Abstract

The pulsed excitation of acoustic resonances was studied by means of a high-Q photoacoustic resonator with different types of microphone. The signal strength of the first radial mode was calculated by the basic theory as well as by a modeling program, which takes into account the acoustic impedances of the resonator, the acoustic filter system, and the influence of the microphone coupling on the photoacoustic cavity. When the calculated signal strength is used, the high-Q system can be calibrated for trace-gas analysis without a certified gas mixture. The theoretical results were compared with measurements and show good agreement for different microphone configurations. From the measured pressure signal (in pascals per joule), the absorption coefficient of ethylene was calculated; it agreed within 10% with literature values. In addition, a Helmholtz configuration with a highly sensitive 1-in. (2.54-cm) microphone was realized. Although the Q factor was reduced, the sensitivity could be increased by the Helmholtz resonator in the case of pulsed experiments. A maximum sensitivity of the coupled system of 341 mV/Pa was achieved.

© 1997 Optical Society of America

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References

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  1. L. G. Rosengren, “Optimal optoacoustic detector design,” Appl. Opt. 14, 1960–1975 (1975).
    [CrossRef] [PubMed]
  2. L. B. Kreuzer, “The physics of signal generation and Detection,” in Optoacoustic Spectroscopy and Detection, Y. H. Pao, ed. (Academic, New York, 1977), Chap. 1, pp. 1–25.
  3. E. Max, L. G. Rosengren, “Characteristics of a resonant opto-acoustic gas concentration detector,” Opt. Commun. 11, 422–426 (1974).
    [CrossRef]
  4. A. Karbach, P. Hess, “High precision acoustic spectroscopy by laser excitation of resonator modes,” J. Chem. Phys. 83, 1075–1084 (1985).
    [CrossRef]
  5. P. L. Meyer, M. W. Sigrist, “Atmospheric pollution monitoring using CO2-laser photoacoustic spectroscopy and other techniques,” Rev. Sci. Instrum. 61, 1779–1807 (1990).
    [CrossRef]
  6. M. W. Sigrist, “Environmental and chemical trace gas analysis by photoacoustic methods,” in Principles and Perspectives of Photothermal and Photoacoustic Phenomena, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, Chap. 7, pp. 369–427.
  7. P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
    [CrossRef]
  8. P. Repond, M. W. Sigrist, “Photoacoustic spectroscopy on trace gases with continuously tunable CO2 laser,” Appl. Opt. 35, 4065–4085 (1996).
    [CrossRef] [PubMed]
  9. M. Fiedler, P. Hess, “Frequency domain analysis of acoustic resonances excited with single laser pulses,” in Photoacoustic and Photothermal Phenomena, J. C. Murphy, J. C. Maclachlan Spicer, L. C. Aamodt, B. S. H. Royce, eds., Vol. 62 of the Springer Series on Optical Science (Springer, Berlin, 1990), pp. 344–346.
  10. S. Schäfer, A. Miklós, P. Hess, “Laser pulsed resonant photoacoustics/Applications to trace gas analysis,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, P. Hess, eds. (SPIE, Bellingham, Wash., 1997), Vol. 3, Chap. 7, pp. 254–289.
  11. A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).
  12. C. Brand, A. Winkler, P. Hess, A. Miklós, Z. Bozóki, J. Sneider, “Pulsed laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace-gas monitoring: results for C2H4,” Appl. Opt. 34, 3257–3266 (1995).
    [CrossRef] [PubMed]
  13. P. M. Morse, K. U. Ingard, Theoretical Acoustics (Princeton U. Press, Princeton, N.J., 1968), Chap. 7.1, pp. 306–332.
  14. P. Hess, “Resonant photoacoustic spectrocopy,” in Vol. 111 of Springer Topics in Current Chemistry Series (Springer-Verlag, Berlin, 1983), pp. 1–32.
  15. J. P. M. Trusler, Physical Acoustics and Metrology of Fluids (Hilger, Bristol, 1991), pp. 68–72.
  16. A. Miklós, A. Lörincz, “Windowless resonant acoustic chamber for laser-photoacoustic applications,” Appl. Phys. B 48, 213–218 (1989).
    [CrossRef]
  17. Z. Bozóki, I. Gaspar, A. Miklós, “Three dimensional acoustical modeling of resonant photoacoustic cells,” in Photoacoustic and Photothermal Phenomena, D. Bicanic, ed. (Springer-Verlag, Berlin, 1991), pp. 590–593.
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  19. M. Fehér, Y. Jiang, J. P. Maier, A. Miklós, “Optoacoustic trace-gas monitoring with near-infrared diode lasers,” Appl. Opt. 33, 1655–1658 (1994).
    [CrossRef] [PubMed]
  20. J. Sneider, Z. Bozóki, G. Szabó, Z. Bor, “Photoacoustic gas detection based on external cavity diode laser light sources,” Opt. Eng. 36 (1997).
  21. F. G. C. Bijnen, J. Reuss, F. J. M. Harren, “Geometrical optimization of a longitudinal resonant photoacoustic cell for sensitive and fast trace gas detection,” Rev. Sci. Instrum. 67, 2914–2923 (1996).
    [CrossRef]
  22. R. J. Brewer, C. W. Bruce, J. L. Mater, “Optoacoustic spectroscopy of C2H4 at the 9- and 10-µm C12O2 laser wavelengths,” Appl. Opt. 21, 4092–4100 (1982).
    [CrossRef] [PubMed]
  23. A. Ólafsson, M. Hammerich, J. Henningsen, “Photoacoustic spectroscopy of C2H4 with a tunable waveguide CO2 laser,” Appl. Opt. 31, 2657–2668 (1992).
    [CrossRef]

