Abstract

The performance and measurement accuracy of Na narrowband wind–temperature lidar systems are characterized. Error budgets are derived that include several effects not previously reported, such as power-dependent spectral characteristics in the frequency reference, magnetic-field-dependent oscillator line strengths (Hanle effect), saturation, and optical pumping. It is shown that the overall system uncertainty is dependent on the power, pulse temporal characteristics, and beam divergence of the laser transmitter. Results indicate that even systems with significant saturation can produce accurate measurements, which implies the prospect of continuous daytime wind and temperature measurements on semidiurnal and diurnal time periods.

© 1995 Optical Society of America

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References

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  1. R. E. Bills, C. S. Gardner, C. Y. She, “Narrowband lidar technique for sodium temperature and Doppler wind observations of the upper atmosphere,” Opt. Eng. 30, 13–21 (1991).
    [CrossRef]
  2. C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
    [CrossRef]
  3. C. Y. She, J. R. Yu, H. Chen, “Observed thermal structure of a midlatitude mesopause,” Geophys. Res. Lett. 20, 567–570 (1993).
    [CrossRef]
  4. R. E. Bills, C. S. Gardner, S. J. Franke, “Na Doppler/temperature lidar: initial mesopause region observations and comparison with the Urbana medium frequency radar,” J. Geophys. Res. 96, 22701–22707 (1991).
    [CrossRef]
  5. C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).
  6. J. M. C. Plane, “The chemistry of meteoric metals in the earth's atmosphere,” Int. Rev. Phys. Chem. 10, 55–106 (1991).
    [CrossRef]
  7. C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
    [CrossRef] [PubMed]
  8. K. H. Fricke, U. von Zahn, “Mesopause temperatures derived from probing the hyperfine structure of the D2 resonance line of sodium by lidar,” J. Atmos. Terr. Phys. 47, 499–512 (1985).
    [CrossRef]
  9. R. M. Measures, Laser Remote Sensing—Fundamentals and Applications (Wiley, New York, 1984).
  10. E. Arimondo, M. Inguscio, P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
    [CrossRef]
  11. I. M. Reid, “MF Doppler and spaced antenna radar measurements of upper middle atmosphere winds,” J. Atmos. Terr. Phys. 50, 117–134 (1988).
    [CrossRef]
  12. A. Corney, Atomic and Laser Spectroscopy (Oxford U. Press, Oxford, 1977).
  13. B. Welsh, C. S. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
    [CrossRef] [PubMed]
  14. P. von der Gathen, “Saturation effects in Na lidar temperature measurements,” J. Geophys. Res. 96, 3679–3690 (1991).
    [CrossRef]
  15. D. C. Senft, C. S. Gardner, “Seasonal variability of gravity wave activity and spectra in the mesopause region at Urbana,” J. Geophys. Res. 96, 17229–17264 (1991).
    [CrossRef]
  16. R. E. Bills, C. S. Gardner, “Iron and sodium Doppler/temperature lidar studies of the upper mesosphere,” Rep. EOSL 91–002 (Electro-Optic Systems Laboratory, University of Illinois, Urbana, Ill., 1991).
  17. A. Gaupp, P. Kuske, H. J. Andrä, “Accurate lifetime measurements of the 2P1/2 states in neutral lithium and sodium,” Phys. Rev. A 26, 3351–3359 (1982).
    [CrossRef]
  18. P. W. Atkins, Molecular Quantum Mechanics (Oxford U. Press, New York, 1983).
  19. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  20. M. I. D'Yakonov, “Theory of resonance scattering of light by a gas in the presence of a magnetic field,” Sov. Phys. JETP 20, 1484–1489 (1965).
  21. R. N. Zare, Angular Momentum—Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York, 1988).
  22. D. Zimmermann, “Determination of the lifetime of the 4P1/2 state of potassium by Hanle-effect,” Z. Phys. A 275, 5–10 (1975).
    [CrossRef]
  23. International Association of Geomagnetism and Aeronomy, Division 1, Working Group 1, “International Geomagnetic Reference Fields: DGRF 1965, DGRF 1970, DGRF 1975 and IGRF 1980,” EOS Trans. AGU 62, 1169 (1981).
  24. J. R. Morris, “Efficient excitation of a mesospheric sodium laser guide star by intermediate-duration pulses,” J. Opt. Soc. Am. A 11, 832–845 (1994).
    [CrossRef]
  25. P. W. Milonni, L. E. Throde, “Theory of mesospheric sodium fluorescence excited by pulse trains,” Appl. Opt. 31, 785–799 (1992).
    [CrossRef] [PubMed]
  26. C. A. Hostetler, C. S. Gardner, “Observations of horizontal and vertical wave-number spectra of gravity wave motions in the stratosphere and mesosphere over the mid-Pacific,” J. Geophys. Res. 99, 1283–1302 (1994).
    [CrossRef]

