Abstract

An analysis of the ultimate detectivity of ideal optoacoustic cells, based on viscous gas equations, gives rigorous expressions for both signal and noise for a one-dimensional optoacoustic cell. Choice of boundary conditions for the noise calculations is dictated by the dissipation fluctuation theorem. Results of noise equivalent power calculations indicate superior performances near dc frequencies over those obtained at resonant conditions. A simplifying dissipative acoustic transmission line model describing optoacoustic cells of quite general geometric configurations is developed that is particularly useful for noise evaluation. In contrast to ideal cells, current optoacoustic cells’ detectivities are practically limited by interfering signals induced by windows’ absorption of infrared radiation; acoustical resonant conditions can help reduce such interference. A resonant optoacoustic cell exhibiting high immunity to windows interference is described that yields two orders of magnitude interference reduction compared with previously operated optoacoustic cells. The cell uses the longitudinal modes of a narrow open tube. Its minimum detectable concentration of ethylene in nitrogen is less than 0.3 parts in 109 for 1 Hz detection bandwidth using a 1 W, 10.5326 μm CO2 laser beam. Electronic noise limits the detectivity, and is ~15 dB higher than the expected Brownian noise of an ideal cell of the same configuration. Measurements with flowing trace gas are given.

© 1978 Optical Society of America

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  1. L. B. Kreuzer, “Ultra Low Gas Concentration Infrared Absorption Spectroscopy.” J. Appl. Phys. 42, 2934 (1971).
    [Crossref]
  2. G. Diebold and D. L. McFadden, “Observation of the Optoacoustic Effect in the Microwave Region,” Appl. Phys. Lett. 29, 447 (1976).
    [Crossref]
  3. P. C. Claspy, Chang Ha, and Yoh-Han Pao, “Application of a Pulsed Dye Laser to Optoacoustic Detection of NO2,” J. Opt. Soc. Am. 66, 1072 (1976).
  4. A. G. Bell, Philos. Mag. 11, 510, (1881).
  5. W. C. Röntgen, Philos. Mag. 11, 308 (1881).
  6. J. Tyndall, Proc. R. Soc. London,  31, 307 (1881).
  7. K. F. Luft, Z. Tech. Phys. 24, 97–104 (1943).
  8. D. W. Hill and T. Powell, Non-Dispersive Infrared Gas Analysis in Science, Medicine and Industry (Plenum, New York, 1968).
  9. M. L. Veingerov, Dokl. Akad, Nauk SSSR 46, 182 (1945).
  10. E. L. Kerr and J. G. Atwood, “The Laser Illuminated Absorptivity Spectrophone: A Method for Measurement of Weak Absorptivity in Gases at Laser Wavelengths,” Appl. Opt. 7, 915 (1968).
    [Crossref] [PubMed]
  11. L. B. Kreuzer, N. D. Kenyon, and C. K. N. Patel, “Sensitive Detection of Ten Pollutant Gases by Carbon Monoxide and Carbon Dioxide Lasers,” Science 177, 347 (1972).
    [Crossref] [PubMed]
  12. L. B. Kreuzer, “Measurements of Concentration of Components of Gaseous Mixtures,” U. S. Patent No. 3, 820, 901 (June28, 1974).
  13. C. K. N. Patel, E. G. Burkhardt, and C. A. Lambert, “Spectroscopic Measurements of Stratospheric Nitric Oxide and Water Vapor,” Science 184, 1173 (1974).
    [Crossref] [PubMed]
  14. C. K. N. Patel, “Spectroscopic Measurements of the Stratosphere using Tunable Infrared Lasers,” Opt. Quantum Electron. 8, 145–154 (1976).
    [Crossref]
  15. L. G. Rosengren, Infrared Phys. 13, 109 (1973); Infrared Phys. 13, 173 (1973).
    [Crossref]
  16. L. G. Rosengren, E. Max, and S. T. Eng, “A Study of Laser Acoustic Air Pollution Monitors,” J. Phys. Sci. Instrum. 7, 125 (1974).
    [Crossref]
  17. E. Max and L. G. Rosengren, “Characteristics of a Resonant Optoacoustic Gas Concentration Detector,” Opt. Commun. 11, 422 (1974).
    [Crossref]
  18. L. G. Rosengren, “Optimal Optoacoustic Detector Design,” Appl. Opt. 14, 1960 (1975).
    [Crossref] [PubMed]
  19. T. F. Deaton, D. A. Depatie, and T. W. Walker, “Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths,” Appl. Phys. Lett. 26, 300 (1975).
    [Crossref]
  20. C. F. Dewey, R. D. Kamm, and C. E. Hackett, “Acoustic Amplifiers for Detection of Atmospheric Pollutants,” Appl. Phys. Lett. 23, 633 (1973).
    [Crossref]
  21. Roger D. Kamm, “Detection of Weakly Absorbing Gases using a Resonant Optoacoustic Method,” J. Appl. Phys. 47, 3550 (1976).
    [Crossref]
  22. P. D. Goldan and Kenya Gato, “An Acoustically Resonant System for Detection of Low Level Infrared Absorption in Atmospheric Pollutants,” J. Appl. Phys. 43, 4350 (1974).
    [Crossref]
  23. R. T. Menzies and M. S. Shumate, “Optoacoustic Measurements of Water Vapor Absorption at Selected CO Laser Wavelengths in the 5 μ m Region,” Appl. Opt. 15, 2023 (1976).
    [Crossref]
  24. M. S. Shumate, R. T. Menzies, J. S. Margolis, and L. G. Rosengren, “Water Vapor Absorption of Carbon Dioxide Laser Radiation,” Appl. Opt. 15, 2480 (1976).
    [Crossref] [PubMed]
  25. W. Schnell and G. Fischer, “Detection of Air Pollutants with a CO2 Laser,” Z. Angew, Math. Phys. 26, 133 (1975).
    [Crossref]
  26. G. L. Trusty, “Absorption Measurements of the 10.4 Micron Region using a CO2 Laser and a Spectrophone,” (1973).
  27. W. Schnell and G. Fisher, “Carbon Dioxide Laser Absorption Coefficients of Various Air Pollutants,” Appl. Opt. 14, 2058 (1975).
    [Crossref] [PubMed]
  28. P. C. Claspy, Y. H. Pao, S. Kwong, and E. Nodov, “Laser Optoacoustic Detection of Explosive Vapors,” Appl. Opt. 15, 1506 (1976).
    [Crossref] [PubMed]
  29. J. G. Parker, “Optical Absorption in Glass: Investigations Using an Acoustic Technique,” Appl. Opt. 12, 2974 (1973).
    [Crossref] [PubMed]
  30. H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34 (1951).
    [Crossref]
  31. M. J. G. Golay, “Theoretical Consideration in Heat and Infrared Detection, with Particular Reference to the Pneumatic Detector,” Rev. Sci. Instrum. 18, 347 (1947).
    [Crossref] [PubMed]
  32. M. J. Golay, “The Theoretical and Practical Sensitivity of the Pneumatic Infrared Detectors,” Rev. Sci. Instrum. 20, 816 (1949).
    [Crossref] [PubMed]
  33. P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), Chap. 6.
  34. R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation (Oxford University, New York, 1968).
  35. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (Wiley, New York, 1962).
  36. Attention is drawn to the fact that Eq. (4.1) can be conveniently used to calibrate optoacoustic cells. This method lacks many drawbacks to the usual method of calibration which is based on careful production of preknown concentrations.
  37. P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
    [Crossref]
  38. E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938).

