## Calibration-free wavelength modulated TDLAS under high absorbance conditions |

Optics Express, Vol. 19, Issue 23, pp. 23104-23110 (2011)

http://dx.doi.org/10.1364/OE.19.023104

Acrobat PDF (1087 KB)

### 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 NH_{3} mole fraction in a cell with NH_{3}-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

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]

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]

*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. 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]

*f*) signal to normalize the second harmonic (2

*f*) signal, and the absorption information such as gas concentration can be gained from the 2

*f/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]

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]

_{3}mole fraction at different absorbance levels in the laboratory.

## 2. Derivation of second-order algorithm

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]

*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:where

*τ*(

*v*) is the laser transmission;

*I*

_{t}and

*I*

_{0}are the transmitted and incident laser intensities, respectively; and

*α*(

*v*) is the spectral absorbance. For the isolated transition

*α*(

*v*) =

*PLS*(

*T*)

*Xφ*(

*v*),

*P*(

*atm*) is the total gas pressure,

*S*(

*T*) (

*cm*) is the line strength,

^{−2}atm^{−1}*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]

*ξ = PLS*(

*T*), the functions

*A*are given as

_{k}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]

*i*

_{1},

*i*

_{2},

*ψ*

_{1}and

*ψ*

_{2}are the characteristic parameters of the diode-laser. Substituting Eq. (3) into Eq. (1) for harmonic detection, the magnitude of the 1

*f*and 2

*f*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]

*f*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 (

*A*

_{0}= 1,

*A*= 0), the magnitude of the 1

_{k}*f*signal can be written as follows, where

*f*signal:

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

*τ*(

*v*) can be expanded by a first-order Taylor series when the absorbance is less than 5.0%.where

*H*can be expressed as:

_{k}*i*

_{2}<<1; substituting Eq. (8) into Eq. (4), the 1

*f*, 2

*f*, and 2

*f*/1

*f*signals at the line center can be simplified as

*f*/1

*f*signal (

*S*) is measured through experiments:

### 2.2 Second-order algorithm

*f*signal can be expressed aswhere

*T*

_{2}will attain convergence and stability quickly and can be expanded as

*S*instead of

_{1f}*R*in the

_{1f}*2f/1f*calibration-free method, the second-order algorithm uses the background of the 1

*f*signal (

*R*) to determine the gas concentration, and the 2

_{1f}*f*/1

*f*signal at the line center can be written as

*i*

_{1},

*P*,

*S*(

*T*),

*L*,

*H*

_{2},

*T*

_{2}and

*R*) are known:

## 3. Experimental results

_{3}-air mixture as the research object. The absorption transition at 6529.184 cm

^{−1}is selected to measure the NH

_{3}concentration, and the spectroscopic parameters are shown in Table 1 [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]

^{−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.

*f*and 2

*f*signals. Then the cell is filled with the NH

_{3}-air mixture controlled by the two mass flow controllers, and the NH

_{3}mole fraction can be chosen according to the experimental requirements. Figure 2 shows a typical experimental result. The cell is filled with a mixture gas of 10.0% NH

_{3}, 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.

*A*and

*B*are the incident (no NH

_{3}absorption) and transmitted (with NH

_{3}absorption) laser intensities recorded by the digital oscilloscope, and the laser parameter

*i*

_{1}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 1

*f*signal amplitude is very large (

*R*= 459) and the 2

_{1f}*f*signal amplitude (

*R*= 5.0) is very small under no-NH

_{2f}_{3}absorption conditions. However, the 1

*f*signal amplitude decreases gradually (

*S*= 444) and the 2

_{1f}*f*signal amplitude increases rapidly (

*S*= 194) when the laser is absorbed by NH

_{2f}_{3}. Here, we can obtain the

*2f/1f*signals as follows:

*S*=

*S*= 0.437,

_{2f}/S_{1f}*R*=

*S*= 0.423. Moreover, the values of

_{2f}/R_{1f}*H*

_{2}and

*T*

_{2}can be calculated according to the line-shape function and the modulation index (

*H*

_{2}= −7.56,

*T*

_{2}= −145.51). Substituting these parameters (

*S, R,*

*P*,

*S*(

*T*),

*L, H*and

_{2}*T*) into Eq. (11) and Eq. (18), we can infer that the NH

_{2}_{3}mole fractions are about 9.574% and 10.069%, respectively.

*a*= 0.0392cm

^{−1},

*i*

_{1}= 0.136,

*P*= 0.1atm,

*T*= 296 K). The NH

_{3}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) compares the known NH

_{3}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 NH

_{3}mole fraction.

_{3}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% (

*X*

_{NH3}= 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 NH

_{3}mole fraction are clearly seen. For example, the relative error does not exceed 2.10%, and even the absorbance is about 30.61% (

*X*

_{NH3}= 26.0%) when the second-order algorithm is used.

## 4. Conclusions

## Acknowledgments

## 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 |

2. | R. Sur, T. J. Boucher, M. W. Renfro, and B. M. Cetegen, “ |

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. |

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. |

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. |

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. |

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 |

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. |

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 |

10. | J. Reid and D. Labrie, “Second harmonic detection with tunable diode lasers comparison of experiment and theory,” Appl. Phys. B |

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. |

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. |

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 |

14. | H. Jia, W. Zhao, T. Cai, W. Chen, W. Zhang, and X. Gao, “Absorption spectroscopy of ammonia between 6526 and 6538cm |

**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

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### References

- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]

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