1994 (2)

C. A. Hostetler, C. S. Gardner, “Observations of horizontal and vertical wave-number spectra of gravity wave motions in the stratosphere and mesosphere over the mid-Pacific,” J. Geophys. Res. 99, 1283–1302 (1994).
[CrossRef]

J. R. Morris, “Efficient excitation of a mesospheric sodium laser guide star by intermediate-duration pulses,” J. Opt. Soc. Am. A 11, 832–845 (1994).
[CrossRef]

1993 (1)

C. Y. She, J. R. Yu, H. Chen, “Observed thermal structure of a midlatitude mesopause,” Geophys. Res. Lett. 20, 567–570 (1993).
[CrossRef]

1992 (2)

1991 (6)

R. E. Bills, C. S. Gardner, C. Y. She, “Narrowband lidar technique for sodium temperature and Doppler wind observations of the upper atmosphere,” Opt. Eng. 30, 13–21 (1991).
[CrossRef]

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

R. E. Bills, C. S. Gardner, S. J. Franke, “Na Doppler/temperature lidar: initial mesopause region observations and comparison with the Urbana medium frequency radar,” J. Geophys. Res. 96, 22701–22707 (1991).
[CrossRef]

J. M. C. Plane, “The chemistry of meteoric metals in the earth's atmosphere,” Int. Rev. Phys. Chem. 10, 55–106 (1991).
[CrossRef]

P. von der Gathen, “Saturation effects in Na lidar temperature measurements,” J. Geophys. Res. 96, 3679–3690 (1991).
[CrossRef]

D. C. Senft, C. S. Gardner, “Seasonal variability of gravity wave activity and spectra in the mesopause region at Urbana,” J. Geophys. Res. 96, 17229–17264 (1991).
[CrossRef]

1989 (1)

1988 (1)

I. M. Reid, “MF Doppler and spaced antenna radar measurements of upper middle atmosphere winds,” J. Atmos. Terr. Phys. 50, 117–134 (1988).
[CrossRef]

1985 (1)

K. H. Fricke, U. von Zahn, “Mesopause temperatures derived from probing the hyperfine structure of the D2 resonance line of sodium by lidar,” J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

1982 (1)

A. Gaupp, P. Kuske, H. J. Andrä, “Accurate lifetime measurements of the 2P1/2 states in neutral lithium and sodium,” Phys. Rev. A 26, 3351–3359 (1982).
[CrossRef]

1981 (1)

International Association of Geomagnetism and Aeronomy, Division 1, Working Group 1, “International Geomagnetic Reference Fields: DGRF 1965, DGRF 1970, DGRF 1975 and IGRF 1980,” EOS Trans. AGU 62, 1169 (1981).

1977 (1)

E. Arimondo, M. Inguscio, P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

1975 (1)

D. Zimmermann, “Determination of the lifetime of the 4P1/2 state of potassium by Hanle-effect,” Z. Phys. A 275, 5–10 (1975).
[CrossRef]

1965 (1)

M. I. D'Yakonov, “Theory of resonance scattering of light by a gas in the presence of a magnetic field,” Sov. Phys. JETP 20, 1484–1489 (1965).

Andrä, H. J.

A. Gaupp, P. Kuske, H. J. Andrä, “Accurate lifetime measurements of the 2P1/2 states in neutral lithium and sodium,” Phys. Rev. A 26, 3351–3359 (1982).
[CrossRef]

Arimondo, E.

E. Arimondo, M. Inguscio, P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Atkins, P. W.

P. W. Atkins, Molecular Quantum Mechanics (Oxford U. Press, New York, 1983).

Beatty, T. J.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).

Bills, R. E.

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[CrossRef] [PubMed]

R. E. Bills, C. S. Gardner, C. Y. She, “Narrowband lidar technique for sodium temperature and Doppler wind observations of the upper atmosphere,” Opt. Eng. 30, 13–21 (1991).
[CrossRef]

R. E. Bills, C. S. Gardner, S. J. Franke, “Na Doppler/temperature lidar: initial mesopause region observations and comparison with the Urbana medium frequency radar,” J. Geophys. Res. 96, 22701–22707 (1991).
[CrossRef]

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).

R. E. Bills, C. S. Gardner, “Iron and sodium Doppler/temperature lidar studies of the upper mesosphere,” Rep. EOSL 91–002 (Electro-Optic Systems Laboratory, University of Illinois, Urbana, Ill., 1991).

Chen, H.

