Abstract

The equivalent absorption path length in an integrating cavity is examined. In an otherwise excellent paper, Tranchart et al. [Appl. Opt. 35, 7070 (1996)] made an important error in obtaining the expressions for the equivalent path length in an integrating cavity. This error has been propagated through several other publications in the literature. Since the equivalent path length is the sine qua non for obtaining an accurate absorption coefficient when using an integrating cavity, it is our intent here to give the correct formulas to prevent further errors when extracting absorption coefficients.

© 2010 Optical Society of America

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References

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  1. S. Tranchart, I. H. Bachir, and J.-L. Destombes, “Sensitive trace gas detection with near-infrared laser diodes and an integrating sphere,” Appl. Opt. 35, 7070-7074 (1996).
    [CrossRef] [PubMed]
  2. D. W. T. Griffith and I. M. Jamie, “Fourier transform infrared spectrometry in atmospheric and trace gas analysis,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed (Wiley, 2000), pp. 1979-2007.
  3. F. K. Tittel and K. P. Petrov, “Diode laser spectroscopic monitoring of trace gases,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed. (Wiley, 2000), pp. 1959-1979.
  4. H. P. Zappe, M. Hess, M. Moser, R. Hövel, K. Gulden, H. Gauggel, and F. Monti di Sopra, “Narrow-linewidth vertical-cavity surface-emitting lasers for oxygen detection,” Appl. Opt. 39, 2475-2479 (2000).
    [CrossRef]
  5. J. E. Thompson, B. W. Smith, and J. D. Winefordner, “Monitoring atmospheric particulate matter through cavity ring-down spectroscopy,” Anal. Chem. 74, 1962-1967 (2002).
    [CrossRef] [PubMed]
  6. E. Hawe, E. Lewis, and C. Fitzpatrick, “Hazardous gas detection with an integrating sphere in the near-infrared,” J. Phys. Conf. Ser. 15, 250-255 (2005).
    [CrossRef]
  7. E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
    [CrossRef]
  8. H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
    [CrossRef]
  9. E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).
  10. E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
    [CrossRef]
  11. D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Methodology for investigation of diffuse reflections in tunable diode laser absorption spectroscopy,” J. Phys. Conf. Ser. 76, 012052(2007).
    [CrossRef]
  12. D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements,” Appl. Phys. B 90, 279-288 (2008).
    [CrossRef]
  13. J. Hodgkinson, D. Masiyano, and R. P. Tatam, “Using integrating spheres as absorption cells: path-length distribution and application of Beer's law,” Appl. Opt. 48, 5748-5758(2009).
    [CrossRef] [PubMed]
  14. E. Berger, D. W. T. Griffith, G. Schuster, and S. R. Wilson, “Spectroscopy of matrices and thin films with an integrating sphere,” Appl. Spectrosc. 43, 320-324 (1989).
    [CrossRef]
  15. E. S. Fry, J. Musser, G. W. Kattawar, and P. Zhai, “Integrating cavities: temporal response,” Appl. Opt. 45, 9053-9065(2006).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements,” Appl. Phys. B 90, 279-288 (2008).
[CrossRef]

2007 (3)

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
[CrossRef]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Methodology for investigation of diffuse reflections in tunable diode laser absorption spectroscopy,” J. Phys. Conf. Ser. 76, 012052(2007).
[CrossRef]

2006 (2)

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

E. S. Fry, J. Musser, G. W. Kattawar, and P. Zhai, “Integrating cavities: temporal response,” Appl. Opt. 45, 9053-9065(2006).
[CrossRef] [PubMed]

2005 (1)

E. Hawe, E. Lewis, and C. Fitzpatrick, “Hazardous gas detection with an integrating sphere in the near-infrared,” J. Phys. Conf. Ser. 15, 250-255 (2005).
[CrossRef]

2002 (1)

J. E. Thompson, B. W. Smith, and J. D. Winefordner, “Monitoring atmospheric particulate matter through cavity ring-down spectroscopy,” Anal. Chem. 74, 1962-1967 (2002).
[CrossRef] [PubMed]

2000 (1)

1996 (1)

1989 (1)

Al-Shamma'a, A.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Bachir, I. H.

Berger, E.

Bramman, G.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Chambers, P.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
[CrossRef]

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

Degner, M.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Destombes, J.-L.

Dooly, G.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

Ewald, H.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Faraldi, P.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Fitzpatrick, C.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
[CrossRef]

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

E. Hawe, E. Lewis, and C. Fitzpatrick, “Hazardous gas detection with an integrating sphere in the near-infrared,” J. Phys. Conf. Ser. 15, 250-255 (2005).
[CrossRef]

Fry, E. S.

Gauggel, H.

Grattan, K. T. V.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Griffith, D. W. T.

E. Berger, D. W. T. Griffith, G. Schuster, and S. R. Wilson, “Spectroscopy of matrices and thin films with an integrating sphere,” Appl. Spectrosc. 43, 320-324 (1989).
[CrossRef]

D. W. T. Griffith and I. M. Jamie, “Fourier transform infrared spectrometry in atmospheric and trace gas analysis,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed (Wiley, 2000), pp. 1979-2007.

Gulden, K.

Hawe, E.

E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
[CrossRef]

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

E. Hawe, E. Lewis, and C. Fitzpatrick, “Hazardous gas detection with an integrating sphere in the near-infrared,” J. Phys. Conf. Ser. 15, 250-255 (2005).
[CrossRef]

Hess, M.

Hitchen, D.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Hodgkinson, J.

J. Hodgkinson, D. Masiyano, and R. P. Tatam, “Using integrating spheres as absorption cells: path-length distribution and application of Beer's law,” Appl. Opt. 48, 5748-5758(2009).
[CrossRef] [PubMed]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements,” Appl. Phys. B 90, 279-288 (2008).
[CrossRef]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Methodology for investigation of diffuse reflections in tunable diode laser absorption spectroscopy,” J. Phys. Conf. Ser. 76, 012052(2007).
[CrossRef]

Hövel, R.

Jamie, I. M.

D. W. T. Griffith and I. M. Jamie, “Fourier transform infrared spectrometry in atmospheric and trace gas analysis,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed (Wiley, 2000), pp. 1979-2007.

Kakuma, S.

H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
[CrossRef]

Kattawar, G. W.

Lewis, E.

E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
[CrossRef]

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

E. Hawe, E. Lewis, and C. Fitzpatrick, “Hazardous gas detection with an integrating sphere in the near-infrared,” J. Phys. Conf. Ser. 15, 250-255 (2005).
[CrossRef]

Lochmann, S.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Lucas, J.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Masiyano, D.

J. Hodgkinson, D. Masiyano, and R. P. Tatam, “Using integrating spheres as absorption cells: path-length distribution and application of Beer's law,” Appl. Opt. 48, 5748-5758(2009).
[CrossRef] [PubMed]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements,” Appl. Phys. B 90, 279-288 (2008).
[CrossRef]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Methodology for investigation of diffuse reflections in tunable diode laser absorption spectroscopy,” J. Phys. Conf. Ser. 76, 012052(2007).
[CrossRef]

Merlone-Borla, E.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Monti di Sopra, F.

Moser, M.

Musser, J.

Noda, K.

H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
[CrossRef]

Okajima, H.

H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
[CrossRef]

Petrov, K. P.

F. K. Tittel and K. P. Petrov, “Diode laser spectroscopic monitoring of trace gases,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed. (Wiley, 2000), pp. 1959-1979.

Pidria, M.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Schuster, G.

Smith, B. W.

J. E. Thompson, B. W. Smith, and J. D. Winefordner, “Monitoring atmospheric particulate matter through cavity ring-down spectroscopy,” Anal. Chem. 74, 1962-1967 (2002).
[CrossRef] [PubMed]

Sun, T.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Tatam, R. P.

J. Hodgkinson, D. Masiyano, and R. P. Tatam, “Using integrating spheres as absorption cells: path-length distribution and application of Beer's law,” Appl. Opt. 48, 5748-5758(2009).
[CrossRef] [PubMed]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements,” Appl. Phys. B 90, 279-288 (2008).
[CrossRef]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Methodology for investigation of diffuse reflections in tunable diode laser absorption spectroscopy,” J. Phys. Conf. Ser. 76, 012052(2007).
[CrossRef]

Thompson, J. E.

J. E. Thompson, B. W. Smith, and J. D. Winefordner, “Monitoring atmospheric particulate matter through cavity ring-down spectroscopy,” Anal. Chem. 74, 1962-1967 (2002).
[CrossRef] [PubMed]

Tittel, F. K.

F. K. Tittel and K. P. Petrov, “Diode laser spectroscopic monitoring of trace gases,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed. (Wiley, 2000), pp. 1959-1979.

Tranchart, S.

Uchida, K.

H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
[CrossRef]

Wakimoto, Y.

H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
[CrossRef]

Wei, C.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Wilson, S. R.

Winefordner, J. D.

J. E. Thompson, B. W. Smith, and J. D. Winefordner, “Monitoring atmospheric particulate matter through cavity ring-down spectroscopy,” Anal. Chem. 74, 1962-1967 (2002).
[CrossRef] [PubMed]

Zappe, H. P.

Zhai, P.

Zhao, W. Z.

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

Anal. Chem. (1)

J. E. Thompson, B. W. Smith, and J. D. Winefordner, “Monitoring atmospheric particulate matter through cavity ring-down spectroscopy,” Anal. Chem. 74, 1962-1967 (2002).
[CrossRef] [PubMed]

Appl. Opt. (4)

Appl. Phys. B (1)

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements,” Appl. Phys. B 90, 279-288 (2008).
[CrossRef]

Appl. Spectrosc. (1)

Int. J. Intell. Syst. Technol. Appl. (1)

E. Hawe, G. Dooly, C. Fitzpatrick, P. Chambers, E. Lewis, W. Z. Zhao, T. Sun, K. T. V. Grattan, M. Degner, H. Ewald, S. Lochmann, G. Bramman, C. Wei, D. Hitchen, J. Lucas, A. Al-Shamma'a, E. Merlone-Borla, P. Faraldi, and M. Pidria, “Measuring of exhaust gas emissions using absorption spectroscopy,” Int. J. Intell. Syst. Technol. Appl. 3, 33-51 (2007).

J. Phys. Conf. Ser. (2)

E. Hawe, E. Lewis, and C. Fitzpatrick, “Hazardous gas detection with an integrating sphere in the near-infrared,” J. Phys. Conf. Ser. 15, 250-255 (2005).
[CrossRef]

D. Masiyano, J. Hodgkinson, and R. P. Tatam, “Methodology for investigation of diffuse reflections in tunable diode laser absorption spectroscopy,” J. Phys. Conf. Ser. 76, 012052(2007).
[CrossRef]

Meas. Sci. Technol. (1)

E. Hawe, P. Chambers, C. Fitzpatrick, and E. Lewis, “CO2 monitoring and detection using an integrating sphere as a multipass absorption cell,” Meas. Sci. Technol. 18, 3187-3194(2007).
[CrossRef]

Proc. SPIE (1)

E. Hawe, G. Dooly, C. Fitzpatrick, E. Lewis, and P. Chambers, “UV based pollutant quantification in automotive exhausts,” Proc. SPIE 6198, 619807 (2006).
[CrossRef]

Other (3)

H. Okajima, S. Kakuma, K. Uchida, Y. Wakimoto, and K. Noda, “Measurement of methane gas concentration using an infrared LED,” in Proceedings of the SICE-ICASE International Joint Conference (IEEE, 2006), pp. 1652-1655.
[CrossRef]

D. W. T. Griffith and I. M. Jamie, “Fourier transform infrared spectrometry in atmospheric and trace gas analysis,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed (Wiley, 2000), pp. 1979-2007.

F. K. Tittel and K. P. Petrov, “Diode laser spectroscopic monitoring of trace gases,” in Encyclopedia of Analytical Chemistry: Applications, Theory, and Instrumentation, R. A. Meyer, ed. (Wiley, 2000), pp. 1959-1979.

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Figures (2)

Fig. 1
Fig. 1

For radiation incident upon the interior of the cavity that is collimated, the appropriate prefactor corresponding to the first reflection is ρ exp [ α ( ν ) D ] . However, for isotropic incident radiation, the appropriate prefactor is ρ ( 1 h ) exp [ α ( ν ) L eff ] .

Fig. 2
Fig. 2

Relative percent error between Eq. (2) and the more accurate Eq. (7) as a function of absorption of the medium and reflectivity of the cavity walls. The inner diameter of the integrating cavity is 10 cm , whereas the fractional area open for ports is 0.01. The color mapping is linear from 0 to 150 relative percent error.

Equations (14)

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Δ Φ Φ e ( 0 ) = α ( ν ) L eff 1 ρ [ 1 α ( ν ) L eff ] ( 1 h ) ,
L e q = L eff 1 ρ = 2 D 3 ( 1 ρ )
ρ [ 1 α ( ν ) L eff ] Φ .
Φ ρ exp [ α ( ν ) L eff ] .
Φ f ,
Δ Φ Φ e ( 0 ) = 1 Φ e ( α ) Φ e ( 0 ) = 1 exp [ α ( ν ) L eff ] 1 ρ ( 1 h ) exp [ α ( ν ) L eff ] .
L e q = L eff 1 ρ ( 1 h ) ( 1 α ( ν ) L eff ) L eff 1 ρ + ρ h + ρ α ( ν ) L eff .
Φ ( t ) = Φ 0 exp [ t τ ] ,
Φ ( t ¯ ) = ρ ( 1 h ) Φ 0 exp [ α ( ν ) L eff ] ,
Φ ( n t ¯ ) = ρ n ( 1 h ) n Φ 0 exp [ n α ( ν ) L eff ] = Φ 0 exp [ n ln ρ + n ln ( 1 h ) n α ( ν ) L eff ] .
1 = n ln ρ + n ln ( 1 h ) n α ( ν ) L eff .
n = 1 α ( ν ) L eff ln ρ ln ( 1 h ) .
τ = n t ¯ = n L eff c = L eff c ( α ( ν ) L eff ln ρ ln ( 1 h ) ) .
L e q = c τ = L eff α ( ν ) L eff ln ρ ln ( 1 h ) L eff 1 ρ + h + α ( ν ) L eff ,

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