Abstract

In high resolution absorption spectrometers with conventional light sources, the signal-to-noise ratio (SNR) is usually limited by the thermal noise level of the detector–preamplifier combination, which is independent of the light source power. However, the noise in many laser absorption spectrometers is dominated by the excess or shot noise which is dependent on the transmitted laser power, and which in turn is dependent on the number of reflections in a multipass cell. The optimum absorption path length for a high frequency modulated (FM) and a conventional wavelength modulated (WM) diode laser absorption spectrometer is investigated in this paper. The major result is that, due to the power attenuation by the multipass cell, the best SNR of a shot noise limited FM spectrometer is achieved at substantially shorter absorption paths, when compared with the excess noise limited WM spectrometer. This finding implies that the implementation of the FM technique in absorption spectrometers with multipass cells can improve the SNR only by 1 order of magnitude. Although desirable, this is substantially less than the improvement of 2 orders of magnitude expected in quantum limited conditions with a single pass cell.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. L. Hanst, “Spectroscopic Methods for Air Pollution Measurements,” Adv. Environ. Sci. Technol. 2, 91 (1971).
  2. E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).
  3. D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
    [PubMed]
  4. J. U. White, “Long Optical Paths of Large Aperture,” J. Opt. Soc. Am. 32, 285 (1942).
    [Crossref]
  5. J. U. White, “Very Long Optical Paths in Air,” J. Opt. Soc. Am. 66, 411–416 (1976).
    [Crossref]
  6. D. R. Herriott, H. Kogelnik, R. Kompfner, “Off-Axis Paths in Spherical Mirror Interferometers,” Appl. Opt. 3, 523 (1964).
    [Crossref]
  7. D. R. Herriott, H. J. Schulte, “Folded Optical Delay Lines,” Appl. Opt. 4, 883 (1965).
    [Crossref]
  8. E. R. Stephens, “Long-Path Infrared Spectroscopy for Air Pollution Research,” Appl. Spectrosc. 3, 80–84 (1958).
    [Crossref]
  9. G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
    [Crossref]
  10. J. L. Hall, T. Baer, L. Hallberg, H. G. Robinson, “Precision Spectroscopy and Laser Frequency Control Using FM Sideband Optical Heterodyne Techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, Eds. (Springer-Verlag, Berlin, 1981), p. 16.
  11. P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Wideband Noise Characteristics of a Lead-Salt Diode Laser: Possibility of Quantum Noise Limited TDLAS Performance,” Appl. Opt. 28, 1638–1642 (1989).
    [Crossref] [PubMed]
  12. G. C. Bjorklund, “Frequency-Modulation Spectroscopy: a New Method for Measuring Weak Absorptions and Dispersions,” Opt. Lett. 5, 15–17 (1980).
    [Crossref] [PubMed]
  13. P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
    [Crossref]
  14. H. I. Schiff, G. W. Harris, G. I. Mackay, “Measurement of Atmospheric Gases by Laser Absorption Spectrometry,” in The Chemistry of Acid Rain: Sources and Atmospheric Processes, R. W. Johnson, G. E. Gordon, W. Calkins, A. Z. Elzerman, Eds., ACS Symposium Series No. 349 (ACS, Washington, DC, 1987).
    [Crossref]

1989 (2)

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Wideband Noise Characteristics of a Lead-Salt Diode Laser: Possibility of Quantum Noise Limited TDLAS Performance,” Appl. Opt. 28, 1638–1642 (1989).
[Crossref] [PubMed]

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
[Crossref]

1984 (1)

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

1983 (1)

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

1980 (1)

1979 (1)

E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).

1976 (1)

1971 (1)

P. L. Hanst, “Spectroscopic Methods for Air Pollution Measurements,” Adv. Environ. Sci. Technol. 2, 91 (1971).

1965 (1)

1964 (1)

1958 (1)

E. R. Stephens, “Long-Path Infrared Spectroscopy for Air Pollution Research,” Appl. Spectrosc. 3, 80–84 (1958).
[Crossref]

1942 (1)

Baer, T.

J. L. Hall, T. Baer, L. Hallberg, H. G. Robinson, “Precision Spectroscopy and Laser Frequency Control Using FM Sideband Optical Heterodyne Techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, Eds. (Springer-Verlag, Berlin, 1981), p. 16.

Bjorklund, G. C.

Braüchle, C.

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
[Crossref]

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Wideband Noise Characteristics of a Lead-Salt Diode Laser: Possibility of Quantum Noise Limited TDLAS Performance,” Appl. Opt. 28, 1638–1642 (1989).
[Crossref] [PubMed]

Ehhalt, D. H.

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

Gehrtz, M.

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
[Crossref]

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Wideband Noise Characteristics of a Lead-Salt Diode Laser: Possibility of Quantum Noise Limited TDLAS Performance,” Appl. Opt. 28, 1638–1642 (1989).
[Crossref] [PubMed]

Graham, R. A.

E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).

Hall, J. L.

J. L. Hall, T. Baer, L. Hallberg, H. G. Robinson, “Precision Spectroscopy and Laser Frequency Control Using FM Sideband Optical Heterodyne Techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, Eds. (Springer-Verlag, Berlin, 1981), p. 16.

Hallberg, L.

J. L. Hall, T. Baer, L. Hallberg, H. G. Robinson, “Precision Spectroscopy and Laser Frequency Control Using FM Sideband Optical Heterodyne Techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, Eds. (Springer-Verlag, Berlin, 1981), p. 16.

Hanst, P. L.

P. L. Hanst, “Spectroscopic Methods for Air Pollution Measurements,” Adv. Environ. Sci. Technol. 2, 91 (1971).

Harris, G. W.

H. I. Schiff, G. W. Harris, G. I. Mackay, “Measurement of Atmospheric Gases by Laser Absorption Spectrometry,” in The Chemistry of Acid Rain: Sources and Atmospheric Processes, R. W. Johnson, G. E. Gordon, W. Calkins, A. Z. Elzerman, Eds., ACS Symposium Series No. 349 (ACS, Washington, DC, 1987).
[Crossref]

Hastie, D. R.

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

Herriott, D. R.

Hübler, G.

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

Iguchi, T.

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

Kogelnik, H.

Kompfner, R.

Mackay, G. I.

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

H. I. Schiff, G. W. Harris, G. I. Mackay, “Measurement of Atmospheric Gases by Laser Absorption Spectrometry,” in The Chemistry of Acid Rain: Sources and Atmospheric Processes, R. W. Johnson, G. E. Gordon, W. Calkins, A. Z. Elzerman, Eds., ACS Symposium Series No. 349 (ACS, Washington, DC, 1987).
[Crossref]

Perner, D.

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

Pitts, J. N.

E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).

Platt, U.

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

Ridley, B. A.

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

Robinson, H. G.

J. L. Hall, T. Baer, L. Hallberg, H. G. Robinson, “Precision Spectroscopy and Laser Frequency Control Using FM Sideband Optical Heterodyne Techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, Eds. (Springer-Verlag, Berlin, 1981), p. 16.

Schiff, H. I.

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

H. I. Schiff, G. W. Harris, G. I. Mackay, “Measurement of Atmospheric Gases by Laser Absorption Spectrometry,” in The Chemistry of Acid Rain: Sources and Atmospheric Processes, R. W. Johnson, G. E. Gordon, W. Calkins, A. Z. Elzerman, Eds., ACS Symposium Series No. 349 (ACS, Washington, DC, 1987).
[Crossref]

Schulte, H. J.

Slemr, F.

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
[Crossref]

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Wideband Noise Characteristics of a Lead-Salt Diode Laser: Possibility of Quantum Noise Limited TDLAS Performance,” Appl. Opt. 28, 1638–1642 (1989).
[Crossref] [PubMed]

Stephens, E. R.

E. R. Stephens, “Long-Path Infrared Spectroscopy for Air Pollution Research,” Appl. Spectrosc. 3, 80–84 (1958).
[Crossref]

Tönissen, A.

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

Tuazon, E. C.

E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).

Werle, P.

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
[Crossref]

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Wideband Noise Characteristics of a Lead-Salt Diode Laser: Possibility of Quantum Noise Limited TDLAS Performance,” Appl. Opt. 28, 1638–1642 (1989).
[Crossref] [PubMed]

White, J. U.

Winer, A. M.

E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).

Adv. Environ. Sci. Technol. (2)

P. L. Hanst, “Spectroscopic Methods for Air Pollution Measurements,” Adv. Environ. Sci. Technol. 2, 91 (1971).

E. C. Tuazon, A. M. Winer, R. A. Graham, J. N. Pitts, “Atmospheric Measurements of Trace Pollutants by Kilometer Pathlength FT-IR Spectroscopy,” Adv. Environ. Sci. Technol. 10, (1979).

Appl. Opt. (3)

Appl. Phys. B (1)

P. Werle, F. Slemr, M. Gehrtz, C. Braüchle, “Quantum Limited FM-Spectroscopy with Lead-Salt Diode Laser,” Appl. Phys. B 49, 99–108 (1989) and references therein.
[Crossref]

Appl. Spectrosc. (1)

E. R. Stephens, “Long-Path Infrared Spectroscopy for Air Pollution Research,” Appl. Spectrosc. 3, 80–84 (1958).
[Crossref]

Environ. Sci. Technol. (1)

D. R. Hastie, G. I. Mackay, T. Iguchi, B. A. Ridley, H. I. Schiff, “Tunable Diode Laser System for Measuring Trace Gases in Tropospheric Air,” Environ. Sci. Technol. 17, 352A–364A (1983).
[PubMed]

J. Geophys. Res. (1)

G. Hübler, D. Perner, U. Platt, A. Tönissen, D. H. Ehhalt, “Ground Level OH Radical Concentration: New Measurements by Optical Absorption,” J. Geophys. Res. 89, 1309 (1984).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (2)

H. I. Schiff, G. W. Harris, G. I. Mackay, “Measurement of Atmospheric Gases by Laser Absorption Spectrometry,” in The Chemistry of Acid Rain: Sources and Atmospheric Processes, R. W. Johnson, G. E. Gordon, W. Calkins, A. Z. Elzerman, Eds., ACS Symposium Series No. 349 (ACS, Washington, DC, 1987).
[Crossref]

J. L. Hall, T. Baer, L. Hallberg, H. G. Robinson, “Precision Spectroscopy and Laser Frequency Control Using FM Sideband Optical Heterodyne Techniques,” in Laser Spectroscopy V, A. R. W. McKellar, T. Oka, B. P. Stoicheff, Eds. (Springer-Verlag, Berlin, 1981), p. 16.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Noise frequency spectrum of a lead-salt diode laser.

Fig. 2
Fig. 2

Light power incident on detector P D and variable γ as a function of number of passes in a multipass cell. Variable γ describes how much higher the white noise, consisting of thermal noise and shot noise, is in comparison with the detector thermal noise.

Fig. 3
Fig. 3

Signal-to-noise ratio of a frequency modulated laser absorption spectrometer as a function of number of passes in a multipass cell for different laser output power. The calculation is based on detector noise equivalent power of 67 μW, mirror reflectivity of 97.5%, cell base length of 62.5 cm, and variable δ(ω) (see definition in text) equal to 3 × 10−5.

Fig. 4
Fig. 4

Signal-to-noise ratio of a wavelength modulated laser absorption spectrometer as a function of number of passes in a multipass cell for different laser output power. The input parameters are the same as in Fig. 3 with the exception of variable δ(ω) which is 0.3 in this case.

Fig. 5
Fig. 5

Signal-to-noise ratio of frequency modulated (FM) and wavelength modulated (WM) laser absorption spectrometers and their ratio as a function of number of passes in a multipass cell for laser power of 521 μW. The input parameters are the same as in Figs. 3 and 4.

Fig. 6
Fig. 6

Signal-to-noise ratio of a wavelength modulated (WM) laser absorption spectrometer as a function of number of passes at different mirror reflectivities.

Fig. 7
Fig. 7

Signal-to-noise ratio of a frequency modulated (FM) laser absorption spectrometer as a function of number of passes at different mirror reflectivities.

Equations (16)

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

S n P D = n R n 1 P 0 ,
N TN 2 = constant ,
N SN 2 = α P D ,
N EX 2 = β ( ω ) P D 2 ,
SNR n P D / ( N TN 2 + N SN 2 + N EX 2 ) 1 / 2 n P D / ( N TN 2 + α P D + β ( ω ) P D 2 ) 1 / 2 ,
N SN ( P min ) 2 = N TN 2 = α P min .
γ ( P D ) = 1 + P D / P min ,
δ ( ω ) = β ( ω ) / N TN 2 ,
SNR n P D / N TN [ γ ( P D ) + δ ( ω ) P D 2 ] 1 / 2 .
N EX 2 / ( N TN 2 + N S N 2 ) = δ ( ω ) P D 2 / γ ( P D ) .
δ ( ω WN ) P D 2 = γ ( P D ) .
SNR ( n ) n R n 1 P 0 / N T N [ γ ( n ) + δ ( ω ) R 2 n 2 P 0 2 ] 1 / 2 ,
SNR ( n ) n R n 1 P 0 / N T N [ γ ( n ) + δ ( ω ) R 2 n 2 P 0 2 ] 1 / 2 .
SNR ( n ) n R n 1 P 0 / N T N γ ( n ) 1 / 2 .
lim n SNR = n R n 1 P 0 / N T N .
WM : δ ( ω ω WN ) = 0 . 3 μ W 2 , FM : δ ( ω ω WN ) = 0 . 3 × 10 5 μ W 2 ,

Metrics