C. Y. She, J. R. Yu, H. Chen, “Observed thermal structure of a midlatitude mesopause,” Geophys. Res. Lett. 20, 567–570 (1993).
[CrossRef]

Corney, A.

A. Corney, Atomic and Laser Spectroscopy (Oxford U. Press, Oxford, 1977).

D'Yakonov, M. I.

M. I. D'Yakonov, “Theory of resonance scattering of light by a gas in the presence of a magnetic field,” Sov. Phys. JETP 20, 1484–1489 (1965).

Franke, S. J.

R. E. Bills, C. S. Gardner, S. J. Franke, “Na Doppler/temperature lidar: initial mesopause region observations and comparison with the Urbana medium frequency radar,” J. Geophys. Res. 96, 22701–22707 (1991).
[CrossRef]

Fricke, K. H.

K. H. Fricke, U. von Zahn, “Mesopause temperatures derived from probing the hyperfine structure of the D2 resonance line of sodium by lidar,” J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

Gardner, C. S.

C. A. Hostetler, C. S. Gardner, “Observations of horizontal and vertical wave-number spectra of gravity wave motions in the stratosphere and mesosphere over the mid-Pacific,” J. Geophys. Res. 99, 1283–1302 (1994).
[CrossRef]

D. C. Senft, C. S. Gardner, “Seasonal variability of gravity wave activity and spectra in the mesopause region at Urbana,” J. Geophys. Res. 96, 17229–17264 (1991).
[CrossRef]

R. E. Bills, C. S. Gardner, S. J. Franke, “Na Doppler/temperature lidar: initial mesopause region observations and comparison with the Urbana medium frequency radar,” J. Geophys. Res. 96, 22701–22707 (1991).
[CrossRef]

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

R. E. Bills, C. S. Gardner, C. Y. She, “Narrowband lidar technique for sodium temperature and Doppler wind observations of the upper atmosphere,” Opt. Eng. 30, 13–21 (1991).
[CrossRef]

B. Welsh, C. S. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
[CrossRef] [PubMed]

R. E. Bills, C. S. Gardner, “Iron and sodium Doppler/temperature lidar studies of the upper mesosphere,” Rep. EOSL 91–002 (Electro-Optic Systems Laboratory, University of Illinois, Urbana, Ill., 1991).

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).

Gaupp, A.

A. Gaupp, P. Kuske, H. J. Andrä, “Accurate lifetime measurements of the 2P1/2 states in neutral lithium and sodium,” Phys. Rev. A 26, 3351–3359 (1982).
[CrossRef]

Hostetler, C.

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).

Hostetler, C. A.

C. A. Hostetler, C. S. Gardner, “Observations of horizontal and vertical wave-number spectra of gravity wave motions in the stratosphere and mesosphere over the mid-Pacific,” J. Geophys. Res. 99, 1283–1302 (1994).
[CrossRef]

Huang, J. W.

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

Inguscio, M.

E. Arimondo, M. Inguscio, P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Kuske, P.

A. Gaupp, P. Kuske, H. J. Andrä, “Accurate lifetime measurements of the 2P1/2 states in neutral lithium and sodium,” Phys. Rev. A 26, 3351–3359 (1982).
[CrossRef]

Latifi, H.

Measures, R. M.

R. M. Measures, Laser Remote Sensing—Fundamentals and Applications (Wiley, New York, 1984).

Milonni, P. W.

Morris, J. R.

Nagasawa, C.

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

Plane, J. M. C.

J. M. C. Plane, “The chemistry of meteoric metals in the earth's atmosphere,” Int. Rev. Phys. Chem. 10, 55–106 (1991).
[CrossRef]

Reid, I. M.

I. M. Reid, “MF Doppler and spaced antenna radar measurements of upper middle atmosphere winds,” J. Atmos. Terr. Phys. 50, 117–134 (1988).
[CrossRef]

Senft, D. C.

D. C. Senft, C. S. Gardner, “Seasonal variability of gravity wave activity and spectra in the mesopause region at Urbana,” J. Geophys. Res. 96, 17229–17264 (1991).
[CrossRef]

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).

She, C. Y.

C. Y. She, J. R. Yu, H. Chen, “Observed thermal structure of a midlatitude mesopause,” Geophys. Res. Lett. 20, 567–570 (1993).
[CrossRef]

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[CrossRef] [PubMed]

R. E. Bills, C. S. Gardner, C. Y. She, “Narrowband lidar technique for sodium temperature and Doppler wind observations of the upper atmosphere,” Opt. Eng. 30, 13–21 (1991).
[CrossRef]

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Throde, L. E.

Violino, P.

E. Arimondo, M. Inguscio, P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

von der Gathen, P.

P. von der Gathen, “Saturation effects in Na lidar temperature measurements,” J. Geophys. Res. 96, 3679–3690 (1991).
[CrossRef]

von Zahn, U.

K. H. Fricke, U. von Zahn, “Mesopause temperatures derived from probing the hyperfine structure of the D2 resonance line of sodium by lidar,” J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

Welsh, B.

Yu, J. R.

C. Y. She, J. R. Yu, H. Chen, “Observed thermal structure of a midlatitude mesopause,” Geophys. Res. Lett. 20, 567–570 (1993).
[CrossRef]

C. Y. She, J. R. Yu, H. Latifi, R. E. Bills, “High-spectral-resolution fluorescence light detection and ranging for mesospheric sodium temperature measurements,” Appl. Opt. 31, 2095–2106 (1992).
[CrossRef] [PubMed]

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

Zare, R. N.

R. N. Zare, Angular Momentum—Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York, 1988).

Zimmermann, D.

D. Zimmermann, “Determination of the lifetime of the 4P1/2 state of potassium by Hanle-effect,” Z. Phys. A 275, 5–10 (1975).
[CrossRef]

Appl. Opt. (3)

EOS Trans. AGU (1)

International Association of Geomagnetism and Aeronomy, Division 1, Working Group 1, “International Geomagnetic Reference Fields: DGRF 1965, DGRF 1970, DGRF 1975 and IGRF 1980,” EOS Trans. AGU 62, 1169 (1981).

Geophys. Res. Lett. (2)

C. Y. She, J. R. Yu, J. W. Huang, C. Nagasawa, C. S. Gardner, “Na temperature lidar measurements of gravity wave perturbations of winds, density, and temperature in the mesopause region,” Geophys. Res. Lett. 18, 1329–1331 (1991).
[CrossRef]

C. Y. She, J. R. Yu, H. Chen, “Observed thermal structure of a midlatitude mesopause,” Geophys. Res. Lett. 20, 567–570 (1993).
[CrossRef]

Int. Rev. Phys. Chem. (1)

J. M. C. Plane, “The chemistry of meteoric metals in the earth's atmosphere,” Int. Rev. Phys. Chem. 10, 55–106 (1991).
[CrossRef]

J. Atmos. Terr. Phys. (2)

K. H. Fricke, U. von Zahn, “Mesopause temperatures derived from probing the hyperfine structure of the D2 resonance line of sodium by lidar,” J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

I. M. Reid, “MF Doppler and spaced antenna radar measurements of upper middle atmosphere winds,” J. Atmos. Terr. Phys. 50, 117–134 (1988).
[CrossRef]

J. Geophys. Res. (4)

P. von der Gathen, “Saturation effects in Na lidar temperature measurements,” J. Geophys. Res. 96, 3679–3690 (1991).
[CrossRef]

D. C. Senft, C. S. Gardner, “Seasonal variability of gravity wave activity and spectra in the mesopause region at Urbana,” J. Geophys. Res. 96, 17229–17264 (1991).
[CrossRef]

R. E. Bills, C. S. Gardner, S. J. Franke, “Na Doppler/temperature lidar: initial mesopause region observations and comparison with the Urbana medium frequency radar,” J. Geophys. Res. 96, 22701–22707 (1991).
[CrossRef]

C. A. Hostetler, C. S. Gardner, “Observations of horizontal and vertical wave-number spectra of gravity wave motions in the stratosphere and mesosphere over the mid-Pacific,” J. Geophys. Res. 99, 1283–1302 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

R. E. Bills, C. S. Gardner, C. Y. She, “Narrowband lidar technique for sodium temperature and Doppler wind observations of the upper atmosphere,” Opt. Eng. 30, 13–21 (1991).
[CrossRef]

Phys. Rev. A (1)

A. Gaupp, P. Kuske, H. J. Andrä, “Accurate lifetime measurements of the 2P1/2 states in neutral lithium and sodium,” Phys. Rev. A 26, 3351–3359 (1982).
[CrossRef]

Rev. Mod. Phys. (1)

E. Arimondo, M. Inguscio, P. Violino, “Experimental determinations of the hyperfine structure in the alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977).
[CrossRef]

Sov. Phys. JETP (1)

M. I. D'Yakonov, “Theory of resonance scattering of light by a gas in the presence of a magnetic field,” Sov. Phys. JETP 20, 1484–1489 (1965).

Z. Phys. A (1)

D. Zimmermann, “Determination of the lifetime of the 4P1/2 state of potassium by Hanle-effect,” Z. Phys. A 275, 5–10 (1975).
[CrossRef]

Other (7)

R. N. Zare, Angular Momentum—Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York, 1988).

P. W. Atkins, Molecular Quantum Mechanics (Oxford U. Press, New York, 1983).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

R. E. Bills, C. S. Gardner, “Iron and sodium Doppler/temperature lidar studies of the upper mesosphere,” Rep. EOSL 91–002 (Electro-Optic Systems Laboratory, University of Illinois, Urbana, Ill., 1991).

A. Corney, Atomic and Laser Spectroscopy (Oxford U. Press, Oxford, 1977).

R. M. Measures, Laser Remote Sensing—Fundamentals and Applications (Wiley, New York, 1984).

C. S. Gardner, D. C. Senft, T. J. Beatty, R. E. Bills, C. Hostetler, “Rayleigh and sodium lidar techniques for measuring middle atmosphere density, temperature and wind perturbations and their spectra,” in World Ionosphere/Thermosphere Study (WITS) Handbood, C. H. Liu, ed. (Scientific Committee on Solar Terrestrial Physics, Urbana, Illinois, 1989).

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Figures (10)

Fig. 1
Fig. 1

Linear absorption backscatter cross section of the Na D2 line as a function of frequency for several temperatures. As the temperature increases, the ratio (RT = Nfc/Nfa) of the backscatter from two frequencies fc and fa increases and thereby provides a discriminant for the determination of the temperature.

Fig. 2
Fig. 2

Absorption backscatter cross section of the Na D2 line as a function of frequency for two radial-wind velocities. For radial-wind velocities toward the receiver, the ratio of the backscatter from two frequencies f+ and f that are shown in the figure decreases.

Fig. 3
Fig. 3

(a) Deviation from linear response (percent saturation) as a function of the total pulse energy for a 1-mrad, 7-ns rms pulse. Details of the calculation are presented in Appendix B. The calculated points are represented by the filled and open circles. The curves are drawn to aid the viewer. (b) The same as in (a) except that the pulse energy is held at a constant 100 mJ and the independent variable is the pulse duration. The limit of the response at ∼0.3% for pulses longer than 600 ns is caused by optical-pumping effects.

Fig. 4
Fig. 4

(a) Percent saturation as a function of divergence at fa and fc for two pulse energies (35 mJ and 100 mJ) for a 7-ns rms pulse. (b) Temperature error for the same parameters as given for Fig. 3. The y axis on the left-hand side of the figure shows the relative error in the ratio ΔRT/RT. The right-hand-side y axis shows the temperature error determined with the values in Table 2. (c) Wind-velocity error for both wind-measurement techniques (W1 and W2) for the same parameters given for Fig. 3.

Fig. 5
Fig. 5

Measurement of the jitter at fa for the night of 17 January 1993 at the UAO in Urbana, Illinois.

Fig. 6
Fig. 6

Energy levels that compose the Na D2 transition. Numbers preceded by ‘×’ indicate the magnifications of the energy difference.

Fig. 7
Fig. 7

Six-transition model used for the vapor-cell calibration and saturation simulations. The number of the transition is shown in boldface. The relative oscillator strength in the absence of a magnetic field is shown in parentheses. Upper states are designed by the total angular momentum quantum number F, and ground states are designated by f.

Fig. 8
Fig. 8

Geometry for the coordinate transformation required to determine the Hanle effect.

Fig. 9
Fig. 9

Relation of k ̂ and b ̂ to geographical coordinates.

Fig. 10
Fig. 10

(a) Data for the model of the Na Doppler-free features compared with the experimental data. (b) Expanded view near peak fa. (c) Expanded view near the crossover fc. The fit between the experimental data and the model provides calibration to within ±2 MHz.

Tables (6)

Tables Icon

Table 1 rms Jitter Measurements at fa for the University of Illinois Wind-Temperature Lidar for the Night of 17 January 1993

Tables Icon

Table 2 Ratio Ra Calculated with Eqs. (7) and (10)(12), Measurement Errors, and Derivativesb Calculated with Eq. (13) for Wind and Temperature Differentials

Tables Icon

Table 3 Magnitude of Wind- and Temperature-Measurement Errors for Each System Parameter and Measurement Techniquea

Tables Icon

Table 4 Total System Error for Each Measurement Technique and the Number of Photons Required to Produce the Same Error as the Total System Errora

Tables Icon

Table 5 Relative Oscillator Strengths for a Beam Traveling West through the Vapor Cell

Tables Icon

Table 6 Magnitude of the Percent Relative Density Errora as a Function of z and the Time Between Profiles Δt

Equations (78)

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N ( z , t ) = C z 2 σ eff ( f , T , v R , g , I ) ρ Na ( z , t ) + N B ,
C = η T a 2 P l Δ z Δ t ( h c / λ ) A R 4 π .
σ eff ( f l , T , v R , g , I ) = g ( f f l ) σ Na ( f , T , v R , I ) d f ,
R ( z , t , τ ) = N f 1 ( z , t + τ ) N f 2 ( z , t ) = σ eff ( f 1 , T , v R , g , I ) ρ s ( z , t + τ ) σ eff ( f 2 , T , v R , g , I ) ρ s ( z , t ) ,
R = N f 1 ( z , t + τ ) N f 2 ( z , t ) σ eff ( f 1 , T , v R , g ) σ eff ( f 2 , T , v R , g ) .
σ ̂ Na ( f , T , v R ) = 1 ( 2 π σ D 2 ) 1 / 2 i A i × exp [ ( f f i + v R / λ ) 2 2 σ D 2 ] ,
ĝ ( f ) = 1 ( 2 π σ rms 2 ) 1 / 2 exp [ f 2 2 σ rms 2 ] .
σ ̂ eff ( f l , T , v R , σ rms ) = 1 ( 2 π σ e 2 ) 1 / 2 i A i × exp [ ( f l f i + v R / λ ) 2 2 σ e 2 ] ,
Δ R ( z , τ ) R 1 T rms ( 2 π Δ t ) ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] ( r a 2 ) 1 / 2 ,
Δ R T R T 1 ( N f a ) 1 / 2 ( 1 + 1 R T ) 1 / 2
Δ R W 1 R W 1 1 ( N f + ) 1 / 2 ( 1 + 1 R W 1 ) 1 / 2 = 1 ( N f a ) 1 / 2 ( R W 1 R W 2 + 1 R W 2 ) 1 / 2 1 ( N f a ) 1 / 2 ( 2 R W 2 ) 1 / 2 ,
Δ R W 2 R W 2 1 ( N f a ) 1 / 2 ( 1 + 1 R W 2 ) 1 / 2 ,
R ̂ T ( f a , f c , T , v R , σ rms ) = σ ̂ eff ( f c , T , v R , σ rms ) σ ̂ eff ( f a , T , v R , σ rms ) ,
R ̂ W 1 ( f , f + , T , v R , σ rms ) = σ ̂ eff ( f + , T , v R , σ rms ) σ ̂ eff ( f , T , v R , σ rms ) ,
R ̂ W 2 ( f a , f + , T , v R , σ rms ) = σ ̂ eff ( f + , T , v R , σ rms ) σ ̂ eff ( f a , T , v R , σ rms ) .
R ̂ χ = R ̂ [ σ ̂ eff ( f 1 ) σ ̂ eff ( f 1 ) σ ̂ eff ( f 2 ) σ ̂ eff ( f 2 ) ] ,
Δ T = Δ R T T R ̂ T Q T = Δ R T R ̂ T [ σ ̂ eff ( f c ) σ ̂ eff ( f c ) σ ̂ eff ( f a ) σ ̂ eff ( f a ) ] 1 Q T .
Δ T = R ̂ T v R / R ̂ T T Q T Δ v R ,
Δ v R = R ̂ W T / R ̂ W v R Q W Δ T .
σ total = ( i σ i 2 ) 1 / 2 ,
Δ T = 118 Δ R T R T
Δ v R = 116 Δ R W 1 R W 1
Δ v R = 262 Δ R W 2 R W 2
T f a = 0.0002 K MHz
v R f = 0.327 m / s MHz
v R f a = 0.0004 m / s MHz
T f c = 0.102 K MHz
v R f + = 0.262 m / s MHz
v R f + = 0.570 m / s MHz
T σ rms = 0.115 m / s MHz
v R σ rms = 0.0101 m / s MHz
v R σ rms = 0.146 m / s MHz
T v R = 0.174 K m / s
v R T = 0.0874 m / s K
v R T = 1.27 m / s K
d ρ m m d t = i [ V , ρ ] m m m 1 m 1 Γ m m m 1 m 1 ρ m 1 m 1 + F m m ,
d ρ q k d t = i μ B gqB ρ q k γ k ρ q k + F q k ,
R f F ( ê , û , B ) = R 0 ( 1 ) I f J 0 A f F [ f ] [ F ] 2 × { J F I f J 0 1 } 2 k , q ( 1 ) k + q { 1 1 k J J J 0 } × { J J k F F I } { 1 1 k F F f } × Φ q k ( ê ) Φ q k ( û ) ( 1 + i q g F μ B τ B / ) 1 ,
Φ q k ( ê ) = ( 1 ) q ( 2 k + 1 ) 1 / 2 q 1 q 2 ( 1 ) q 2 ê q 1 ê q 2 * × [ 1 1 k q 1 q 2 q ] , 1 q 1 , q 2 1 ,
ê ± 1 = 1 2 ( x ̂ ± i ŷ ) , σ ± polarizations , ê 0 = z , π polarization .
ê = cos γ x ̂ + i sin γ ŷ , π / 4 γ π / 4 , x ̂ = cos β θ ̂ 0 + sin β ϕ ̂ 0 , 0 β π , ŷ = sin β θ ̂ 0 + cos β ϕ ̂ 0 ,
θ ̂ 0 = cos ϕ cos θ x ̂ + sin ϕ cos θ ŷ sin θ z ̂ , ϕ ̂ 0 = sin ϕ x ̂ + cos ϕ ŷ .
ê ± 1 = 1 2 [ cos β ( cos γ cos θ sin γ ) i sin β ( sin γ cos θ cos γ ) ] exp ( ± i ϕ ) , ê 0 = ( cos γ cos β i sin γ sin β ) sin θ .
Φ 0 0 ( ê ) = 1 / 3 , Φ 0 1 ( ê ) = 1 / 2 sin ( 2 γ ) cos θ , Φ ± 1 1 ( ê ) = 1 / 2 sin ( 2 γ ) sin θ exp ( ± i ϕ ) , Φ 0 2 ( ê ) = 1 / 6 { 1 ( 3 / 2 ) [ 1 + cos ( 2 β ) cos ( 2 γ ) ] sin 2 ( θ ) } , Φ ± 1 2 ( ê ) = ± 1 / 2 { [ 1 + cos ( 2 β ) cos ( 2 γ ) ] cos θ ± i sin ( 2 β ) cos ( 2 γ ) } sin θ exp ( ± i ϕ ) , Φ ± 2 2 ( ê ) = 1 / 2 { cos ( 2 β ) cos ( 2 γ ) ( ½ ) [ 1 + cos ( 2 β ) cos ( 2 γ ) ] × sin 2 ( θ ) ± i sin ( 2 β ) cos ( 2 γ ) cos θ } exp ( ± i 2 ϕ ) .
Φ 0 0 ( û ) = 2 / 3 , Φ 0 , ± 1 1 ( û ) = 0 , Φ 0 2 ( û ) = 2 / 6 [ 1 3 / 2 sin 2 ( θ r ) ] Φ ± 1 2 ( û ) = ± sin ( θ r ) cos ( θ r ) exp ( ± i ϕ r ) , Φ ± 2 2 ( û ) = 1 / 2 sin 2 ( θ r ) exp ( ± i 2 ϕ r ) .
Φ 0 0 ( ê ) Φ 0 0 ( û ) = , Φ 0 , 1 1 ( ê ) Φ 0 , ± 1 1 ( û ) = 0 , Φ 0 2 ( ê ) Φ 0 2 ( û ) = ( ) [ 1 ( 3 / 2 ) sin 2 ( θ r ) ] { 1 ( 3 / 2 ) × [ 1 + cos ( 2 β ) ] sin 2 ( θ t ) } , Φ 1 2 ( ê ) Φ ± 1 2 ( û ) = ( ½ ) sin ( θ r ) cos ( θ r ) sin ( θ t ) × { [ 1 + cos ( 2 β ) ] cos ( θ t ) i sin ( 2 β ) } × exp [ ± i ( ϕ r ϕ t ) ] , Φ 2 2 ( ê ) Φ ± 2 2 ( û ) = ( ¼ ) sin 2 ( θ r ) { cos ( 2 β ) ( ½ ) × [ 1 + cos ( 2 β ) ] sin 2 ( θ t ) i sin ( 2 β ) × cos ( θ t ) } exp [ ± i 2 ( ϕ r ϕ t ) ] .
V n = [ cos D sin D 0 sin D sin I cos D sin I cos I sin D cos I cos D cos I sin I ] V l ,
d N F 0 d t = ξ 3 ( t ) ( N f 1 g F 0 g f 1 N F 0 ) N F 0 τ 3 ( N F 0 0 ) τ C , d N F 1 d t = ξ 2 ( t ) ( N f 1 g F 1 g f 1 N F 1 ) + ξ 6 ( t ) ( N f 2 g F 1 g f 2 N F 1 ) N F 1 τ 2 N F 1 τ 6 ( N F 1 0 ) τ C , d N F 2 d t = ξ 1 ( t ) ( N f 1 g F 2 g f 1 N F 2 ) + ξ 5 ( t ) ( N f 2 g F 2 g f 2 N F 2 ) N F 2 τ 1 N F 2 τ 5 ( N F 2 0 ) τ C , d N F 3 d t = ξ 4 ( t ) ( N f 2 g F 3 g f 2 N F 3 ) N F 3 τ 4 ( N F 3 0 ) τ C , d N f 1 d t = ξ 3 ( t ) ( N f 1 g F 0 g f 1 N F 0 ) ξ 2 ( t ) ( N f 1 g F 1 g f 1 N F 1 ) ξ 1 ( t ) ( N f 1 g F 2 g f 1 N F 2 ) + N F 0 τ 3 + N F 1 τ 2 + N F 2 τ 1 ( N f 1 g f 1 g f 1 + g f 2 ) τ C , d N f 2 d t = ξ 6 ( t ) ( N f 2 g F 1 g f 2 N F 1 ) ξ 5 ( t ) ( N f 2 g F 2 g f 2 N F 2 ) ξ 4 ( t ) ( N f 2 g F 3 g f 2 N F 3 ) + N F 1 τ 6 + N F 2 τ 5 + N F 3 τ 4 ( N f 2 g f 2 g f 1 + g f 2 ) τ C .
ξ y ( t , v R , r ) = 1 h f d f σ y ( f ) I 1 ( f , t , v R , r ) .
τ y = τ Na S y S y .
σ y ( f ) = 1 4 π ɛ 0 π q e 2 m e c S os S y S y 1 2 π Δ f y ( f f y ) 2 + ( Δ f y 2 ) 2 ,
Δ f y = Δ ω FWHM 2 π = 1 τ y π .
I 1 ( f , t , v R , r ) = 1 ( 2 π ) 1 / 2 σ r ( z ) exp ( | r | 2 2 σ r 2 ( z ) ) ( 1 ( 2 π ) 1 / 2 σ 1 ) × exp { [ f ( f 1 + f 0 v R c ) ] 2 2 σ 1 2 } ϕ ( t ) .
σ r ( z ) = σ 0 + z θ 2 .
ϕ ( t ) = E t 2 T r 2 exp { t 2 4 t r 2 } ,
t r = Δ t rms ( 2 π / 2 ) 1 / 2 .
R Sat ( f 1 ) = d v R d r d t x N F x ( t , v R , r ) τ F x ,
ξ y ( v R , r ) = 1 h f d f σ y ( f ) [ I 1 ( f , v R , r ) + I 1 ( f , v R , r ) ] .
Fluorescence ( f 1 ) = d v R d r x N F x ( v R , r ) τ F x .
R ( z , t , Δ t ) = N f 1 ( z , t + Δ t ) N f 2 ( z , t ) = σ eff ( f 1 ) ρ s ( z , t + Δ t ) σ eff ( f 2 ) ρ s ( z , t ) ,
ρ s ( z , t + Δ t ) = ρ ̅ s + ρ s ,
R R ( 1 + ρ s ρ s ) ,
Δ R R ρ s ρ ̅ s ,
R r s ,
r s = 1 ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] r a ,
R ( z ) 1 ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] r a .
Δ R ( z , Δ t ) 1 ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] r a t Δ t .
[ Δ R ( z , Δ t ) ] 2 r a 2 Δ t 2 ( γ 1 ) 2 [ 1 ( z z 0 ) γ H / σ 0 2 ] 2 × [ ( r a t ) 2 / r a 2 ] .
( [ Δ R ( z , Δ t ) ] 2 ) 1 / 2 1 T rms ( 2 π Δ t ) ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] × ( r a 2 ) 1 / 2 .
R ( Δ t ) = r s p r s c ,
r s p = α r s ( t 2 Δ t ) + r s ( t ) + α r s ( t + 2 Δ t ) 1 + 2 α ,
r s c = β r s ( t 3 Δ t ) + r s ( t Δ t ) + r s ( t + Δ t ) + β r s ( t + 3 Δ t ) 2 ( 1 + β ) .
R ( Δ t ) ( Δ t ) 6 32 r s 6 t 6 .
R ( z , Δ t ) ( Δ t ) 6 32 1 ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] r a 6 t 6 ,
[ R ( z , Δ t ) ] 2 [ ( Δ t ) 6 32 ] 2 1 ( γ 1 ) 2 [ 1 ( z z 0 ) γ H / σ 0 2 ] 2 × 1 2 π f ω c ω 12 F a ( ω ) d ω ,
F a ( ω ) = 2 π f ω 2 r a 2 ,
( [ R ( Δ t ) ] 2 ) 1 / 2 ( r a 2 ) 1 / 2 ( 4 11 f ω c ) 1 / 2 [ ( ω c Δ t ) 2 ] 6 × 1 ( γ 1 ) [ 1 ( z z 0 ) γ H / σ 0 2 ] .
[ 2 π Δ t T rms ] / ( 4 11 f ω c ) 1 / 2 [ ( ω c Δ t ) 2 ] 6 .

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