1997

J. Sneider, Z. Bozóki, G. Szabó, Z. Bor, “Photoacoustic gas detection based on external cavity diode laser light sources,” Opt. Eng. 36 (1997).

1996

F. G. C. Bijnen, J. Reuss, F. J. M. Harren, “Geometrical optimization of a longitudinal resonant photoacoustic cell for sensitive and fast trace gas detection,” Rev. Sci. Instrum. 67, 2914–2923 (1996).
[CrossRef]

P. Repond, M. W. Sigrist, “Photoacoustic spectroscopy on trace gases with continuously tunable CO2 laser,” Appl. Opt. 35, 4065–4085 (1996).
[CrossRef] [PubMed]

1995

1994

A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).

M. Fehér, Y. Jiang, J. P. Maier, A. Miklós, “Optoacoustic trace-gas monitoring with near-infrared diode lasers,” Appl. Opt. 33, 1655–1658 (1994).
[CrossRef] [PubMed]

1992

1990

P. L. Meyer, M. W. Sigrist, “Atmospheric pollution monitoring using CO2-laser photoacoustic spectroscopy and other techniques,” Rev. Sci. Instrum. 61, 1779–1807 (1990).
[CrossRef]

1989

A. Miklós, A. Lörincz, “Windowless resonant acoustic chamber for laser-photoacoustic applications,” Appl. Phys. B 48, 213–218 (1989).
[CrossRef]

1987

P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
[CrossRef]

1985

A. Karbach, P. Hess, “High precision acoustic spectroscopy by laser excitation of resonator modes,” J. Chem. Phys. 83, 1075–1084 (1985).
[CrossRef]

1982

1975

1974

E. Max, L. G. Rosengren, “Characteristics of a resonant opto-acoustic gas concentration detector,” Opt. Commun. 11, 422–426 (1974).
[CrossRef]

Atkinson, G. H.

P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
[CrossRef]

Bijnen, F. G. C.

F. G. C. Bijnen, J. Reuss, F. J. M. Harren, “Geometrical optimization of a longitudinal resonant photoacoustic cell for sensitive and fast trace gas detection,” Rev. Sci. Instrum. 67, 2914–2923 (1996).
[CrossRef]

Bor, Z.

J. Sneider, Z. Bozóki, G. Szabó, Z. Bor, “Photoacoustic gas detection based on external cavity diode laser light sources,” Opt. Eng. 36 (1997).

Bozóki, Z.

J. Sneider, Z. Bozóki, G. Szabó, Z. Bor, “Photoacoustic gas detection based on external cavity diode laser light sources,” Opt. Eng. 36 (1997).

C. Brand, A. Winkler, P. Hess, A. Miklós, Z. Bozóki, J. Sneider, “Pulsed laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace-gas monitoring: results for C2H4,” Appl. Opt. 34, 3257–3266 (1995).
[CrossRef] [PubMed]

Z. Bozóki, I. Gaspar, A. Miklós, “Three dimensional acoustical modeling of resonant photoacoustic cells,” in Photoacoustic and Photothermal Phenomena, D. Bicanic, ed. (Springer-Verlag, Berlin, 1991), pp. 590–593.

