Abstract

The birefringence of the atmosphere under the onset of a wind speed gradient has been studied near flat ground. Some characteristics and performances of the ellipsometer are given. The setup of the experiment is described; the results show that a birefringent effect is measurable. The numerical value of β = Δn/G is in good agreement with a previous experiment, but to an improved accuracy.

© 1978 Optical Society of America

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References

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  1. F. Bass, Phys. Lett. A 36, 107(1971).
    [Crossref]
  2. S. Hess, Phys. Lett. A 30, 239(1969).
    [Crossref]
  3. G. Boyer and B. Prade, Surf. Sci. 56, 449(1976).
    [Crossref]
  4. G. Boyer, B. Lamouroux, and B. Prade, J. Opt. Soc. Am. 65, 1319 (1975).
    [Crossref]
  5. X. Shurcliff, Polarized Light (Oxford U. P., London, 1964).
  6. X. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” Israel, Program of Scientific Translations, Jerusalem (1971).
  7. F. Wilcoxon, Biométrie 1, 80 (1945)
  8. L. Lebart and J. P. Fenelon, Statistique et Informatique Appliquée, (Dunod, Paris, 1971).

1976 (1)

G. Boyer and B. Prade, Surf. Sci. 56, 449(1976).
[Crossref]

1975 (1)

1971 (1)

F. Bass, Phys. Lett. A 36, 107(1971).
[Crossref]

1969 (1)

S. Hess, Phys. Lett. A 30, 239(1969).
[Crossref]

1945 (1)

F. Wilcoxon, Biométrie 1, 80 (1945)

Bass, F.

F. Bass, Phys. Lett. A 36, 107(1971).
[Crossref]

Boyer, G.

Fenelon, J. P.

L. Lebart and J. P. Fenelon, Statistique et Informatique Appliquée, (Dunod, Paris, 1971).

Hess, S.

S. Hess, Phys. Lett. A 30, 239(1969).
[Crossref]

Lamouroux, B.

Lebart, L.

L. Lebart and J. P. Fenelon, Statistique et Informatique Appliquée, (Dunod, Paris, 1971).

Prade, B.

Shurcliff, X.

X. Shurcliff, Polarized Light (Oxford U. P., London, 1964).

Tatarskii, X.

X. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” Israel, Program of Scientific Translations, Jerusalem (1971).

Wilcoxon, F.

F. Wilcoxon, Biométrie 1, 80 (1945)

Biométrie (1)

F. Wilcoxon, Biométrie 1, 80 (1945)

J. Opt. Soc. Am. (1)

Phys. Lett. A (2)

F. Bass, Phys. Lett. A 36, 107(1971).
[Crossref]

S. Hess, Phys. Lett. A 30, 239(1969).
[Crossref]

Surf. Sci. (1)

G. Boyer and B. Prade, Surf. Sci. 56, 449(1976).
[Crossref]

Other (3)

X. Shurcliff, Polarized Light (Oxford U. P., London, 1964).

X. Tatarskii, “The Effects of the Turbulent Atmosphere on Wave Propagation,” Israel, Program of Scientific Translations, Jerusalem (1971).

L. Lebart and J. P. Fenelon, Statistique et Informatique Appliquée, (Dunod, Paris, 1971).

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Figures (6)

FIG. 1
FIG. 1

Sketch of the experiment. G is the vertical velocity gradient, k the wave vector, v the velocity of wind, and A1, A2 the anemometers.

FIG. 2
FIG. 2

Cross correlation coefficient ig.

FIG. 3
FIG. 3

λ′ − g′ cross-correlation product for file 1.

FIG. 4
FIG. 4

λ′ − g′ cross-correlation product for file 3.

FIG. 5
FIG. 5

λ′ − g′ cross-correlation product for file 5.

FIG. 6
FIG. 6

λ′ − g′ cross-correlation product file 6.

Tables (1)

Tables Icon

TABLE I Test of stationarity of Wilcoxon Z ¯ and σZ are theoretically computed after the number of samples N; the experimental value of Z is then compared to Z ¯ ± 2σZ and provides an estimate of the stationarity. L is the optical path length; T the time constant of the lock-in amplifiers; Δt the time duration of the experiment.

Equations (17)

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E = ( ½ ) [ I + M sin ( ψ 0 cos Ω t ) - C cos ( ψ 0 cos Ω t ) ] ,
E = ( I 0 / 2 ) [ 1 - 2 J 0 ( ψ 0 ) cos 2 λ sin 2 θ - 2 J 2 ( ψ 0 ) cos 2 λ sin 2 θ cos Ω t + 2 J 1 ( ψ 0 ) cos 2 λ cos 2 θ cos 2 Ω t ] ,
σ ln I = ln 1 + σ I 2 / I 2 ,
σ ln I 2 = 1.23 C n 2 k 7 / 6 L 11 / 6 ,
l = v ¯ Δ t
Z = i , j I i j .
ρ ( τ ) = lim T 1 T 1 σ g σ λ 0 T λ ( t ) g ( t + λ ) d t .
σ f = k σ g
σ λ 2 = σ f 2 + σ n 2 ,
λ ( t ) = f ( t ) + n ( t ) .
ρ ( τ ) = lim T 1 σ g ( σ f 2 + σ n 2 ) 1 / 2 × 0 T f ( t ) g ( t + τ ) d t ,
lim T 1 T 0 T n ( t ) g ( t + τ ) d t = 0
lim T 1 T 1 σ g σ f 0 T f ( t ) g ( t + τ ) d t = 1
ρ ( τ 0 ) = ( 1 + α 2 ) - 1 / 2
k = ( σ λ / σ g ) ρ ( τ 0 ) .
f ( t ) = k g ( t ) = ( 2 π / λ 0 ) ( n e - n 0 ) L
β = σ λ λ 0 ρ ( τ 0 ) / σ g 2 π L .