OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23104–23110
« Show journal navigation

Calibration-free wavelength modulated TDLAS under high absorbance conditions

Peng Zhimin, Ding Yanjun, Che Lu, Li Xiaohang, and Zheng Kangjie  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 23104-23110 (2011)
http://dx.doi.org/10.1364/OE.19.023104


View Full Text Article

Acrobat PDF (1087 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Currently, the method that uses a first-order Taylor series to approximate laser transmission has seriously affected the gas concentration measurement accuracy of tunable diode laser-absorption spectroscopy (TDLAS). This paper employs a second-order Taylor series to approximate laser transmission, and a high-precision second-order algorithm has been established that can determine the gas concentration directly. Then, this algorithm is used to test the NH3 mole fraction in a cell with NH3-Air mixtures. Experimental results show that the second-order algorithm not only effectively improves the measurement accuracy of gas concentration but also greatly broadens the scope of TDLAS.

© 2011 OSA

1. Introduction

With the development of tunable diode laser-absorption spectroscopy (TDLAS) and with gas concentration measurement precision improvement, the traditional direct absorption method, easily affected by particles concentration, laser intensity fluctuations, and baseline-fitting errors often hamper the accurate determination of line shapes, which satisfy more difficult measurement requirements [1

1. J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3-4), 503–511 (2004). [CrossRef]

]. During the past ten years, recognizing the power of wavelength modulation spectroscopy (WMS) for highly sensitive measurements, many scientists have applied WMS in many areas to measure gas concentration and have achieved many valuable research results [2

2. R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010). [CrossRef]

4

4. T. D. Cai, H. Jia, G. S. Wang, W. D. Chen, and X. M. Gao, “A sensor for measurements of temperature and water concentration using a single tunable diode laser near 1.4um,” Sens. Actuators A Phys. 152(1), 5–12 (2009). [CrossRef]

]. However, one of the key drawbacks of WMS is that the gas concentration cannot be obtained directly from measured harmonic signals in practical measurements. In the early stage of WMS, scientists use a first-order Taylor series to approximate laser transmission when the absorbance is less than 5.0%, derive that the second harmonic peak is a liner with gas concentration, and then determine the gas concentration through calibration experiments [5

5. F. Wang, K. F. Cen, N. Li, Q. X. Huang, X. Chao, J. H. Yan, and Y. Chi, “Simultaneous measurement on gas concentration and particle mass concentration by tunable diode laser,” Flow Meas. Instrum. 21(3), 382–387 (2010). [CrossRef]

]. Recently, R. K. Hanson et al. [6

6. H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006). [CrossRef] [PubMed]

,7

7. H. Li, A. Farooq, J. B. Jeffries, and R. K. Hanson, “Near-infrared diode laser absorption sensor for rapid measurements of temperature and water vapor in a shock tube,” Appl. Phys. B 89(2-3), 407–416 (2007). [CrossRef]

] developed a method that enables “calibration-free” measurements using WMS, based on residual amplitude modulation (RAM). This method uses the first harmonic (1f) signal to normalize the second harmonic (2f) signal, and the absorption information such as gas concentration can be gained from the 2f/1f signal. More importantly, an expression that can be used to determine the absolute value of the gas concentration has been derived when the absorbance is less than 5.0% [8

8. G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009). [CrossRef] [PubMed]

]. From the above analysis, at present the WMS seem to be limited to optically thin conditions (absorbance is less than 5.0%) [9

9. A. L. Chakraborty, K. Ruxton, W. Johnstone, M. Lengden, and K. Duffin, “Elimination of residual amplitude modulation in tunable diode laser wavelength modulation spectroscopy using an optical fiber delay line,” Opt. Express 17(12), 9602–9607 (2009). [CrossRef] [PubMed]

], but this restriction precludes many interesting cases such as absorbance of more than 5.0%.

To improve the measuring accuracy of TDLAS and widen its scope of application in the industrial field, a second-order Taylor series is employed to approximate laser transmission, and an expression for measuring gas concentration has been derived based on the absorption spectral theory in this paper. Meanwhile, a second-order algorithm has been established, and it is used to determine the NH3 mole fraction at different absorbance levels in the laboratory.