Brand, C.

C. Brand, A. Winkler, P. Hess, A. Miklós, Z. Bozóki, J. Sneider, “Pulsed laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace-gas monitoring: results for C2H4,” Appl. Opt. 34, 3257–3266 (1995).
[CrossRef] [PubMed]

A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).

Brewer, R. J.

Bruce, C. W.

Cvijin, P. V.

P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
[CrossRef]

Fehér, M.

Fiedler, M.

M. Fiedler, P. Hess, “Frequency domain analysis of acoustic resonances excited with single laser pulses,” in Photoacoustic and Photothermal Phenomena, J. C. Murphy, J. C. Maclachlan Spicer, L. C. Aamodt, B. S. H. Royce, eds., Vol. 62 of the Springer Series on Optical Science (Springer, Berlin, 1990), pp. 344–346.

Gaspar, I.

Z. Bozóki, I. Gaspar, A. Miklós, “Three dimensional acoustical modeling of resonant photoacoustic cells,” in Photoacoustic and Photothermal Phenomena, D. Bicanic, ed. (Springer-Verlag, Berlin, 1991), pp. 590–593.

Gilmore, D. A.

P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
[CrossRef]

Hammerich, M.

Harren, F. J. M.

F. G. C. Bijnen, J. Reuss, F. J. M. Harren, “Geometrical optimization of a longitudinal resonant photoacoustic cell for sensitive and fast trace gas detection,” Rev. Sci. Instrum. 67, 2914–2923 (1996).
[CrossRef]

Henningsen, J.

Hess, P.

C. Brand, A. Winkler, P. Hess, A. Miklós, Z. Bozóki, J. Sneider, “Pulsed laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace-gas monitoring: results for C2H4,” Appl. Opt. 34, 3257–3266 (1995).
[CrossRef] [PubMed]

A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).

A. Karbach, P. Hess, “High precision acoustic spectroscopy by laser excitation of resonator modes,” J. Chem. Phys. 83, 1075–1084 (1985).
[CrossRef]

M. Fiedler, P. Hess, “Frequency domain analysis of acoustic resonances excited with single laser pulses,” in Photoacoustic and Photothermal Phenomena, J. C. Murphy, J. C. Maclachlan Spicer, L. C. Aamodt, B. S. H. Royce, eds., Vol. 62 of the Springer Series on Optical Science (Springer, Berlin, 1990), pp. 344–346.

S. Schäfer, A. Miklós, P. Hess, “Laser pulsed resonant photoacoustics/Applications to trace gas analysis,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, P. Hess, eds. (SPIE, Bellingham, Wash., 1997), Vol. 3, Chap. 7, pp. 254–289.

P. Hess, “Resonant photoacoustic spectrocopy,” in Vol. 111 of Springer Topics in Current Chemistry Series (Springer-Verlag, Berlin, 1983), pp. 1–32.

P. Hess, “Principles of photoacoustic and photothermal detection in gases,” in Principles and Perspectives of Photothermal and Photoacoustic Phenomena, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, Chap. 4, pp. 155–206.

Ingard, K. U.

P. M. Morse, K. U. Ingard, Theoretical Acoustics (Princeton U. Press, Princeton, N.J., 1968), Chap. 7.1, pp. 306–332.

Jiang, Y.

Karbach, A.

A. Karbach, P. Hess, “High precision acoustic spectroscopy by laser excitation of resonator modes,” J. Chem. Phys. 83, 1075–1084 (1985).
[CrossRef]

Kreuzer, L. B.

L. B. Kreuzer, “The physics of signal generation and Detection,” in Optoacoustic Spectroscopy and Detection, Y. H. Pao, ed. (Academic, New York, 1977), Chap. 1, pp. 1–25.

Leugers, M. A.

P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
[CrossRef]

Lörincz, A.

A. Miklós, A. Lörincz, “Windowless resonant acoustic chamber for laser-photoacoustic applications,” Appl. Phys. B 48, 213–218 (1989).
[CrossRef]

Maier, J. P.

Mater, J. L.

Max, E.

E. Max, L. G. Rosengren, “Characteristics of a resonant opto-acoustic gas concentration detector,” Opt. Commun. 11, 422–426 (1974).
[CrossRef]

Meyer, P. L.