1976 (8)

G. Diebold and D. L. McFadden, “Observation of the Optoacoustic Effect in the Microwave Region,” Appl. Phys. Lett. 29, 447 (1976).
[Crossref]

P. C. Claspy, Chang Ha, and Yoh-Han Pao, “Application of a Pulsed Dye Laser to Optoacoustic Detection of NO2,” J. Opt. Soc. Am. 66, 1072 (1976).

C. K. N. Patel, “Spectroscopic Measurements of the Stratosphere using Tunable Infrared Lasers,” Opt. Quantum Electron. 8, 145–154 (1976).
[Crossref]

R. T. Menzies and M. S. Shumate, “Optoacoustic Measurements of Water Vapor Absorption at Selected CO Laser Wavelengths in the 5 μ m Region,” Appl. Opt. 15, 2023 (1976).
[Crossref]

M. S. Shumate, R. T. Menzies, J. S. Margolis, and L. G. Rosengren, “Water Vapor Absorption of Carbon Dioxide Laser Radiation,” Appl. Opt. 15, 2480 (1976).
[Crossref] [PubMed]

P. C. Claspy, Y. H. Pao, S. Kwong, and E. Nodov, “Laser Optoacoustic Detection of Explosive Vapors,” Appl. Opt. 15, 1506 (1976).
[Crossref] [PubMed]

Roger D. Kamm, “Detection of Weakly Absorbing Gases using a Resonant Optoacoustic Method,” J. Appl. Phys. 47, 3550 (1976).
[Crossref]

P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
[Crossref]

1975 (4)

W. Schnell and G. Fischer, “Detection of Air Pollutants with a CO2 Laser,” Z. Angew, Math. Phys. 26, 133 (1975).
[Crossref]

W. Schnell and G. Fisher, “Carbon Dioxide Laser Absorption Coefficients of Various Air Pollutants,” Appl. Opt. 14, 2058 (1975).
[Crossref] [PubMed]

L. G. Rosengren, “Optimal Optoacoustic Detector Design,” Appl. Opt. 14, 1960 (1975).
[Crossref] [PubMed]

T. F. Deaton, D. A. Depatie, and T. W. Walker, “Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths,” Appl. Phys. Lett. 26, 300 (1975).
[Crossref]

1974 (4)

L. G. Rosengren, E. Max, and S. T. Eng, “A Study of Laser Acoustic Air Pollution Monitors,” J. Phys. Sci. Instrum. 7, 125 (1974).
[Crossref]

E. Max and L. G. Rosengren, “Characteristics of a Resonant Optoacoustic Gas Concentration Detector,” Opt. Commun. 11, 422 (1974).
[Crossref]

C. K. N. Patel, E. G. Burkhardt, and C. A. Lambert, “Spectroscopic Measurements of Stratospheric Nitric Oxide and Water Vapor,” Science 184, 1173 (1974).
[Crossref] [PubMed]

P. D. Goldan and Kenya Gato, “An Acoustically Resonant System for Detection of Low Level Infrared Absorption in Atmospheric Pollutants,” J. Appl. Phys. 43, 4350 (1974).
[Crossref]

1973 (3)

J. G. Parker, “Optical Absorption in Glass: Investigations Using an Acoustic Technique,” Appl. Opt. 12, 2974 (1973).
[Crossref] [PubMed]

L. G. Rosengren, Infrared Phys. 13, 109 (1973); Infrared Phys. 13, 173 (1973).
[Crossref]

C. F. Dewey, R. D. Kamm, and C. E. Hackett, “Acoustic Amplifiers for Detection of Atmospheric Pollutants,” Appl. Phys. Lett. 23, 633 (1973).
[Crossref]

1972 (1)

L. B. Kreuzer, N. D. Kenyon, and C. K. N. Patel, “Sensitive Detection of Ten Pollutant Gases by Carbon Monoxide and Carbon Dioxide Lasers,” Science 177, 347 (1972).
[Crossref] [PubMed]

1971 (1)

L. B. Kreuzer, “Ultra Low Gas Concentration Infrared Absorption Spectroscopy.” J. Appl. Phys. 42, 2934 (1971).
[Crossref]

1968 (1)

1951 (1)

H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34 (1951).
[Crossref]

1949 (1)

M. J. Golay, “The Theoretical and Practical Sensitivity of the Pneumatic Infrared Detectors,” Rev. Sci. Instrum. 20, 816 (1949).
[Crossref] [PubMed]

1947 (1)

M. J. G. Golay, “Theoretical Consideration in Heat and Infrared Detection, with Particular Reference to the Pneumatic Detector,” Rev. Sci. Instrum. 18, 347 (1947).
[Crossref] [PubMed]

1945 (1)

M. L. Veingerov, Dokl. Akad, Nauk SSSR 46, 182 (1945).

1943 (1)

K. F. Luft, Z. Tech. Phys. 24, 97–104 (1943).

1881 (3)

A. G. Bell, Philos. Mag. 11, 510, (1881).

W. C. Röntgen, Philos. Mag. 11, 308 (1881).

J. Tyndall, Proc. R. Soc. London,  31, 307 (1881).

Atwood, J. G.