2. Derivation of second-order algorithm

The basic principle of WMS has been introduced in the literature [10

10. J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers comparison of experiment and theory,” Appl. Phys. B 26(3), 203–210 (1981). [CrossRef]

,11

11. P. Kluczynski and O. Axner, “Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt. 38(27), 5803–5815 (1999). [CrossRef] [PubMed]

]. Some of the basic theory will be presented here in order to explain the derivation process of the second-order algorithm in this study. In WMS, the laser transmission of monochromatic radiation at frequency v (cm−1) through a uniform medium is given by the Beer–Lambert relation and can be expanded in a Fourier cosine series as follows:
τ(v)=ItI0=exp[α(v)]=exp[PS(T)LXφ(v)]=k=0Akcos(kωt),
(1)
where τ(v) is the laser transmission; It and I0 are the transmitted and incident laser intensities, respectively; and α(v) is the spectral absorbance. For the isolated transition α(v) = PLS(T)(v), P (atm) is the total gas pressure, S(T) (cm−2atm−1) is the line strength, L (cm) is the optical absorbing path length, X is the mole fraction of the absorbing species, and φ(v) (cm) is the line-shape function for the absorption feature and expressed by the Voigt function [12

12. E. Detommasi, A. Castrillo, G. Casa, and L. Gianfrani, “An efficient approximation for a wavelength modulated 2nd harmonic lineshape from a Voigt absorption profile,” J. Quant. Spectrosc. Radiat. Transf. 109(1), 168–175 (2008). [CrossRef]

]. By using the definition ξ = PLS(T), the functions Ak are given as

{A0=12πππexp[ξXφ(v)]dθ,Ak=1πππexp[ξXφ(v)]coskθdθk=1,2,3....
(2)

The incident laser intensity is also simultaneously modulated and is given by [13

13. J. B. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7 μm,” Appl. Phys. B 96(1), 161–173 (2009). [CrossRef]

]
I0=I¯0(1+i1cos(ωt+ψ1)+i2cos(2ωt+ψ2)),
(3)
where I¯0 is the average laser intensity, and i1, i2, ψ1 and ψ2 are the characteristic parameters of the diode-laser. Substituting Eq. (3) into Eq. (1) for harmonic detection, the magnitude of the 1f and 2f signals at the line center of absorption feature can be written as [13

13. J. B. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7 μm,” Appl. Phys. B 96(1), 161–173 (2009). [CrossRef]

]
{S1f=GI¯02{[i1(A0+A22)cos(ψ1)]2+[i1(A0A22)sin(ψ1)]2}1/2,S2f=GI¯02{[A2+i2(A01+A42)cos(ψ2)]2+[i2(A01A42)sin(ψ2)]2}1/2,
(4)
where the 2f signal is recovered to reduce the RAM background signal, and G is electro-optical gain of the detection system. From Eq. (1), when there is no absorption (A0 = 1, Ak = 0), the magnitude of the 1f signal can be written as follows, where R1f is the background of the 1f signal:

S1f0=R1f=GI¯02i1.
(5)

2.1 First-order algorithm—2f/1f calibration-free method

In Eq. (1), the laser transmission τ(v) can be expanded by a first-order Taylor series when the absorbance is less than 5.0%.
τ(v)=exp[ξXφ(v)]1ξXφ(v)=1ξXk=0Hkcos(kωt),
(6)
where φ(v)=k=0Hkcos(kωt); Hk can be expressed as:

{H0=12πππφ(v)dθ,Hk=1πππφ(v)coskθdθk=1,2,3....
(7)

Comparing Eq. (1) with Eq. (6), we can obtain the following relations:

{A0=1ξXH0,Ak=ξXHkk=1,2,3....
(8)

In most applications, i2<<1; substituting Eq. (8) into Eq. (4), the 1f, 2f, and 2f/1f signals at the line center can be simplified as

{S1fGI¯02i1=R1fS2fGI¯02ξXH2S=S2fS1fPS(T)LXH2i1.
(9)

As shown in Eq. (9), the gas concentration (mole fraction) can be determined by the following equation, where the 2f/1f signal (S) is measured through experiments:

X=Si1PS(T)LH2.
(10)

2.2 Second-order algorithm

A first-order Taylor series is employed to approximate the laser transmission, which will bring larger approximation errors when the absorbance is more than 5.0%. Compared with the first-order Taylor approximation, the approximation errors will be reduced sharply when the laser transmission is approximated by a second-order Taylor series. For example, the error is only 0.56% when the absorbance reaches to 30.0%, and the laser transmission can be expanded as
τ(v)=exp[ξXφ(v)]1ξXk=0Hkcos(kωt)+ξ2X2[k=0Hkcos(kωt)]22,
(11)
where φ(v)=k=0Hkcos(kωt); defining that k=0Tkcos(kωt)=[k=0Hkcos(kωt)]2, we can obtain the following equations:

{T0=12(H02+n=0Hn2),Tk=12n=0kHnHkn+n=0HnHn+kk=1,2,3....
(12)

Comparing Eq. (1) with Eq. (11), the relationships can be obtained as

{A0=1ξXH0+ξ2X2T02,Ak=ξXHn+ξ2X2Tn2k=1,2,3....
(13)

Similarly, substituting Eq. (13) into Eq. (4), the 2f signal can be expressed as
S2fGI¯02(ξXH2+ξ2X22T2),
(14)
where T2 will attain convergence and stability quickly and can be expanded as

T2=H122+2H0H2+H1H3+H2H4+H3H5+...+HnHn+2n=1,2,3....
(15)

To eliminate the errors caused by using S1f instead of R1f in the 2f/1f calibration-free method, the second-order algorithm uses the background of the 1f signal (R1f) to determine the gas concentration, and the 2f/1f signal at the line center can be written as

R=S2fR1fPS(T)LXH2+(PS(T)L)2X2T2/2i1.
(16)

From Eq. (16), the gas concentration can be determined by the following equation when these parameters (i1, P, S(T), L, H2, T2 and R) are known:

X=H2+H22+2T2Ri1PS(T)LT2.
(17)

3. Experimental results

So as to validate the measurement accuracy of the second-order algorithm, we take an NH3-air mixture as the research object. The absorption transition at 6529.184 cm−1 is selected to measure the NH3 concentration, and the spectroscopic parameters are shown in Table 1

Table 1. Spectroscopic Parameters for the Selected NH3 Transition at 6529.184 cm−1

table-icon
View This Table
[14

14. H. Jia, W. Zhao, T. Cai, W. Chen, W. Zhang, and X. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 347–357 (2009). [CrossRef]

].

The schematic of the experimental setup is shown in Fig. 1
Fig. 1 Experimental schematic for measuring ammonia’s concentration.
. The DFB diode laser (NEL NLK1S5EAAA) produced by NTT Electronics Company is used as the spectroscopic source. The laser current and temperature are controlled by a commercial diode laser controller (ITC4001). Light from the fiber-coupled diode laser emitting near 1531.5 nm (6529.5 cm-1) is passed to a fiber collimator (Thorlabs F280FC-1550) and sent through a gas cell (length is 25.5 cm). The optical power exiting from the cell is detected using a large surface (3 mm diameter) Ge photodiode. The laser is tuned to the line center wavelength 1531.585 nm (6529.184 cm−1) of the selected transition using a free-space near-infrared (NIR) wavelength meter (Bristol 621B). Meanwhile, the diode laser is sinusoidally modulated by 1.0 kHz digital waveforms generated by a signal generator (AFG 3021B), and the modulation depths are adjusted to the optimum value (a = 0.0392 cm−1). The detector signals are recorded by a digital oscilloscope (DPO 4034B) and demodulated by a digital lock-in software.

Prior to each experiment, the cell is evacuated by a vacuum pump to an ultimate pressure of 1.0 Pa to record the background of 1f and 2f signals. Then the cell is filled with the NH3-air mixture controlled by the two mass flow controllers, and the NH3 mole fraction can be chosen according to the experimental requirements. Figure 2
Fig. 2 (a) Incident and transmitted laser intensity versus time; (b) n-f signal amplitudes from the data of curve A and B (P = 0.1atm, T = 296K, L = 25.5cm, X = 10.0%, a = 0.0392cm−1).
shows a typical experimental result. The cell is filled with a mixture gas of 10.0% NH3, where the total gas pressure and temperature are 0.1 atm and 296K, respectively. Additionally, calculations show that the absorbance and modulation index are about 16.5% and 2.20 in the experiment.

In Fig. 2(a), curves A and B are the incident (no NH3 absorption) and transmitted (with NH3 absorption) laser intensities recorded by the digital oscilloscope, and the laser parameter i1 is about 0.136, which can be determined by curve A. Meanwhile, in Fig. 2(b), a discrete Fourier transform (DFT) is used to gain the n-f signal amplitudes from the data of curves A and B, and the even harmonic amplitudes have been deducted the background signals. The result of the DFT shows that the 1f signal amplitude is very large (R1f = 459) and the 2f signal amplitude (R2f = 5.0) is very small under no-NH3 absorption conditions. However, the 1f signal amplitude decreases gradually (S1f = 444) and the 2f signal amplitude increases rapidly (S2f = 194) when the laser is absorbed by NH3. Here, we can obtain the 2f/1f signals as follows: S = S2f /S1f = 0.437, R = S2f /R1f = 0.423. Moreover, the values of H2 and T2 can be calculated according to the line-shape function and the modulation index (H2 = −7.56, T2 = −145.51). Substituting these parameters (S, R,i1, P, S(T), L, H2 and T2) into Eq. (11) and Eq. (18), we can infer that the NH3 mole fractions are about 9.574% and 10.069%, respectively.

