Abstract

We have modeled the path-length distribution in an integrating sphere used as a multipass optical cell for absorption measurements. The measured radiant flux as a function of analyte concentration is nonlinear as a result, deviating from that expected for a single path length. We have developed a full numerical model and introduce a new analytical relationship that describes this behavior for high reflectivity spheres. We have tested both models by measuring the optical absorption of methane at 1651nm in a 50mm diameter sphere, with good agreement with experimental data in the absorption range of 00.01cm1. Our results compare well with previous work on the temporal response of integrating spheres.

© 2009 Optical Society of America

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  1. “A guide to integrating sphere theory and applications,” Labsphere, North Sutton, N.H., USA (1998).
  2. P. Elterman, “Integrating cavity spectroscopy,” Appl. Opt. 9, 2140-2142 (1970).
    [CrossRef] [PubMed]
  3. E. S. Fry, G. W. Kattawar, and R. M. Pope, “Integrating cavity absorption meter,” Appl. Opt. 31, 2055-2065 (1992).
    [CrossRef] [PubMed]
  4. I. Fecht and M. Johnson, “Non-contact, scattering-independent water absorption measurement using a falling stream and integrating sphere,” Meas. Sci. Technol. 10612-618 (1999).
    [CrossRef]
  5. J. Hodgkinson, M. Johnson, and J. P. Dakin, “Performance of a photothermal detector with turbid liquids,” Appl. Opt. 44, 4360-4367 (2005).
    [CrossRef] [PubMed]
  6. C. G. Venkatesh, R. S. Eng, and A. W. Mantz, “Tunable diode laser integrating sphere systems: a study of their output intensity characteristics,” Appl. Opt. 19, 1704-1710 (1980).
    [CrossRef] [PubMed]
  7. R. M. Abdullin and A. V. Lebedev, “Use of an integrating sphere as a multipass optical cell,” Sov. J. Opt. Technol. 55, 139-141 (1988).
  8. 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]
  9. J. U. White, “Long optical paths of large aperture,” J. Opt. Soc. Am. 32, 285-288 (1942).
    [CrossRef]
  10. D. R. Herriott, H. Kogelnik, and R. Kompfner, “Off-axis paths in spherical mirror interferometers,” Appl. Opt. 3, 523-526(1964).
    [CrossRef]
  11. S. M. Chernin and E. G. Barskaya, “Optical multipass matrix system,” Appl. Opt. 30, 51-58 (1991).
    [CrossRef] [PubMed]
  12. 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]
  13. E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
    [CrossRef]
  14. S. C. Cutler and A. Vass, “Gas Sensor,” International patent, publication number WO 2005/054827 A1 (2005).
  15. Institution of Gas Engineers and Managers, “Dealing with reported gas escapes,' Safety Recommendations IGEM/SR/20, Ed. 2 (IGEM, London 1998).
  16. J. T. O. Kirk, “Modeling the performance of an integrating cavity absorption meter: theory and calculations for a spherical cavity,” Appl. Opt. 34, 4397-4408 (1995).
    [CrossRef] [PubMed]
  17. E. S. Fry, J. Musser, G. W. Kattawar, and P.-W. Zhai, “Integrating cavities: temporal response,” Appl. Opt. 45, 9053-9065(2006).
    [CrossRef] [PubMed]
  18. J. D. Ingle and S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, 1988).
  19. 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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
    [CrossRef]

2008

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

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]

2006

2005

J. Hodgkinson, M. Johnson, and J. P. Dakin, “Performance of a photothermal detector with turbid liquids,” Appl. Opt. 44, 4360-4367 (2005).
[CrossRef] [PubMed]

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

1999

I. Fecht and M. Johnson, “Non-contact, scattering-independent water absorption measurement using a falling stream and integrating sphere,” Meas. Sci. Technol. 10612-618 (1999).
[CrossRef]

1996

1995

1992

1991

1988

R. M. Abdullin and A. V. Lebedev, “Use of an integrating sphere as a multipass optical cell,” Sov. J. Opt. Technol. 55, 139-141 (1988).

1980

1970

1964

1942

Abdullin, R. M.

R. M. Abdullin and A. V. Lebedev, “Use of an integrating sphere as a multipass optical cell,” Sov. J. Opt. Technol. 55, 139-141 (1988).

Bachir, I. H.

Barbe, A.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Barskaya, E. G.

Benner, D. C.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Birk, M.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Brown, L. R.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Carleer, M. R.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Chackerian, C.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Chambers, P.

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

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]

Chance, K.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Chernin, S. M.

Coudert, L. H.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Crouch, S. R.

J. D. Ingle and S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, 1988).

Cutler, S. C.

S. C. Cutler and A. Vass, “Gas Sensor,” International patent, publication number WO 2005/054827 A1 (2005).

Dakin, J. P.

Dana, V.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Destombes, J.-L.

Devi, V. M.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Dooly, G.

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

Elterman, P.

Eng, R. S.

Fecht, I.

I. Fecht and M. Johnson, “Non-contact, scattering-independent water absorption measurement using a falling stream and integrating sphere,” Meas. Sci. Technol. 10612-618 (1999).
[CrossRef]

Fitzpatrick, C.

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

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]

Flaud, J.-M.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Fry, E. S.

Gamache, R. R.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Goldman, A.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Hartmann, J.-M.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Hawe, E.

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

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]

Herriott, D. R.

Hodgkinson, J.

Ingle, J. D.

J. D. Ingle and S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, 1988).

Jacquemart, D.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Johnson, M.

J. Hodgkinson, M. Johnson, and J. P. Dakin, “Performance of a photothermal detector with turbid liquids,” Appl. Opt. 44, 4360-4367 (2005).
[CrossRef] [PubMed]

I. Fecht and M. Johnson, “Non-contact, scattering-independent water absorption measurement using a falling stream and integrating sphere,” Meas. Sci. Technol. 10612-618 (1999).
[CrossRef]

Jucks, K. W.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Kattawar, G. W.

Kirk, J. T. O.

Kogelnik, H.

Kompfner, R.

Lebedev, A. V.

R. M. Abdullin and A. V. Lebedev, “Use of an integrating sphere as a multipass optical cell,” Sov. J. Opt. Technol. 55, 139-141 (1988).

Lewis, E.

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

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]

Maki, A. G.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Mandin, J.-Y.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Mantz, A. W.

Massie, S. T.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Musser, J.

Orphal, J.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Perrin, A.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Pope, R. M.

Rinsland, C. P.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Rothman, L. S.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Smith, M. A. H.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Tennyson, J.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Tolchenov, R. N.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Toth, R. A.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Tranchart, S.

VanderAuwera, J.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Varanasi, P.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Vass, A.

S. C. Cutler and A. Vass, “Gas Sensor,” International patent, publication number WO 2005/054827 A1 (2005).

Venkatesh, C. G.

Wagner, G.

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

White, J. U.

Zhai, P.-W.

Appl. Opt.

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

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. VanderAuwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 96, 139-204 (2005).
[CrossRef]

Meas. Sci. Technol.

I. Fecht and M. Johnson, “Non-contact, scattering-independent water absorption measurement using a falling stream and integrating sphere,” Meas. Sci. Technol. 10612-618 (1999).
[CrossRef]

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]

Sens. Actuators A

E. Hawe, C. Fitzpatrick, P. Chambers, G. Dooly, and E. Lewis, “Hazardous gas detection using an integrating sphere as a multipass gas cell,” Sens. Actuators A 141, 414-421(2008).
[CrossRef]

Sov. J. Opt. Technol.

R. M. Abdullin and A. V. Lebedev, “Use of an integrating sphere as a multipass optical cell,” Sov. J. Opt. Technol. 55, 139-141 (1988).

Other

“A guide to integrating sphere theory and applications,” Labsphere, North Sutton, N.H., USA (1998).

S. C. Cutler and A. Vass, “Gas Sensor,” International patent, publication number WO 2005/054827 A1 (2005).

Institution of Gas Engineers and Managers, “Dealing with reported gas escapes,' Safety Recommendations IGEM/SR/20, Ed. 2 (IGEM, London 1998).

J. D. Ingle and S. R. Crouch, Spectrochemical Analysis (Prentice-Hall, 1988).

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Figures (13)

Fig. 1
Fig. 1

Simplified model of an integrating sphere, showing the incident beam making a first pass across the cell to the first strike spot. Two examples are shown of light beams making subsequent random multiple passes across the cell.