Bell, A. G.

A. G. Bell, Philos. Mag. 11, 510, (1881).

Burkhardt, E. G.

C. K. N. Patel, E. G. Burkhardt, and C. A. Lambert, “Spectroscopic Measurements of Stratospheric Nitric Oxide and Water Vapor,” Science 184, 1173 (1974).
[Crossref] [PubMed]

Callen, H. B.

H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34 (1951).
[Crossref]

Chasmar, R. P.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation (Oxford University, New York, 1968).

Claspy, P. C.

P. C. Claspy, Y. H. Pao, S. Kwong, and E. Nodov, “Laser Optoacoustic Detection of Explosive Vapors,” Appl. Opt. 15, 1506 (1976).
[Crossref] [PubMed]

P. C. Claspy, Chang Ha, and Yoh-Han Pao, “Application of a Pulsed Dye Laser to Optoacoustic Detection of NO2,” J. Opt. Soc. Am. 66, 1072 (1976).

Deaton, T. F.

T. F. Deaton, D. A. Depatie, and T. W. Walker, “Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths,” Appl. Phys. Lett. 26, 300 (1975).
[Crossref]

Depatie, D. A.

T. F. Deaton, D. A. Depatie, and T. W. Walker, “Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths,” Appl. Phys. Lett. 26, 300 (1975).
[Crossref]

Dewey, C. F.

C. F. Dewey, R. D. Kamm, and C. E. Hackett, “Acoustic Amplifiers for Detection of Atmospheric Pollutants,” Appl. Phys. Lett. 23, 633 (1973).
[Crossref]

Diebold, G.

G. Diebold and D. L. McFadden, “Observation of the Optoacoustic Effect in the Microwave Region,” Appl. Phys. Lett. 29, 447 (1976).
[Crossref]

Eng, S. T.

L. G. Rosengren, E. Max, and S. T. Eng, “A Study of Laser Acoustic Air Pollution Monitors,” J. Phys. Sci. Instrum. 7, 125 (1974).
[Crossref]

Fischer, G.

W. Schnell and G. Fischer, “Detection of Air Pollutants with a CO2 Laser,” Z. Angew, Math. Phys. 26, 133 (1975).
[Crossref]

Fisher, G.

Frey, A. R.

L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (Wiley, New York, 1962).

Gato, Kenya

P. D. Goldan and Kenya Gato, “An Acoustically Resonant System for Detection of Low Level Infrared Absorption in Atmospheric Pollutants,” J. Appl. Phys. 43, 4350 (1974).
[Crossref]

Golay, M. J.

M. J. Golay, “The Theoretical and Practical Sensitivity of the Pneumatic Infrared Detectors,” Rev. Sci. Instrum. 20, 816 (1949).
[Crossref] [PubMed]

Golay, M. J. G.

M. J. G. Golay, “Theoretical Consideration in Heat and Infrared Detection, with Particular Reference to the Pneumatic Detector,” Rev. Sci. Instrum. 18, 347 (1947).
[Crossref] [PubMed]

Goldan, P. D.

P. D. Goldan and Kenya Gato, “An Acoustically Resonant System for Detection of Low Level Infrared Absorption in Atmospheric Pollutants,” J. Appl. Phys. 43, 4350 (1974).
[Crossref]

Ha, Chang

P. C. Claspy, Chang Ha, and Yoh-Han Pao, “Application of a Pulsed Dye Laser to Optoacoustic Detection of NO2,” J. Opt. Soc. Am. 66, 1072 (1976).

Hackett, C. E.

C. F. Dewey, R. D. Kamm, and C. E. Hackett, “Acoustic Amplifiers for Detection of Atmospheric Pollutants,” Appl. Phys. Lett. 23, 633 (1973).
[Crossref]

Hill, D. W.

D. W. Hill and T. Powell, Non-Dispersive Infrared Gas Analysis in Science, Medicine and Industry (Plenum, New York, 1968).

Ingard, K. U.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), Chap. 6.

Jones, F. E.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation (Oxford University, New York, 1968).

Kamm, R. D.

C. F. Dewey, R. D. Kamm, and C. E. Hackett, “Acoustic Amplifiers for Detection of Atmospheric Pollutants,” Appl. Phys. Lett. 23, 633 (1973).
[Crossref]

Kamm, Roger D.

Roger D. Kamm, “Detection of Weakly Absorbing Gases using a Resonant Optoacoustic Method,” J. Appl. Phys. 47, 3550 (1976).
[Crossref]

Kelley, P. L.

P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
[Crossref]

Kennard, E. H.

E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938).

Kenyon, N. D.

L. B. Kreuzer, N. D. Kenyon, and C. K. N. Patel, “Sensitive Detection of Ten Pollutant Gases by Carbon Monoxide and Carbon Dioxide Lasers,” Science 177, 347 (1972).
[Crossref] [PubMed]

Kerr, E. L.

Kinsler, L. E.

L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (Wiley, New York, 1962).

Kreuzer, L. B.

