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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 30 — Oct. 20, 2009
  • pp: 5748–5758

Using integrating spheres as absorption cells: path-length distribution and application of Beer’s law

Jane Hodgkinson, Dackson Masiyano, and Ralph P. Tatam  »View Author Affiliations

Applied Optics, Vol. 48, Issue 30, pp. 5748-5758 (2009)

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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 1651 nm in a 50 mm diameter sphere, with good agreement with experimental data in the absorption range of 0 0.01 cm 1 . Our results compare well with previous work on the temporal response of integrating spheres.

© 2009 Optical Society of America

OCIS Codes
(120.3150) Instrumentation, measurement, and metrology : Integrating spheres
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(300.1030) Spectroscopy : Absorption
(280.4788) Remote sensing and sensors : Optical sensing and sensors

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: April 30, 2009
Revised Manuscript: August 4, 2009
Manuscript Accepted: September 24, 2009
Published: October 14, 2009

Jane Hodgkinson, Dackson Masiyano, and Ralph P. Tatam, "Using integrating spheres as absorption cells: path-length distribution and application of Beer's law," Appl. Opt. 48, 5748-5758 (2009)

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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]

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