Fig. 2
Fig. 2

Illustration of different phases of a photon’s journey within the integrating sphere, from entrance aperture to detector.

Fig. 3
Fig. 3

Geometry used to model integrating sphere path-length distribution, including elemental surface areas d S 1 and d S 2 .

Fig. 4
Fig. 4

Illustration of numerical modeling procedure for path-length distribution: (a) determining the values of path lengths in discrete intervals and (b) determining the corresponding PDF.

Fig. 5
Fig. 5

Experimental configuration used for direct line scanning or wavelength modulation spectroscopy of methane absorption in an integrating sphere.

Fig. 6
Fig. 6

Examples of detected signals recorded while the laser wavelength was scanned across a single methane line at 1651 nm . (a) Raw data from the detector for HC-free air and for a methane concentration of 5770 ppm . (b) Methane transmission normalized by division by the background signal.

Fig. 7
Fig. 7

Comparison of experimentally determined response and the results of Eq. (12) using optimized values of ρ and z . Also shown for comparison is the response predicted by the Beer–Lambert law for a single path-length cell.

Fig. 8
Fig. 8

Residual error in modeled response of the system (as Δ I / I 0 ) compared to experimental results, comparing the results of Eq. (12) for different values of ρ and z . Agreement with the optimized model is within our estimated experimental error.

Fig. 9
Fig. 9

Optical path-length distribution for a 50.8 mm diameter sphere. (a) Numerical model for three different average sphere reflectivities and (b) expanded linear scale showing the correspondence between the numerical and the analytical models for the first few passes across the cell. The launch path z and the offset z 0 / 2 [see Eq. (12)] are indicated for clarity.

Fig. 10
Fig. 10

Comparison of experimentally determined response and the results of a full numerical model for a 2 in. (5 cm) integrating sphere with a range of average internal reflectivities. The response predicted by the Beer–Lambert law for a single path-length cell is also provided as a comparison.

Fig. 11
Fig. 11

Residual error in response of the system predicted by the full numerical model (as Δ I / I 0 ) compared to experimental results, for three modeled values of ρ including the optimum value of ρ = 97.15 % .

Fig. 12
Fig. 12

Sensitivity analysis for modeled response of a 50.8 mm integrating sphere, showing the variation of (a)  Z eff (the mean effective path length for zero absorption) and (b) rms residual error with the modeled reflectivity ρ.

Fig. 13
Fig. 13

Extrapolated response of integrating sphere to methane concentrations in the range 0.1 to 100 vol . % , compared to the response predicted by the Beer–Lambert law for the single path length given in Table 2 for the optimized model.

Tables (3)

Tables Icon

Table 1 Summary of Modeled Passes Across the Integrating Sphere

Tables Icon

Table 2 Levels of Residual Error for Comparisons Between Modeled and Experimental Data

Tables Icon

Table 3 Comparison of the Results of Our Model with the Previous Theoretical Work of Fry et al. [17]

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

Φ = Φ 0 exp ( α z ) ,
Δ Φ Φ 0 α z ,
Δ Φ Φ 0 α z 0 ( 1 ρ ) ,
Z eff 4 3 R ( 1 ρ ) .
0 Ψ ( z ) d z = 1.
Φ = Φ 0 0 Ψ ( z ) exp ( α z ) d z .
E ( t ) = E 0 exp ( t τ ) and τ = t ¯ ln ρ ,
E ( z ) = E 0 exp ( z δ ) and δ = z 0 ln ρ .
Ψ ( z ) = Ψ 0 exp ( z z 0 ln ρ ) ,
Φ Φ 0 = 0 exp ( z z 0 ln ρ α z ) d z 0 exp ( z z 0 ln ρ ) d z ,
Φ Φ 0 = ln ρ ln ρ α z 0 .
I I 0 = exp ( α ( z + z 0 2 ) ) ln ρ ln ρ α z 0 .
d 2 Φ d S 1 = L cos 2 θ z 2 d S 2 ,
d 2 Φ d S 1 = L 4 R 2 d S 2 .
d 2 Φ d S 1 = π L z 2 R 2 d z .
d Φ = π L d S 1 .
ψ ( z ) = d Φ d z = z 2 R 2 .
z 0 = 0 2 R z ψ ( z ) d z ,

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