Abstract

The theory of the double-edge technique is described by a generalized formulation that substantially extends the capabilities of the edge technique. It uses two edges with opposite slopes located about the laser frequency. This doubles the signal change for a given Doppler shift and yields a factor of 1.6 improvement in the measurement accuracy compared with the single-edge technique. Use of two high-resolution edge filters reduces the effects of Rayleigh scattering on the measurement by as much as an order of magnitude and allows the signal-to-noise ratio to be substantially improved in areas of low aerosol backscatter. We describe a method that allows the Rayleigh and aerosol components of the signal to be independently determined. The effects of Rayleigh scattering are then subtracted from the measurement, and we show that the correction process does not significantly increase the measurement noise for Rayleigh-to-aerosol ratios as high as 10. We show that for small Doppler shifts a measurement accuracy of 0.4 m/s can be obtained for 5000 detected photons, 1.2 m/s for 1000 detected photons, and 3.7 m/s for 50 detected photons for a Rayleigh-to-aerosol ratio of 5. Methods for increasing the dynamic range to more than ±100 m/s are given.

© 1998 Optical Society of America

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References

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  1. C. L. Korb, B. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.
  2. C. L. Korb, B. Gentry, C. Weng, “The edge technique—theory and application to the lidar measurement of atmospheric winds,” Appl. Opt. 31, 4202–4213 (1992).
    [CrossRef] [PubMed]
  3. B. Gentry, C. L. Korb, “Edge technique for high-accuracy Doppler velocimetry,” Appl. Opt. 33, 5770–5777 (1994).
    [CrossRef] [PubMed]
  4. C. L. Korb, B. M. Gentry, S. X. Li, “Edge technique Doppler lidar wind measurements with high vertical resolution,” Appl. Opt. 36, 5976–5983 (1997).
    [CrossRef] [PubMed]
  5. V. J. Abreu, J. E. Barnes, P. B. Hays, “Observations of winds with an incoherent lidar detector,” Appl. Opt. 31, 4509–4514 (1992).
    [CrossRef] [PubMed]
  6. M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
    [CrossRef]
  7. G. Benedetti-Michelangeli, F. Congeduti, G. Fiocco, “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” J. Atmos. Sci. 29, 906–910 (1972).
    [CrossRef]
  8. C. Flesia, C. L. Korb, “Theory of the double edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. (to be published).
  9. P. Jacquinot, “The luminosity of spectrometers with prisms, gratings, or Fabry–Perot etalons,” J. Opt. Soc. Am. 44, 761–765 (1954).
    [CrossRef]
  10. T. R. Hicks, N. K. Reay, P. D. Atherton, “The application of capacitance micrometry to the control of Fabry–Perot etalons,” J. Phys. E 17, 49–55 (1984).
    [CrossRef]
  11. H. Mark, J. Workman, Statistics in Spectroscopy (Academic, San Diego, Calif., 1991).

1997 (1)

1994 (1)

1992 (2)

1989 (1)

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

1984 (1)

T. R. Hicks, N. K. Reay, P. D. Atherton, “The application of capacitance micrometry to the control of Fabry–Perot etalons,” J. Phys. E 17, 49–55 (1984).
[CrossRef]

1972 (1)

G. Benedetti-Michelangeli, F. Congeduti, G. Fiocco, “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” J. Atmos. Sci. 29, 906–910 (1972).
[CrossRef]

1954 (1)

Abreu, V. J.

Atherton, P. D.

T. R. Hicks, N. K. Reay, P. D. Atherton, “The application of capacitance micrometry to the control of Fabry–Perot etalons,” J. Phys. E 17, 49–55 (1984).
[CrossRef]

Barnes, J. E.

Benedetti-Michelangeli, G.

G. Benedetti-Michelangeli, F. Congeduti, G. Fiocco, “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” J. Atmos. Sci. 29, 906–910 (1972).
[CrossRef]

Chanin, M. L.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Congeduti, F.

G. Benedetti-Michelangeli, F. Congeduti, G. Fiocco, “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” J. Atmos. Sci. 29, 906–910 (1972).
[CrossRef]

Fiocco, G.

G. Benedetti-Michelangeli, F. Congeduti, G. Fiocco, “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” J. Atmos. Sci. 29, 906–910 (1972).
[CrossRef]

Flesia, C.

C. Flesia, C. L. Korb, “Theory of the double edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. (to be published).

Garnier, A.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Gentry, B.

B. Gentry, C. L. Korb, “Edge technique for high-accuracy Doppler velocimetry,” Appl. Opt. 33, 5770–5777 (1994).
[CrossRef] [PubMed]

C. L. Korb, B. Gentry, C. Weng, “The edge technique—theory and application to the lidar measurement of atmospheric winds,” Appl. Opt. 31, 4202–4213 (1992).
[CrossRef] [PubMed]

C. L. Korb, B. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.

Gentry, B. M.

Hauchecorne, A.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Hays, P. B.

Hicks, T. R.