P. L. Meyer, M. W. Sigrist, “Atmospheric pollution monitoring using CO2-laser photoacoustic spectroscopy and other techniques,” Rev. Sci. Instrum. 61, 1779–1807 (1990).
[CrossRef]

Miklós, A.

C. Brand, A. Winkler, P. Hess, A. Miklós, Z. Bozóki, J. Sneider, “Pulsed laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace-gas monitoring: results for C2H4,” Appl. Opt. 34, 3257–3266 (1995).
[CrossRef] [PubMed]

A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).

M. Fehér, Y. Jiang, J. P. Maier, A. Miklós, “Optoacoustic trace-gas monitoring with near-infrared diode lasers,” Appl. Opt. 33, 1655–1658 (1994).
[CrossRef] [PubMed]

A. Miklós, A. Lörincz, “Windowless resonant acoustic chamber for laser-photoacoustic applications,” Appl. Phys. B 48, 213–218 (1989).
[CrossRef]

S. Schäfer, A. Miklós, P. Hess, “Laser pulsed resonant photoacoustics/Applications to trace gas analysis,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, P. Hess, eds. (SPIE, Bellingham, Wash., 1997), Vol. 3, Chap. 7, pp. 254–289.

Z. Bozóki, I. Gaspar, A. Miklós, “Three dimensional acoustical modeling of resonant photoacoustic cells,” in Photoacoustic and Photothermal Phenomena, D. Bicanic, ed. (Springer-Verlag, Berlin, 1991), pp. 590–593.

Morse, P. M.

P. M. Morse, K. U. Ingard, Theoretical Acoustics (Princeton U. Press, Princeton, N.J., 1968), Chap. 7.1, pp. 306–332.

Ólafsson, A.

Repond, P.

Reuss, J.

F. G. C. Bijnen, J. Reuss, F. J. M. Harren, “Geometrical optimization of a longitudinal resonant photoacoustic cell for sensitive and fast trace gas detection,” Rev. Sci. Instrum. 67, 2914–2923 (1996).
[CrossRef]

Rosengren, L. G.

L. G. Rosengren, “Optimal optoacoustic detector design,” Appl. Opt. 14, 1960–1975 (1975).
[CrossRef] [PubMed]

E. Max, L. G. Rosengren, “Characteristics of a resonant opto-acoustic gas concentration detector,” Opt. Commun. 11, 422–426 (1974).
[CrossRef]

Schäfer, S.

S. Schäfer, A. Miklós, P. Hess, “Laser pulsed resonant photoacoustics/Applications to trace gas analysis,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, P. Hess, eds. (SPIE, Bellingham, Wash., 1997), Vol. 3, Chap. 7, pp. 254–289.

Sigrist, M. W.

P. Repond, M. W. Sigrist, “Photoacoustic spectroscopy on trace gases with continuously tunable CO2 laser,” Appl. Opt. 35, 4065–4085 (1996).
[CrossRef] [PubMed]

P. L. Meyer, M. W. Sigrist, “Atmospheric pollution monitoring using CO2-laser photoacoustic spectroscopy and other techniques,” Rev. Sci. Instrum. 61, 1779–1807 (1990).
[CrossRef]

M. W. Sigrist, “Environmental and chemical trace gas analysis by photoacoustic methods,” in Principles and Perspectives of Photothermal and Photoacoustic Phenomena, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, Chap. 7, pp. 369–427.

Sneider, J.

Szabó, G.

J. Sneider, Z. Bozóki, G. Szabó, Z. Bor, “Photoacoustic gas detection based on external cavity diode laser light sources,” Opt. Eng. 36 (1997).

Trusler, J. P. M.

J. P. M. Trusler, Physical Acoustics and Metrology of Fluids (Hilger, Bristol, 1991), pp. 68–72.

Winkler, A.

C. Brand, A. Winkler, P. Hess, A. Miklós, Z. Bozóki, J. Sneider, “Pulsed laser excitation of acoustic modes in open high-Q photoacoustic resonators for trace-gas monitoring: results for C2H4,” Appl. Opt. 34, 3257–3266 (1995).
[CrossRef] [PubMed]

A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).

Anal. Chem.