L. B. Kreuzer, N. D. Kenyon, and C. K. N. Patel, “Sensitive Detection of Ten Pollutant Gases by Carbon Monoxide and Carbon Dioxide Lasers,” Science 177, 347 (1972).
[Crossref] [PubMed]

L. B. Kreuzer, “Ultra Low Gas Concentration Infrared Absorption Spectroscopy.” J. Appl. Phys. 42, 2934 (1971).
[Crossref]

L. B. Kreuzer, “Measurements of Concentration of Components of Gaseous Mixtures,” U. S. Patent No. 3, 820, 901 (June28, 1974).

Kwong, S.

Lambert, C. A.

C. K. N. Patel, E. G. Burkhardt, and C. A. Lambert, “Spectroscopic Measurements of Stratospheric Nitric Oxide and Water Vapor,” Science 184, 1173 (1974).
[Crossref] [PubMed]

Long, R. K.

P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
[Crossref]

Luft, K. F.

K. F. Luft, Z. Tech. Phys. 24, 97–104 (1943).

Margolis, J. S.

Max, E.

E. Max and L. G. Rosengren, “Characteristics of a Resonant Optoacoustic Gas Concentration Detector,” Opt. Commun. 11, 422 (1974).
[Crossref]

L. G. Rosengren, E. Max, and S. T. Eng, “A Study of Laser Acoustic Air Pollution Monitors,” J. Phys. Sci. Instrum. 7, 125 (1974).
[Crossref]

McClatchy, R. A.

P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
[Crossref]

McFadden, D. L.

G. Diebold and D. L. McFadden, “Observation of the Optoacoustic Effect in the Microwave Region,” Appl. Phys. Lett. 29, 447 (1976).
[Crossref]

Menzies, R. T.

Morse, P. M.

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), Chap. 6.

Nodov, E.

Pao, Y. H.

Pao, Yoh-Han

P. C. Claspy, Chang Ha, and Yoh-Han Pao, “Application of a Pulsed Dye Laser to Optoacoustic Detection of NO2,” J. Opt. Soc. Am. 66, 1072 (1976).

Parker, J. G.

Patel, C. K. N.

C. K. N. Patel, “Spectroscopic Measurements of the Stratosphere using Tunable Infrared Lasers,” Opt. Quantum Electron. 8, 145–154 (1976).
[Crossref]

C. K. N. Patel, E. G. Burkhardt, and C. A. Lambert, “Spectroscopic Measurements of Stratospheric Nitric Oxide and Water Vapor,” Science 184, 1173 (1974).
[Crossref] [PubMed]

L. B. Kreuzer, N. D. Kenyon, and C. K. N. Patel, “Sensitive Detection of Ten Pollutant Gases by Carbon Monoxide and Carbon Dioxide Lasers,” Science 177, 347 (1972).
[Crossref] [PubMed]

Powell, T.

D. W. Hill and T. Powell, Non-Dispersive Infrared Gas Analysis in Science, Medicine and Industry (Plenum, New York, 1968).

Röntgen, W. C.

W. C. Röntgen, Philos. Mag. 11, 308 (1881).

Rosengren, L. G.

M. S. Shumate, R. T. Menzies, J. S. Margolis, and L. G. Rosengren, “Water Vapor Absorption of Carbon Dioxide Laser Radiation,” Appl. Opt. 15, 2480 (1976).
[Crossref] [PubMed]

L. G. Rosengren, “Optimal Optoacoustic Detector Design,” Appl. Opt. 14, 1960 (1975).
[Crossref] [PubMed]

L. G. Rosengren, E. Max, and S. T. Eng, “A Study of Laser Acoustic Air Pollution Monitors,” J. Phys. Sci. Instrum. 7, 125 (1974).
[Crossref]

E. Max and L. G. Rosengren, “Characteristics of a Resonant Optoacoustic Gas Concentration Detector,” Opt. Commun. 11, 422 (1974).
[Crossref]

L. G. Rosengren, Infrared Phys. 13, 109 (1973); Infrared Phys. 13, 173 (1973).
[Crossref]

Schnell, W.

W. Schnell and G. Fischer, “Detection of Air Pollutants with a CO2 Laser,” Z. Angew, Math. Phys. 26, 133 (1975).
[Crossref]

W. Schnell and G. Fisher, “Carbon Dioxide Laser Absorption Coefficients of Various Air Pollutants,” Appl. Opt. 14, 2058 (1975).
[Crossref] [PubMed]

Shumate, M. S.

Smith, R. A.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation (Oxford University, New York, 1968).

Snelson, A.

P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
[Crossref]

Trusty, G. L.

G. L. Trusty, “Absorption Measurements of the 10.4 Micron Region using a CO2 Laser and a Spectrophone,” (1973).

Tyndall, J.

J. Tyndall, Proc. R. Soc. London,  31, 307 (1881).

Veingerov, M. L.

M. L. Veingerov, Dokl. Akad, Nauk SSSR 46, 182 (1945).

Walker, T. W.

T. F. Deaton, D. A. Depatie, and T. W. Walker, “Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths,” Appl. Phys. Lett. 26, 300 (1975).
[Crossref]

Welton, T. A.

H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34 (1951).
[Crossref]

Appl. Opt. (7)

Appl. Phys. Lett. (3)

T. F. Deaton, D. A. Depatie, and T. W. Walker, “Absorption Coefficient Measurements of Nitrous Oxide and Methane at DF Laser Wavelengths,” Appl. Phys. Lett. 26, 300 (1975).
[Crossref]

C. F. Dewey, R. D. Kamm, and C. E. Hackett, “Acoustic Amplifiers for Detection of Atmospheric Pollutants,” Appl. Phys. Lett. 23, 633 (1973).
[Crossref]

G. Diebold and D. L. McFadden, “Observation of the Optoacoustic Effect in the Microwave Region,” Appl. Phys. Lett. 29, 447 (1976).
[Crossref]

Dokl. Akad, Nauk SSSR (1)

M. L. Veingerov, Dokl. Akad, Nauk SSSR 46, 182 (1945).

Infrared Phys. (1)

L. G. Rosengren, Infrared Phys. 13, 109 (1973); Infrared Phys. 13, 173 (1973).
[Crossref]

J. Appl. Phys. (3)

Roger D. Kamm, “Detection of Weakly Absorbing Gases using a Resonant Optoacoustic Method,” J. Appl. Phys. 47, 3550 (1976).
[Crossref]

P. D. Goldan and Kenya Gato, “An Acoustically Resonant System for Detection of Low Level Infrared Absorption in Atmospheric Pollutants,” J. Appl. Phys. 43, 4350 (1974).
[Crossref]

L. B. Kreuzer, “Ultra Low Gas Concentration Infrared Absorption Spectroscopy.” J. Appl. Phys. 42, 2934 (1971).
[Crossref]

J. Opt. Soc. Am. (1)

P. C. Claspy, Chang Ha, and Yoh-Han Pao, “Application of a Pulsed Dye Laser to Optoacoustic Detection of NO2,” J. Opt. Soc. Am. 66, 1072 (1976).

J. Phys. Sci. Instrum. (1)

L. G. Rosengren, E. Max, and S. T. Eng, “A Study of Laser Acoustic Air Pollution Monitors,” J. Phys. Sci. Instrum. 7, 125 (1974).
[Crossref]

Opt. Commun. (1)

E. Max and L. G. Rosengren, “Characteristics of a Resonant Optoacoustic Gas Concentration Detector,” Opt. Commun. 11, 422 (1974).
[Crossref]

Opt. Quantum Electron. (2)

C. K. N. Patel, “Spectroscopic Measurements of the Stratosphere using Tunable Infrared Lasers,” Opt. Quantum Electron. 8, 145–154 (1976).
[Crossref]

P. L. Kelley, R. A. McClatchy, R. K. Long, and A. Snelson, “Molecular Absorption of Infrared Laser Radiation in the Natural Atmosphere,” Opt. Quantum Electron. 8, 177 (1976).
[Crossref]

Philos. Mag. (2)

A. G. Bell, Philos. Mag. 11, 510, (1881).

W. C. Röntgen, Philos. Mag. 11, 308 (1881).

Phys. Rev. (1)

H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83, 34 (1951).
[Crossref]

Proc. R. Soc. London (1)

J. Tyndall, Proc. R. Soc. London,  31, 307 (1881).

Rev. Sci. Instrum. (2)

M. J. G. Golay, “Theoretical Consideration in Heat and Infrared Detection, with Particular Reference to the Pneumatic Detector,” Rev. Sci. Instrum. 18, 347 (1947).
[Crossref] [PubMed]

M. J. Golay, “The Theoretical and Practical Sensitivity of the Pneumatic Infrared Detectors,” Rev. Sci. Instrum. 20, 816 (1949).
[Crossref] [PubMed]

Science (2)

L. B. Kreuzer, N. D. Kenyon, and C. K. N. Patel, “Sensitive Detection of Ten Pollutant Gases by Carbon Monoxide and Carbon Dioxide Lasers,” Science 177, 347 (1972).
[Crossref] [PubMed]

C. K. N. Patel, E. G. Burkhardt, and C. A. Lambert, “Spectroscopic Measurements of Stratospheric Nitric Oxide and Water Vapor,” Science 184, 1173 (1974).
[Crossref] [PubMed]

Z. Angew, Math. Phys. (1)

W. Schnell and G. Fischer, “Detection of Air Pollutants with a CO2 Laser,” Z. Angew, Math. Phys. 26, 133 (1975).
[Crossref]

Z. Tech. Phys. (1)

K. F. Luft, Z. Tech. Phys. 24, 97–104 (1943).

Other (8)

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L. B. Kreuzer, “Measurements of Concentration of Components of Gaseous Mixtures,” U. S. Patent No. 3, 820, 901 (June28, 1974).

G. L. Trusty, “Absorption Measurements of the 10.4 Micron Region using a CO2 Laser and a Spectrophone,” (1973).

E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, New York, 1938).

P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968), Chap. 6.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infrared Radiation (Oxford University, New York, 1968).

L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (Wiley, New York, 1962).

Attention is drawn to the fact that Eq. (4.1) can be conveniently used to calibrate optoacoustic cells. This method lacks many drawbacks to the usual method of calibration which is based on careful production of preknown concentrations.

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Figures (9)

FIG. 1
FIG. 1

The optoacoustic effect: General scheme of experimental setup for detection and identification of an atmospheric pollutant by recording its ir spectrum using an optoacoustic cell. Part of the chopped radiation is directed to an ir detector for monitoring and compensation of changes in laser’s intensity while tuning it from line to line, thus rendering the recorded spectra independent of lasers intensity. Apart from narrow bandpass filtration the use of two synchronized lock-in amplifiers in the detection system provides compensation for possible phase changes due to beam walking while tuning the laser. A mechanical chopper with narrow slits converts beam walking to phase changes.

FIG. 2
FIG. 2

Ideal two-parallel walls optoacoustic cell: (a) Cells configuration, rigorously analyzed in Sec. II. For infinitely large A, the only spatial variable is X. (b) Schematic representation of the symmetric case n = 1, m = 1, for Zl = ∞. The input power spatial distribution Q(x) and pressure response spatial dependence p(x) are plotted.

FIG. 3
FIG. 3

Pressure response (dyn s/erg), velocity response (cm3/erg) and 1/D* (erg cm−1 s1/2) vs. normalized frequency: (a) and (b) represent computed results for the symmetric case n = 1. Rpis calculated for boundary condition |Zl| = ∞, whereas Ru is calculated for boundary condition Zl = 0. Part (a) shows computed results for normalized frequencies wL = wL/π up to first resonance. We can observe three main normalized frequency subregions: (a) wL/π = dc − ~ 10−5, which is below the cell’s thermal relaxation frequency. We observe that Rp is frequency independent, Ru has a w frequency dependence, and 1/D* is frequency independent. (b) wL/π = 10−5 ~1. In this intermediate frequency region the main features of the results are a 1/w frequency dependence of Rp, frequency independence of Ru and w1/4 frequency dependence of 1/D*. (c) wL/π ≃ 1 is the first resonant frequency, where Ru has a sharp resonance, while 1/D* has a much flatter antiresonance. Rp does not resonate at all. In part (b), computed results up to wL/π ≃ 8 are given. wL/π ≃ 1 frequency region is given once again. The main features of the figure are (i) Ru has only one resonant frequency (wL/π = 1). (ii) We obtain resonances in Rp at wL/π = 2, 4, 6, …. The highest resonant pressure response is approximately two orders of magnitude lower than the dc response (due to poor Q). (iii) We obtain resonances in 1/D* at wL/π = 3, 5, 7, …. This is due to existence of pressure noise resonances together with pressure response antiresonances.

FIG. 4
FIG. 4

Normalized pressure rise and temperature rise vs normalized distance from cell’s rigid walls. Figure 4 brings out the pressure rise and temperature rise distribution across the cell for the first frequency resonances in Rp, the cell being symmetrically (m = 1, n = 1). The computations were carried out for a 10 cm cell’s width. Only the 0 < x < L/2 region is included, the figure being symmetric relative to the x = L/2 plane. The normalized distance scale is logarithmic. Notice that the temperature rise τ(x) tends to follow p(x), up to a distance dh from the walls. The boundary condition τ(0) = τ(L) = 0 induces the relatively sharp decrease in τ(x). dh turns out to be the gas thermal diffusion length. The sharp decrease in τ(x) induces a thermal dissipation mechanism which determines most noise properties of the cell.

FIG. 5
FIG. 5

Acoustic transmission line models for different optoacoustic cells. (a) Left: A one-dimensional optoacoustic cell (consisting of two parallel walls). The first pressure resonant mode is indicated. This case corresponds to the symmetric case n = m = 1 of Sec. II. Right: the dominating dissipative mechanisms are taken into account by loading the line by a pneumatic impedance 2Rpn at χ = L, where thermal losses to the walls occur. (b) Left: Open tube optoacoustic cell. The longitudinal resonant mode of pressure response used in experiments of Sec. IV is indicated. Right: the corresponding transmission line. The line is short circuited at χ = L/2 since pressure node is obtained there (maximum gas velocity). The dominating thermal and viscous losses are distributed along the whole tube. As explained in the text, we load the transmission line with a pneumatic impedance Rpn at a single point χ = L/4.

FIG. 6
FIG. 6

Longitudinal resonant optoacoustic cell. Experimental resonant cell RC-1. The resonant conditions are obtained as longitudinal standing waves in an open tube enclosed in an external chamber. The internal brass tube is supported by three thin rods to minimize external acoustic noise interference. The two low-noise-sensitive microphones are wired in parallel as to reduce sensitivity to external vibrations (push-pull). Due to high immunity to windows interference induced by their absorption of infrared radiation, rather poor quality windows may be used to close the external chamber. The cell is also operated as an open one without any window. The Q ≃ 20 resonant quality factor enables operation through a large temperature range (more than 20 °C) without need of frequency adjustment.

FIG. 7
FIG. 7

Optoacoustic signal near resonance. (a) A resonance curve induced by 500 ppb of ethylene in nitrogen is given. A is the optoacoustic signal component in phase with the resonant signal; B is the component out of phase with the resonant signal. Point C indicates the contribution of a single totally absorbing window to the optoacoustic signal at “gas” resonant frequency. It is equivalent to 20 ppb of ethylene. (b) An optoacoustic resonant curve induced by a single totally absorbing window is given. The resonant curve (fr = 1775 Hz) is much sharper than the former one and well separated from it. We thus observe a discrimination between trace gas absorption and windows absorption. Notice residual gas signal near 1075 Hz, which disappears by flushing the cell with N2, up to point C level [same as in Fig. 7(a)].

FIG. 8
FIG. 8

Resonant optoacoustic cell operation with gas in flow condition. Figure 1 has been obtained by dispersing ethylene at concentration of 500 ppb in the resonant optoacoustic cell already filled with one atmosphere of N2. Then flushing nitrogen flow at a rate of 4 lit/min was turned on. An exponential decrease of the optoacoustic signal is observed. As the amplified signal decreased, the lock-in-amplifier was switched to a more sensitive scale. The first voltage signal indicated in the figure was obtained through amplification of 500. From the time scale, we see that the cells time response is less than 10 s at the actual 4 lit/min flow rate.

FIG. 9
FIG. 9

Optoacoustic measurement of concentration of ethylene in the laboratory air, as function of time. The measurement was continuously taken with an open cell (without windows). Ethylene at concentration of 20 ppm was initially dispersed in the room, and then diluted by operating the air conditioning system. A constant background mainly due to natural pollutants in the laboratory atmosphere was subtracted. ~50 dB A ambient acoustic noise limited the open cell detectivity to ~50 ppb.

Tables (2)

Tables Icon

TABLE I Comparison between longitudinal resonant cell (Fig. 6) and radial resonant cell (Refs. 20, 21). We choose the cell in Refs. 20 and 21 for comparison since complete information about it is published in Ref. 21, particularly about window interference. Most of the experimental results given in ref. 21 was obtained by using an absorbing trace gas with absorbtion coeffiecient of 13 cm−1 atm−1 at atmospheric pressure. For comparison with the longitudinal cell, we bring in Table I equivalent values of ethylene.

Tables Icon

TABLE II Comparative evaluation of optoacoustic cells of different configuration.

Equations (60)

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2 p x 2 = γ c 2 ( 2 t 2 - l v c t 2 x 2 ) ( p - α τ ) , l h c 2 τ x 2 = t ( τ - γ - 1 α γ p ) - Q ρ C p , ρ u t = - x ( p + α l v c t ( p - α τ ) ) ,
2 p x 2 = - γ ( w 2 + i w l v 2 x 2 ) ( p - α τ ) , l h 2 τ x 2 = i w ( τ - γ - 1 α γ p ) - Q ρ c C p , ρ c i w u = - x [ p + i w γ l v ( p - α τ ) ] ,
[ p τ u ] ( x , ω ) = A + + [ p + 1 u + ] e i K + x + A + - [ p + 1 u - + ] e - i K + x + A - + [ p - 1 u - ] e i K - x + A - - [ p - 1 u - - ] e - i K - x ,
K ± = ( - w ( i w l 1 ) ± [ w 2 ( i - w l 1 ) 2 + 4 i w 3 l h ( 1 + w l 2 i ) ] 1 / 2 2 l h ( 1 + w l 2 i ) ) 1 / 2 ,
u ± = - K ± w ρ c ( ( 1 + i w l 2 ) α γ ( i w + K ± 2 l h ) i w ( γ - 1 ) - α i w l 2 ) ,
p ± = α γ i w ( γ - 1 ) ( i w + K ± 2 l h ) , [ l 1 γ l h + l v , and l 2 γ l v .
Q ( x , ω ) = n = 1 A n sin n π x L .
Q n ( x , ω ) = π L q 0 ( ω ) sin ( n π x L )
p n ( x , ω ) = p 0 ( n ) sin n π x L , τ n ( x , ω = τ 0 ( n ) sin n π x L , u n ( x , ω ) = u 0 ( n ) cos n π x L ,
p 0 ( n ) = α γ q 0 w L ( n ) ( w L ( n ) - i l L v ( n ) ) n f ( w L ( n ) ) 1 n G ω ( L n ) , τ 0 ( n ) = q 0 [ - 1 + w L ( n ) γ ( w L ( n ) - i l L v ( n ) ) ] n f ( w L ( n ) ) , u 0 ( n ) = α γ q 0 i w L ( n ) n ρ c f ( w L ( n ) ) 1 n F ω ( L n ) ;
f ( w L ( n ) ) ρ c C p × [ i ( w L ( n ) ) 3 + ( w L ( n ) ) 2 l L 1 ( n ) - W L ( n ) ( i + l L h ( n ) l L 2 ( n ) ) - l L h ( n ) ] , w L ( n ) w L n π ,             l L ( n ) l n π L
A + + ( n ) = A + - ( n ) = A - + ( n ) = A - - ( n ) = 0.
A + ( n ) = u 0 ( n ) ( u + - u - ) ( e - - - e - + ) ( - cos n π + e + + ) + ( - cos n π + e - - ) 2 u - ( e + + - e + ) ( u + 2 - u - 2 ) ( e - - - e - + ) ( e + + - e + - ) + 2 u - ( u + + u - ) ( e + + - e - + ) ( e - - - e + - ) - 2 u - ( u + - u - ) ( e + - - e - + ) ( e + + - e - ) , A + + ( n ) = - u 0 ( n ) ( e - - - e - + ) - [ ( e + - - e - + ) 2 u - - ( u - + u + ) ( e - - - e - + ) ] A + - ( n ) 2 u - ( e + + - e - + ) + ( u + - u - ) ( e - - - e - + ) .
p ± ( 0 , ω ) = ( A + + + A + - ) ± ( p + - p - ) .
z ( ω ) ± p ( 0 , ω ) u ( 0 , ω ) A , z ± ( ω ) = ( A + + + A + - ) ± α γ l h i w ( γ - 1 ) A ( K + 2 - K - 2 ) ,
( A + + + A + - ) ± ( e - - - e - + ) + 2 [ u - ( e + + - e + - ) + u + ( e - - - e - + ) ] ( A + - ) + 2 u - ( e + + - e - + ) + ( u + - u - ) ( e - - - e - + ) .
R u ( n ) ( ω ) ( u n ( 0 , ω ) Z l = 0 ) / ( 0 L Q n ( x , ω ) d x ) , R p ( n ) ( ω ) ( p n ( 0 , ω ) Z l = ) / ( 0 L Q n ( x , ω ) d x ) .
R u ( n ) ( ω ) = u 0 ( n ) 2 q 0 = F ω ( L / n ) 2 n q 0 .
R p ( n ) ( ω ) = A Z ± ( ω ) R u ( n ) ( ω ) .
N u ( ω ) ± = [ 4 k T B R e ( Z ± ( ω ) ) ] 1 / 2 / A ,
D u * ( ω ) ( n ) R u ( n ) ( ω ) ( A B ) 1 / 2 / ( A N u ( ω ) ± )             ( + for even n , - for odd ) .
N p ( ω ) ± = N u ( ω ) ± A Z ± ( ω ) .
D p * ( ω ) ( n ) R p ( n ) ( ω ) ( A B ) 1 / 2 / ( A N p ( ω ) ± ) .
D p * ( ω ) ( n ) = D u * ( ω ) ( n ) .
Z - ( ω ) - 2 ρ c i γ w L ( 1 + ( γ - 1 ) L 2 w i 12 γ l h A ) ,
R u ( ω ) = d w L / l L h ,             R p ( ω ) = 2 d ρ / π γ l L h ,
D - * ( ω ) α γ 2 π 2 C p ρ c ( 6 L k T ρ c h l ( γ - 1 ) ) 1 / 2 1 2 π 2 T ( 6 L k κ ) 1 / 2 ,