In the following experiments, fixed laser parameters, temperature, and pressure remain unchanged (a = 0.0392cm−1, i1 = 0.136, P = 0.1atm, T = 296 K). The NH3 mole fraction (from 1.0% to 26.0%) is controlled by the mass flow controllers, and the absorbance changes from 2.0% to 30.0%. Figure 3(a)
Fig. 3 (a) Measured fraction of the first-order and second-order algorithms; (b) measurement errors of NH3 mole fraction (i1 = 0.136, P = 0.1atm, T = 296K, L = 25.5cm, a = 0.0392cm−1).
compares the known NH3 mole fraction with the measured fraction determined by the first-order and second-order algorithms. Moreover, the absorbance is also plotted in Fig. 3(a) as a function of the NH3 mole fraction.

In Fig. 3(a), the NH3 mole fractions determined by the first-order and second-order algorithms are in good agreement with the actual values when the absorbance is less than 5.0%. However, whether with the first- or second-order algorithm, the deviations between the measured and actual value increases as absorbance increases, and the former’s deviations are much larger than the latter’s. For example, when the absorbance is 9.41% (XNH3 = 5.0%), the measured fractions determined by the first-order and second-order algorithms are about 4.878% and 5.021%, respectively. In Fig. 3(b), the deviations of the experimental results from the known NH3 mole fraction are clearly seen. For example, the relative error does not exceed 2.10%, and even the absorbance is about 30.61% (XNH3 = 26.0%) when the second-order algorithm is used.

4. Conclusions

A second-order algorithm for measuring gas concentrations is reported in this paper. First, a second-order Taylor series is employed to approximate the laser transmission, and the expression for measuring gas concentrations is derived based on the absorption spectral theory. Second, a second-order algorithm with high precision and wide application is established. Finally, to validate the measurement accuracy of this algorithm, the NH3 mole fractions are determined by the first-order and second-order algorithms, respectively. Compared with the first-order algorithm, the second-order algorithm has greatly improved the gas concentration measurement accuracy and also broadened the scope of application of TDLAS.

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 51176085 and China Postdoctoral Science Foundation No 2011M500301.

References and links

1.

J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B 78(3-4), 503–511 (2004). [CrossRef]

2.

R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc. 157(1), B45–B53 (2010). [CrossRef]

3.

G. B. Rieker, J. B. Jeffries, R. K. Hanson, T. Mathur, M. R. Gruber, and C. D. Carter, “Diode laser-based detection of combustor instabilities with application to a scramjet engine,” Proc. Combust. Inst. 32(1), 831–838 (2009). [CrossRef]

4.

T. D. Cai, H. Jia, G. S. Wang, W. D. Chen, and X. M. Gao, “A sensor for measurements of temperature and water concentration using a single tunable diode laser near 1.4um,” Sens. Actuators A Phys. 152(1), 5–12 (2009). [CrossRef]

5.

F. Wang, K. F. Cen, N. Li, Q. X. Huang, X. Chao, J. H. Yan, and Y. Chi, “Simultaneous measurement on gas concentration and particle mass concentration by tunable diode laser,” Flow Meas. Instrum. 21(3), 382–387 (2010). [CrossRef]

6.

H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt. 45(5), 1052–1061 (2006). [CrossRef] [PubMed]

7.

H. Li, A. Farooq, J. B. Jeffries, and R. K. Hanson, “Near-infrared diode laser absorption sensor for rapid measurements of temperature and water vapor in a shock tube,” Appl. Phys. B 89(2-3), 407–416 (2007). [CrossRef]

8.

G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt. 48(29), 5546–5560 (2009). [CrossRef] [PubMed]

9.

A. L. Chakraborty, K. Ruxton, W. Johnstone, M. Lengden, and K. Duffin, “Elimination of residual amplitude modulation in tunable diode laser wavelength modulation spectroscopy using an optical fiber delay line,” Opt. Express 17(12), 9602–9607 (2009). [CrossRef] [PubMed]

10.

J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers comparison of experiment and theory,” Appl. Phys. B 26(3), 203–210 (1981). [CrossRef]

11.

P. Kluczynski and O. Axner, “Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt. 38(27), 5803–5815 (1999). [CrossRef] [PubMed]

12.