T. R. Hicks, N. K. Reay, P. D. Atherton, “The application of capacitance micrometry to the control of Fabry–Perot etalons,” J. Phys. E 17, 49–55 (1984).
[CrossRef]

Jacquinot, P.

Korb, C. L.

C. L. Korb, B. M. Gentry, S. X. Li, “Edge technique Doppler lidar wind measurements with high vertical resolution,” Appl. Opt. 36, 5976–5983 (1997).
[CrossRef] [PubMed]

B. Gentry, C. L. Korb, “Edge technique for high-accuracy Doppler velocimetry,” Appl. Opt. 33, 5770–5777 (1994).
[CrossRef] [PubMed]

C. L. Korb, B. Gentry, C. Weng, “The edge technique—theory and application to the lidar measurement of atmospheric winds,” Appl. Opt. 31, 4202–4213 (1992).
[CrossRef] [PubMed]

C. L. Korb, B. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.

C. Flesia, C. L. Korb, “Theory of the double edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. (to be published).

Li, S. X.

Mark, H.

H. Mark, J. Workman, Statistics in Spectroscopy (Academic, San Diego, Calif., 1991).

Porteneuve, J.

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

Reay, N. K.

T. R. Hicks, N. K. Reay, P. D. Atherton, “The application of capacitance micrometry to the control of Fabry–Perot etalons,” J. Phys. E 17, 49–55 (1984).
[CrossRef]

Weng, C.

Workman, J.

H. Mark, J. Workman, Statistics in Spectroscopy (Academic, San Diego, Calif., 1991).

Appl. Opt. (4)

Geophys. Res. Lett. (1)

M. L. Chanin, A. Garnier, A. Hauchecorne, J. Porteneuve, “A Doppler lidar for measuring winds in the middle atmosphere,” Geophys. Res. Lett. 16, 1273–1276 (1989).
[CrossRef]

J. Atmos. Sci. (1)

G. Benedetti-Michelangeli, F. Congeduti, G. Fiocco, “Measurement of aerosol motion and wind velocity in the lower troposphere by Doppler optical radar,” J. Atmos. Sci. 29, 906–910 (1972).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E (1)

T. R. Hicks, N. K. Reay, P. D. Atherton, “The application of capacitance micrometry to the control of Fabry–Perot etalons,” J. Phys. E 17, 49–55 (1984).
[CrossRef]

Other (3)

H. Mark, J. Workman, Statistics in Spectroscopy (Academic, San Diego, Calif., 1991).

C. Flesia, C. L. Korb, “Theory of the double edge molecular technique for Doppler lidar wind measurement,” Appl. Opt. (to be published).

C. L. Korb, B. Gentry, “New Doppler lidar methods for atmospheric wind measurements: the edge technique,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 322–324.

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Figures (12)

Fig. 1
Fig. 1

Double-edge schematic diagram. REF, laser reference frequency; ATM, atmospheric measurement frequency.

Fig. 2
Fig. 2

Schematic diagram of the atmospheric backscattered aerosol and molecular signals relative to the location of the double-edge filter (edge 1 and edge 2). The aerosol spectrum is narrow relative to the laser width, and thus the backscattered aerosol spectrum shown has the width and shape of the laser.

Fig. 3
Fig. 3

Sensitivity of the double-edge filter as a function of the Doppler shift in units of etalon HWHM.

Fig. 4
Fig. 4

Error in the wind measurement that is due to a 5 K error in the atmospheric temperature profile is given as a function of the Doppler shift in units of etalon HWHM. Curves are given for atmospheric temperatures of 220, 250, and 290 K for a ratio of Rayleigh-to-aerosol scattering of 5.

Fig. 5
Fig. 5

Error in the wind measurement that is due to a 5 K error in the atmospheric temperature profile is given as a function of the Doppler shift in units of etalon HWHM. Results are given for an atmospheric temperature of 250 K for ratios of the Rayleigh-to-aerosol scattering N of 1, 2, 5, and 10.

Fig. 6
Fig. 6

Standard deviation of the Rayleigh-corrected signals σ I 1c (dotted curves), compared with the standard deviation of the uncorrected signals (solid curves), for ratios of Rayleigh-to-aerosol scattering N of 1, 2, 5, and 10. Results are shown as a function of the Doppler shift in units of etalon HWHM for 50 detected aerosol photons in the edge channel at the zero Doppler-shift location.

Fig. 7
Fig. 7

Signal-to-noise ratio for 500 detected aerosol photons in each edge channel at the zero Doppler-shift location. Results are shown for ratios of the Rayleigh-to-aerosol scattering N of 0, 1, 2, 5, and 10 and as a function of the Doppler shift in units of etalon HWHM.

Fig. 8
Fig. 8

Wind error for 500 detected aerosol photons in each edge channel at the zero Doppler-shift location. Results are shown for ratios of the Rayleigh-to-aerosol scattering N of 0, 1, 2, 5, and 10 and as a function of the Doppler shift in units of etalon HWHM.

