0.348 0.352 0.421 0.343
7air, cm ^ atm ^ VP
0.0681 0.0654 0.0931 0.0850 0.0899 0.0694 0.0703 0.0763 0.0665 0.0627 0.0530 0.0754 0.0719
[10]
0.0708 0.0742 0.0933 0.0842 0.0952 0.0681 0.0754 0.0773 0.0691 0.0621 0.0618 0.0801 0.0725
[11]
0.0708 0.0742 0.0954 0.0849 0.0958 0.0681 0.0774 0.0776 0.0673 0.0621 0.0618 0.0801 0.0725
0 ° .
0 . 9 8 0 "
0 . 0 . 9 3 . ^ , . Air Broadening Ratios
•>
g 1 05
Oo 0 °
0 1.04 0
0 1 2 3 4 5 Intensity ( 1 0 " I
0 1 2 3 4 5
• This work/HITRAN 08 [10]; O TTiis worfc/HITRAN 12 [11]
Figure 7. A comparison of the H^O self- and air-broadening parameter from the present work with those from other studies [10,11]
as a function of line intensity
163
3. Conclusion
Absorption spectta of 13 lines of H2O in the near mfrared specttal were recorded at room temperature using a tunable diode laser system. Line parameters were deterrmned from experiments using three line-shape models: the Voigt profile (VP), the (hard colhsion) Rautian profile (RP) and the speed dependent Voigt profile (SDVP). The results show that the RP and SDVP are in better agreement with measurements than the VP and that they lead to larger values of the line parameters (about 5 % for the line broadening and 0.8% for line intensity). The comparison between our results and the HITRAN database 2008 and 2012 shows good agreement.
REFERENCES
[I] W. Voigt, 1912. Uber das gesetz intensitdtsverteilung innerhalb der linien eines gasspektrams. Sitzber. Bayr Akad., Miinchen Ber., pp. 603-620.
[2] D. Lisak, J. T. Hodges and R. Ciurylo, 2006. Comparison of semiclassical line-shape models to rovibrational H2O spectra measured by frequency-stabilized cavity ring-down spectroscopy. Physical Review, A 73 012507.
[3] H. Tran, D. Bermejo, J. L. Domenech, P. Joubert, R. R. Garnache and J. M. Hartmann, low .CoUisional parameters of H2O lines: Velocity effects on the line-shape. Journal of Quantitative Specttoscopy and Radiative Transfer, 108 pp. 126-145.
[4] M. D. De Vizia, F. Rohart, A. Casttillo, E. Fasci, L. Moretti, L. Gianfrani, 2011. Investigation on speed dependent effects in the near-IR spectrum of self-colliding H2 ^^O molecules.
Physical Review, A 83, 052506.
[5] H. Li, A. Farooq, J. B. Jeffries, R. K. Hanson. Diode laser measurements of temperature-dependent collisional-narrowing and broadening parameters of Ar-perturbed H2O transitions at 1391.7 arui 1397.8 nm. Journal of Quantitative Specttoscopy and Radiative Transfer, 109, pp. 132-143.
[6] D. Lisak, J. T. Hodges, 2008. Low-uncertainty H2O line intensities for the 930 nm region.
Journal of Molecular Specttoscopy, 249, pp. 6-13.
[7] J. M. Harhnann, C. Boulet and D. Robert, 2008. Colhsional effects on molecular spectra.
Laboratory experiments and models, consequences for applications, Elsevier.
[8] F. Rohart, H. Mader and H. W. Nicolaisen, 199A. Speed dependence of rotational relaxation induced by foreign gas collisions: Studies on CH3F by millimeter wave coherent transients.
The Journal of Chemical Physics, 101, pp. 6475-6486.
[9] Toptica Photonics. Diode Laser Series: DL 100, User Manual, http://www.toptica.com.
[10] L. S. Rothman, I. E. Gordon, A. Barbe, D.C. Benner, P. F. Beraath et ai, 2009. The HITRAN 2008 molecular spectroscopic database. Journal of Quantitative Specttoscopy and Radiative Transfer, n o , pp. 533-572.
[II] L. S. Rothman, I. E. Gordon, A. Barbe, D.C. Benner, P. F. Bemath et ai, 2013. The HITRAN 2012 molecular spectroscopic database. Journal of Quantitative Specttoscopy and Radiative Transfer, 130, pp. 4-50.
164