NEP = 1 D * ( A B ) 1 / 2 ( 4 k T 2 B κ A L ) 1 / 2 π 2 6
Z - ( ω ) ρ c [ ( w 2 / 4 ) L l 3 + ( γ - 1 ) ( i w l h ) 1 / 2 + i tan ( w L / 2 ) ] - 1 [ ( 1 / π ) w L - 2 π m 1 ] ,
R e Z - ρ c 2 A ( γ - 1 ) ( π m ) 1 / 2 ( L l h ) 1 / 2 ρ c 2 A ( γ - 1 ) ( π m ) 1 / 2 L d h ,
d h = ( κ / ρ C p ) 1 / 2 / ( ν ) 1 / 2 .
R p 2 α γ 4 ( γ - 1 ) ( π m ) 1 / 2 ρ c C p L d h ( w = 2 m π L , z l = ) , R u d / l L 3 ( w = π L , Z l = 0 ) .
Q Z l ( ω ) = ( m ) 1 γ - 1 ( π L m l ) 1 / 2 = ( π m ) 1 / 2 γ - 1 L d h ( w = 2 m π L ) , Q z l ( ω ) = 0 L π l 3 ρ c L π γ η ( w = π L , μ < η )
N p ( 4 k T B ρ c ) 1 / 2 { 1 / [ 2 ( γ - 1 ) ( π m ) 1 / 2 ] 1 / 2 } ( L / d h ) 1 / 2
1 / D * [ 4 γ - 1 γ ( π m ) 1 / 2 ] 1 / 2 ( 4 k T 2 κ / d h ) 1 / 2 .
D * ( ω = 0 ) D * ( m = 1 ) = 6 π 2 ( 6 L π l h ) 1 / 4 ,
R pn = P 2 / K T ,
R pn = P 2 d h / κ A T .
Z l = 2 P 2 d h / κ A T .
Z 0 = Z [ Z l + j Z tan ( k L ) ] / [ Z + j Z l tan ( k L ) ] ,
z 0 = ρ c A [ 2 P 2 ( 2 π κ / ρ C p ) 1 / 2 1 / ω ] / κ A T + j ( ρ c / A ) tan ( k L ) ( ρ c / A ) + j [ 2 p 2 ( 2 π κ / ρ C p ) 1 / 2 ( 1 / ω ) tan ( k L ) ] / κ A T .
Re Z 0 2 P 2 L / κ A T             ( ω 2 π / τ th ) .
Re Z 0 κ ω 1 / 2 T / [ 2 A ( 2 π κ ρ C p ) 1 / 2 ω 2 L 2 ] .
Re Z 0 2 p 2 κ A T ( 2 π κ ρ C p ) 1 / 2 ( L m π c ) 1 / 2 1 m ρ c A L d h .
Re Z 0 ( ρ 2 c 2 κ T ) ( m π c 2 L ) / [ 2 A P 2 ( 2 π κ ρ C p ) 1 / 2 ] ρ c A d h L .
N p { ( 8 k B P 2 L / κ A ) 1 / 2 , ω 2 π / τ th ( 2 k T 2 B κ / A ) 1 / 2 ( 1 / ω L ) [ ω / ( 2 π κ / ρ C p ) ] 1 / 4 , 2 π / τ th < ω < 2 π c / L ( 4 k T B ρ c / A ) 1 / 2 ( L / m d h ) 1 / 2 , ω = m π c / L ,             m = 1 , 2 , 3 , ( 4 k T B ρ c / A ) 1 / 2 ( m d h / L ) 1 / 2 , ω = m π c / 2 L ,             m = 1 , 3 , 5.
Q = 2 π L / d h ,             ω r = m π c / L ,             m = 1 , 2 , 3 , .
N p { ( 4 k T B ρ c / A ) 1 / 2 ( Q / 2 π ) 1 / 2 , ω = m π c / L ,             m = 1 , 2 , 3 , ( 4 k T B ρ c / A ) 1 / 2 ( 1 / 2 π Q ) 1 / 2 , ω = m π c / 2 L ,             m = 1 , 2 , 3 , .
R p L P κ A T ( ω 2 π τ th ) ,             R p 1 A L ω ( 2 π τ th < ω < 2 π c L ) , R p 1 A L ω r Q ( ω r = m n c L ,             m = 2 , 4 , 6 , ) .
NEP { ( 4 k T 2 B 2 κ A L ) 1 / 2 ,             ω 2 π τ th ( 4 k T 2 B 2 κ A L ) 1 / 2 ( ω ρ C p 2 π κ ) 1 / 4 ( L 1 / 2 2 ) ,             2 π τ th < ω π c L ( 4 k T 2 B κ A d h ) 1 / 2             ω = m π c L ,             m = 2 , 4 , .
R pn P 2 d h / κ A T ,
Re Z 0 = { ρ 2 C 2 A 2 Z l tan 2 ( k L 4 ) [ 1 - tan 2 ( k L 4 ) ] + 2 ρ 2 C 2 A 2 Z l tan 2 ( k L 4 ) } / Y , Im Z 0 = { ρ 3 C 3 A 3 tan 3 ( k L 4 ) + 2 ρ C A Z l 2 tan k L 4 × [ 1 - tan 2 ( k L 4 ) ] } / Y , Y Z l 2 [ 1 - tan 2 ( k L 4 ) ] 2 + ρ 2 C 2 A 2 tan 2 ( k L 4 ) .
Q = ω r / 2 Δ ω = π R / d h .
Re Z 0 2 R pn ( 8 ρ c / A ) ( L / d h ) = ( 4 ρ c ) / ( π R d h ) .
N p = ( 4 k T B Re Z 0 ) 1 / 2 = ( 4 k T B ρ c π R 2 ) 1 / 2 ( 4 R d h ) 1 / 2 ( k T B ρ c A ) 1 / 2 Q 1 / 2 .
R p = ( 1 / ω r V ) Q ,
NEP 2 ( 4 k T 2 B κ A / d h ) 1 / 2 .
C min = 2 c ( 4 π R k T B ρ c ) 1 / 2 ( 2 L κ / ρ c C p ) 1 / 4 / ( α L W in ) .
C equ ( 2 / α L ) ( K 2 C 2 / K 1 C 1 ) 1 / 2 ,
η κ c p ,             1 h κ ρ c c p ,             p 2 ρ 2 c 4 ,             k T m c 2 , d h = ( κ ρ c p ) 1 / 2 1 ν