Fig. 9
Fig. 9

Signal-to-noise ratio for 50, 500, and 5000 detected aerosol photons in each edge channel at the zero Doppler-shift location for a ratio of the Rayleigh-to-aerosol scattering N of 2. Results are shown as a function of the Doppler shift in units of etalon HWHM.

Fig. 10
Fig. 10

Wind error for 50, 500, and 5000 detected aerosol photons in each edge channel at the zero Doppler-shift location for a ratio of the Rayleigh-to-aerosol scattering N of 2. Results are shown as a function of the Doppler shift in units of etalon HWHM.

Fig. 11
Fig. 11

Signal-to-noise ratio for 50, 500, and 5000 detected aerosol photons in each edge channel at the zero Doppler-shift location for a ratio of the Rayleigh-to-aerosol scattering N of 5. Results are shown as a function of the Doppler shift in units of etalon HWHM.

Fig. 12
Fig. 12

Wind error for 50, 500, and 5000 detected aerosol photons in each edge channel at the zero Doppler-shift location for a ratio of the Rayleigh-to-aerosol scattering N of 5. Results are shown as a function of the Doppler shift in units of etalon HWHM.

Equations (29)

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I 1 = c 1 I A τ 1 ν 1 + Δ ν + R 1 ν 1 + Δ ν ,
I 1 = c 1 I A τ 1 ν 1 + Δ ν + I R ν 1 + Δ ν f 1 R T ,
I 2 = c 2 I A τ 2 - ν 2 + Δ ν + I R ν 2 - Δ ν f 2 R T ,
Δ I 1 = I 1 c 1 I A - τ 1 ν 1 = τ 1 ν 1 + Δ ν - τ 1 ν 1 + f 1 R T I A   I R ν 1 + Δ ν ,
Δ I 2 = I 2 c 2 I A - τ 2 - ν 2 = τ 2 - ν 2 + Δ ν - τ 2 - ν 2 + f 2 R T I A   I R ν 2 - Δ ν .
Δ I T = Δ I 1 + Δ I 2 = τ 1 ν 1 + Δ ν - τ 1 ν 1 + τ 2 - ν 2 + Δ ν - τ 2 - ν 2 + R T I A f 1 I R ν 1 + Δ ν + f 2 I R ν 2 - Δ ν = Δ τ 1 + Δ τ 2 + c *   R T I A ,
Δ τ 1 = τ 1 ν 1 + Δ ν - τ 1 ν 1 , Δ τ 2 = τ 2 - ν 2 + Δ ν - τ 2 - ν 2 , c * = f 1 I R ν 1 + Δ ν + f 2 I R ν 2 - Δ ν .
I EM = c 3 I A + R T ,
R T = I EM c 3 - I A ,
Δ I T = I 1 c 1 - τ 1 ν 1 I A I A + I 2 c 2 - τ 2 - ν 2 I A I A ,
Δ I T = Δ τ 1 + Δ τ 2 + c * I EM c 3 - I A I A .
I 1 c 1 - τ 1 ν 1 I A + I 2 c 2 - τ 2 - ν 2 I A = Δ τ 1 + Δ τ 2 I A + c * I EM c 3 - I A .
I A = I 1 c 1 + I 2 c 2 - c *   I EM c 3 τ 1 ν 1 + τ 2 - ν 2 - c * + Δ τ 1 + Δ τ 2 ,
R T = I EM c 3 - I A ,
Δ τ 1 = - Δ τ 2 ,
I 1 c = I 1 c 1 - R T f 1 I R ν 1 + Δ ν = I A τ 1 ν 1 + Δ ν ,
I 2 c = I 2 c 2 - R T f 2 I R ν 2 - Δ ν = I A τ 2 - ν 2 + Δ ν .
I 1 c I 2 c = τ 1 ν 1 + Δ ν τ 2 - ν 2 + Δ ν .
ε = 1 S / N Θ ,
1 F d F d υ = 1 τ 1 d τ 1 d υ - 1 τ 2 d τ 2 d υ ,
Θ = Θ 1 - Θ 2 ,
Θ i = 1 τ i d τ i d υ ,     Θ = 1 F d F d υ .
I ν i = c 1 I 0 1 + ν i - ν 0 Δ ν et 2 2 ,
I EM = c 2 I 0 ,
ν i - ν 0 = ± c 1 I EM c 2 - I ν i I ν i 1 / 2 Δ ν et 2 .
α = 1 + 1 N .
I 1 c = a 1 I 1 + a 2 I 2 + a 3 I EM ,
σ I 1 c 2 = a 1 2 I 1 + a 2 2 I 2 + a 3 2 I EM .
a 1 = 1 + f 1 ζ ,     a 2 = c 1 c 2 f 1 ζ ,     a 3 = c 1 c 3   f 1 1 + c * ζ ,     ζ = τ ν 1 + τ ν 2 - c * + Δ τ 1 + Δ τ 2 .

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