P. V. Cvijin, D. A. Gilmore, M. A. Leugers, G. H. Atkinson, “Determination of sulfur dioxide by pulsed ultraviolet laser photoacoustic spectroscopy,” Anal. Chem. 59, 300–304 (1987).
[CrossRef]

Appl. Opt.

Appl. Phys. B

A. Miklós, A. Lörincz, “Windowless resonant acoustic chamber for laser-photoacoustic applications,” Appl. Phys. B 48, 213–218 (1989).
[CrossRef]

J. Chem. Phys.

A. Karbach, P. Hess, “High precision acoustic spectroscopy by laser excitation of resonator modes,” J. Chem. Phys. 83, 1075–1084 (1985).
[CrossRef]

J. Phys. IV

A. Miklós, C. Brand, A. Winkler, P. Hess, “Effective noise reduction on pulsed laser excitation of modes in a high-Q photoacoustic resonator,” J. Phys. IV 4, 781–784 (1994).

Opt. Commun.

E. Max, L. G. Rosengren, “Characteristics of a resonant opto-acoustic gas concentration detector,” Opt. Commun. 11, 422–426 (1974).
[CrossRef]

Opt. Eng.

J. Sneider, Z. Bozóki, G. Szabó, Z. Bor, “Photoacoustic gas detection based on external cavity diode laser light sources,” Opt. Eng. 36 (1997).

Rev. Sci. Instrum.

F. G. C. Bijnen, J. Reuss, F. J. M. Harren, “Geometrical optimization of a longitudinal resonant photoacoustic cell for sensitive and fast trace gas detection,” Rev. Sci. Instrum. 67, 2914–2923 (1996).
[CrossRef]

P. L. Meyer, M. W. Sigrist, “Atmospheric pollution monitoring using CO2-laser photoacoustic spectroscopy and other techniques,” Rev. Sci. Instrum. 61, 1779–1807 (1990).
[CrossRef]

Other

M. W. Sigrist, “Environmental and chemical trace gas analysis by photoacoustic methods,” in Principles and Perspectives of Photothermal and Photoacoustic Phenomena, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, Chap. 7, pp. 369–427.

L. B. Kreuzer, “The physics of signal generation and Detection,” in Optoacoustic Spectroscopy and Detection, Y. H. Pao, ed. (Academic, New York, 1977), Chap. 1, pp. 1–25.

M. Fiedler, P. Hess, “Frequency domain analysis of acoustic resonances excited with single laser pulses,” in Photoacoustic and Photothermal Phenomena, J. C. Murphy, J. C. Maclachlan Spicer, L. C. Aamodt, B. S. H. Royce, eds., Vol. 62 of the Springer Series on Optical Science (Springer, Berlin, 1990), pp. 344–346.

S. Schäfer, A. Miklós, P. Hess, “Laser pulsed resonant photoacoustics/Applications to trace gas analysis,” in Progress in Photothermal and Photoacoustic Science and Technology, A. Mandelis, P. Hess, eds. (SPIE, Bellingham, Wash., 1997), Vol. 3, Chap. 7, pp. 254–289.

Z. Bozóki, I. Gaspar, A. Miklós, “Three dimensional acoustical modeling of resonant photoacoustic cells,” in Photoacoustic and Photothermal Phenomena, D. Bicanic, ed. (Springer-Verlag, Berlin, 1991), pp. 590–593.

P. Hess, “Principles of photoacoustic and photothermal detection in gases,” in Principles and Perspectives of Photothermal and Photoacoustic Phenomena, A. Mandelis, ed. (Elsevier, New York, 1992), Vol. 1, Chap. 4, pp. 155–206.

P. M. Morse, K. U. Ingard, Theoretical Acoustics (Princeton U. Press, Princeton, N.J., 1968), Chap. 7.1, pp. 306–332.

P. Hess, “Resonant photoacoustic spectrocopy,” in Vol. 111 of Springer Topics in Current Chemistry Series (Springer-Verlag, Berlin, 1983), pp. 1–32.

J. P. M. Trusler, Physical Acoustics and Metrology of Fluids (Hilger, Bristol, 1991), pp. 68–72.

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Figures (6)

Fig. 1
Fig. 1

Frequency spectrum of the PA cell modeled with the pa designer program. The upper curve represents the pressure amplitude for 10-ppmV C2H4 with a laser energy of 10 mJ. The excited modes are denoted by (n, m, n z). The lower spectrum shows the acoustic noise that enters the PA cell through the openings of the acoustic filter system.

Fig. 2
Fig. 2

Influence of a small gap in front of the microphone on the Q factor of the (100) mode. The starred curve represents the computer modeling for a gap of 2.6 mm. The corresponding Q factor is 630. The solid curve shows the ideal cylinder with a Q factor of 1140. The reduction has been confirmed by measurements with different microphone positions (see Table 1).

Fig. 3
Fig. 3

Experimental setup: a, Sennheiser KE 4 microphone (ϕ = 5 mm); b, Brüel & Kjaer 4179 microphone (ϕ = 22.8 mm); c, Brüel & Kjaer 4165 microphone (ϕ = 12.4 mm). Microphones a and c can be placed in normal T configuration flush to the inner surface and at a small displacement of 1–3 mm. Microphone b is positioned in a Helmholtz resonator. The diameter of the neck (d n) is 12.5 mm, and the length (l n) is 2.6 mm. The dimension of the Helmholtz volume (V H) was adjusted by means of a fine thread inside a Teflon tube. A/D, analog-to-digital.

Fig. 4
Fig. 4

(a) PA time signal of the small Sennheiser microphone. The decay time is ∼250 ms. From the corresponding frequency spectrum, a Q factor of 1006 and a conversion factor of K 100 = 6.6 [Eq. (12)] were calculated. This yields a signal strength of the (100) mode of 0.28 mV, which is somewhat smaller than the maximum amplitude of the time signal. In (b) the PA time signal of the 1-in. microphone, B&K 4179, is presented. The decay time here is ∼80 ms (Q = 123) and the calculated conversion factor K100 = 53. The resulting signal strength is 1.2 mV.

Fig. 5
Fig. 5

PA frequency spectrum monitored with the 1/2-in. microphone for 10.3-ppmV C2H4 in N2 (upper curve) and the background signal for N2 (lower curve). The main peaks in the background signal, the azimuthal (010), the second longitudinal (002), and the combination (102) modes are excited mainly by acoustic noise, which can be seen on the modeled spectrum (Fig. 1) as well.

Fig. 6
Fig. 6

PA-signal dependence on pulse energy of the transversely excited atmosphere CO2 laser for the 10P 10 line. The triangles and circles represent the measurements with the B&K 4179 and 4165 microphones, respectively, and the squares are the results obtained with the Sennheiser microphone. A linear dependence is obtained for pulse energies as high as 60 mJ. From the least-squares fits, the signal strengths for the different microphones (see Table 1) were determined.

Tables (2)

Tables Icon

Table 1 Experimental Results for the First Radial Mode (ν ≈ 4140 Hz) and 10.3 ppmV C2H4 in N2a

Tables Icon

Table 2 Comparison of Experimental and Theoretical Resultsa

Equations (20)

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

SαCW,
Hr, tN0hνkvtβrWtks+kvt+2βrWt,
t2pr, t-c22pr, t=γ-1tHr, t,
pr, t=jAjtpjrexpiΩjt,
Ωj=ωj+igj.
Qj=ωj/2gj.
prM, tjγ-1N0σETHVjpjrM×Vcellgrpj*rdV exp-gjt-TH×expiωjt-TH.
Vj=Vcellj1-m2Xmn2Jm2Xmn=VcellDj,
prM, tjγ-1N0σLEVcellpjrMSjDj×exp-gjt-TH+iωjt-TH.
prM, t=ncn expinω0t,
cnexp-gjtdT01+exp-2gjT0-2 exp-gjT0cosωj-nω0T0gj2+ωj-nω021/2,
1Kj=0T0 exp-gjtdtT02QjωjT0.
prM, ω=jBjωpjrMexpiωt.
Bjω=γ-1N0σLWωVCelliω2ωj2-ω2+iωωjQjSjDj.
γ-1N0σLEVCellSjpjrMDjγ-1N0σLWωjVCellQjSjpjrMDj.
prM, ω=γ-1N0σLWρc2jiωρc2SjpjrM/Djωj2-ω2+iωωjQj.
Cj=Vcellρc2DjSjpjrM,  Lj=1ωj2Cj,  Rj=QjωjCj.
1Qj=pj2rMωjC0DjReZMZM2,
prM, t0γ-1N0σLVCellEpjrMSjDjαACellE.
Wequ=EωjQj.

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