E. Detommasi, A. Castrillo, G. Casa, and L. Gianfrani, “An efficient approximation for a wavelength modulated 2nd harmonic lineshape from a Voigt absorption profile,” J. Quant. Spectrosc. Radiat. Transf. 109(1), 168–175 (2008). [CrossRef]

13.

J. B. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7 μm,” Appl. Phys. B 96(1), 161–173 (2009). [CrossRef]

14.

H. Jia, W. Zhao, T. Cai, W. Chen, W. Zhang, and X. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf. 110(6-7), 347–357 (2009). [CrossRef]

OCIS Codes
(300.1030) Spectroscopy : Absorption
(300.6260) Spectroscopy : Spectroscopy, diode lasers

ToC Category:
Spectroscopy

History
Original Manuscript: August 31, 2011
Revised Manuscript: October 13, 2011
Manuscript Accepted: October 16, 2011
Published: October 31, 2011

Citation
Peng Zhimin, Ding Yanjun, Che Lu, Li Xiaohang, and Zheng Kangjie, "Calibration-free wavelength modulated TDLAS under high absorbance conditions," Opt. Express 19, 23104-23110 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23104


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. T. C. Liu, J. B. Jeffries, and R. K. Hanson, “Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows,” Appl. Phys. B78(3-4), 503–511 (2004). [CrossRef]
  2. R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “In situ measurements of water vapor partial pressure and temperature dynamics in a PEM fuel cell,” J. Electrochem. Soc.157(1), B45–B53 (2010). [CrossRef]
  3. G. B. Rieker, J. B. Jeffries, R. K. Hanson, T. Mathur, M. R. Gruber, and C. D. Carter, “Diode laser-based detection of combustor instabilities with application to a scramjet engine,” Proc. Combust. Inst.32(1), 831–838 (2009). [CrossRef]
  4. T. D. Cai, H. Jia, G. S. Wang, W. D. Chen, and X. M. Gao, “A sensor for measurements of temperature and water concentration using a single tunable diode laser near 1.4um,” Sens. Actuators A Phys.152(1), 5–12 (2009). [CrossRef]
  5. F. Wang, K. F. Cen, N. Li, Q. X. Huang, X. Chao, J. H. Yan, and Y. Chi, “Simultaneous measurement on gas concentration and particle mass concentration by tunable diode laser,” Flow Meas. Instrum.21(3), 382–387 (2010). [CrossRef]
  6. H. Li, G. B. Rieker, X. Liu, J. B. Jeffries, and R. K. Hanson, “Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases,” Appl. Opt.45(5), 1052–1061 (2006). [CrossRef] [PubMed]
  7. H. Li, A. Farooq, J. B. Jeffries, and R. K. Hanson, “Near-infrared diode laser absorption sensor for rapid measurements of temperature and water vapor in a shock tube,” Appl. Phys. B89(2-3), 407–416 (2007). [CrossRef]
  8. G. B. Rieker, J. B. Jeffries, and R. K. Hanson, “Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments,” Appl. Opt.48(29), 5546–5560 (2009). [CrossRef] [PubMed]
  9. A. L. Chakraborty, K. Ruxton, W. Johnstone, M. Lengden, and K. Duffin, “Elimination of residual amplitude modulation in tunable diode laser wavelength modulation spectroscopy using an optical fiber delay line,” Opt. Express17(12), 9602–9607 (2009). [CrossRef] [PubMed]
  10. J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers comparison of experiment and theory,” Appl. Phys. B26(3), 203–210 (1981). [CrossRef]
  11. P. Kluczynski and O. Axner, “Theoretical description based on Fourier analysis of wavelength-modulation spectrometry in terms of analytical and background signals,” Appl. Opt.38(27), 5803–5815 (1999). [CrossRef] [PubMed]
  12. E. Detommasi, A. Castrillo, G. Casa, and L. Gianfrani, “An efficient approximation for a wavelength modulated 2nd harmonic lineshape from a Voigt absorption profile,” J. Quant. Spectrosc. Radiat. Transf.109(1), 168–175 (2008). [CrossRef]
  13. J. B. Farooq, J. B. Jeffries, and R. K. Hanson, “Sensitive detection of temperature behind reflected shock waves using wavelength modulation spectroscopy of CO2 near 2.7 μm,” Appl. Phys. B96(1), 161–173 (2009). [CrossRef]
  14. H. Jia, W. Zhao, T. Cai, W. Chen, W. Zhang, and X. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm−1,” J. Quant. Spectrosc. Radiat. Transf.110(6-7), 347–357 (2009). [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited