Abstract

A method for the investigation of the spatiotemporal behavior of wave fronts is described. Two synchronized CCD cameras are used. Temporal resolution of ∼0.5 ms is realized without any loss of spatial resolution. This method was used to investigate the spatiotemporal behavior of an atmospheric-turbulence-disturbed wave front with a time separation of 1 ms. Using the Zernike expansion, we checked the validity of the Taylor hypothesis of “frozen turbulence” along a horizontal path. Our preliminary results show that there may be a lack of compatibility between the theory and the experiment. There are indications that higher-order Zernike terms result in higher wind speeds; further experiments to establish our findings therefore are in progress.

© 1994 Optical Society of America

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References

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  1. G. K. Born, R. Bogenberger, K. D. Erben, F. Frank, F. Mohr, G. Sepp, “Phase-front distortion measurement of laser radiation in a turbulent atmosphere,” Appl. Opt. 14, 2857–2863 (1975).
    [CrossRef] [PubMed]
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  3. M. Abitbol, N. Subovitch, N. Ben-Yossef, “A method for investigation of the spatio-temporal atmospherically perturbed, wavefronts at high temporal frequency,” in Proceedings of the International Commission for Optics Topical Meeting on Atmospheric, Volume, and Surface Scattering and Propagation (International Commission for Optics Secretariat, Florence, Italy, 1991), p. 53.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, Part 2.
  9. D. M. Winker, “Effect of finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A 8, 1568–1573 (1991).
    [CrossRef]

1992 (1)

1991 (2)

N. S. Nightingale, D. F. Busher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

D. M. Winker, “Effect of finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A 8, 1568–1573 (1991).
[CrossRef]

1987 (1)

1976 (1)

1975 (1)

Abitbol, M.

M. Abitbol, N. Subovitch, N. Ben-Yossef, “A method for investigation of the spatio-temporal atmospherically perturbed, wavefronts at high temporal frequency,” in Proceedings of the International Commission for Optics Topical Meeting on Atmospheric, Volume, and Surface Scattering and Propagation (International Commission for Optics Secretariat, Florence, Italy, 1991), p. 53.

Azouit, M.

Ben-Yossef, N.

M. Abitbol, N. Subovitch, N. Ben-Yossef, “A method for investigation of the spatio-temporal atmospherically perturbed, wavefronts at high temporal frequency,” in Proceedings of the International Commission for Optics Topical Meeting on Atmospheric, Volume, and Surface Scattering and Propagation (International Commission for Optics Secretariat, Florence, Italy, 1991), p. 53.

Bogenberger, R.

Born, G. K.

Busher, D. F.

N. S. Nightingale, D. F. Busher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

Caccia, J. L.

Colucci, D.

Erben, K. D.

Frank, F.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, Part 2.

Mohr, F.

Nightingale, N. S.

N. S. Nightingale, D. F. Busher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

Noll, R. J.

Sepp, G.

Subovitch, N.

M. Abitbol, N. Subovitch, N. Ben-Yossef, “A method for investigation of the spatio-temporal atmospherically perturbed, wavefronts at high temporal frequency,” in Proceedings of the International Commission for Optics Topical Meeting on Atmospheric, Volume, and Surface Scattering and Propagation (International Commission for Optics Secretariat, Florence, Italy, 1991), p. 53.

Vernin, J.

Winker, D. M.

Wizinowich, P.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

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

Mon. Not. R. Astron. Soc. (1)

N. S. Nightingale, D. F. Busher, “Interferometric seeing measurements at the La Palma Observatory,” Mon. Not. R. Astron. Soc. 251, 155–166 (1991).

Other (3)

M. Abitbol, N. Subovitch, N. Ben-Yossef, “A method for investigation of the spatio-temporal atmospherically perturbed, wavefronts at high temporal frequency,” in Proceedings of the International Commission for Optics Topical Meeting on Atmospheric, Volume, and Surface Scattering and Propagation (International Commission for Optics Secretariat, Florence, Italy, 1991), p. 53.

CCD Data Book (Thomson-CSF Division Silicum, Boulogne-Billancourt, France, 1988).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, Part 2.

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Figures (13)

Fig. 1
Fig. 1

Time diagram of two synchronized cameras with a given delay.

Fig. 2
Fig. 2

Diagram of the experimental method.

Fig. 3
Fig. 3

Typical fringe pattern of a turbulence-disturbed wave front (the white spots represent the extracted extremes of the interferogram).

Fig. 4
Fig. 4

Phase maps of two reconstructed turbulence-disturbed wave fronts with a time separation of 6 ms.

Fig. 5
Fig. 5

Geometrical representation of Δρ.

Fig. 6
Fig. 6

Theoretical temporal correlation of Zernike coefficient a2 (horizontal tilt) versus time separation, for different wind speeds and Lmax of 80 cm.

Fig. 7
Fig. 7

Theoretical temporal correlation of Zernike coefficients a2, a3, a4, a5, and a6 versus time separation for a wind speed of 2.5 m/s. We can see that the higher coefficients have a higher decrease rate.

Fig. 8
Fig. 8

Structure function of the tilt versus different delays at which saturation occurs at ∼5 ms.

Fig. 9
Fig. 9

Experimental temporal correlation of a2, a4, and a5 Zernike coefficients shows that the higher the coefficient, the faster the decrease (error bars are shown in Figs. 1113).

Fig. 10
Fig. 10

Temporal correlation of the tilt (horizontal and vertical), where the horizontal tilt has a higher rate of decrease than the vertical tilt.

Fig. 11
Fig. 11

Theoretical and experimental temporal correlation of the astigmatism Zernike coefficient; a better fit is obtained with a wind speed of 7.5 m/s.

Fig. 12
Fig. 12

Theoretical and experimental temporal correlation of the defocused Zernike coefficient; a better fit is obtain with a wind speed of 7.5 m/s.

Fig. 13
Fig. 13

Experimental and theoretical results of the horizontal-tilt Zernike coefficient temporal correlation; better compatibility is obtained with a wind speed of 2.5 m/s.

Equations (11)

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I ( x , y ) = I p + I r + 2 I p I r × cos { 2 π λ [ x sin ( θ x ) + y sin ( θ y ) ] + ϕ ( x , y , t ) } ,
I ( x , y ) = I p + I r + 2 I p I r cos ( 2 π λ { x sin [ θ x + Δ θ x ( x , t ) ] + y sin [ θ y + Δ θ y ( y , t ) ] } ) .
n λ = d sin θ n = 0 ± 1 ± 2 ± 3 ,
d n d ϕ 1 θ 2 ,
C n 2 = σ tilt 2 L D 1 / 3 ,
Φ ( R r , θ ) = j = 0 a j Z j ( ρ , θ ) ρ = r / R ,
a j = d 2 ρ w ( ρ ) Φ ( ρ R , θ ) Z j ( ρ , θ ) W ( ρ ) = 1 , ρ 1 ; W ( ρ ) = 0 , ρ > 0 .
a i ( t ) a i ( t + τ ) = d ρ d ρ d θ d θ W ( ρ ) Z ( ρ , θ ) W ( ρ ) × Z ( ρ , θ ) Φ ( R ρ , θ , t ) Φ ( R ρ , θ , t + τ ) W ( ρ ) = 1 , ρ 1 ; W ( ρ ) = 0 , ρ > 0 .
Φ ( R ρ , θ , t ) Φ ( R ρ , θ , t + τ ) = B ( L , Δ ρ ) = ( 2 π ) 2 0 L d x 0 d κ κ J ( κ Δ ρ ) k cos ( L x 2 k κ 2 ) Φ ( κ ) Δ ρ = | ρ ( ρ + V s i n ( θ ) τ ) | ,
Δ ρ ( ρ , θ , ρ , θ ) = ( V τ 2 + ρ 2 + 2 V τ ρ cos θ + ρ 2 2 ρ Q × cos { θ θ + arcsin [ V τ sin ( θ ) Q ] } ) 1 / 2 , Q = [ ( V τ ) 2 + ρ 2 + 2 V τ ρ cos θ ] 1 / 2 .
D s ( τ ) = 1 / N j = 1 N [ tilt ( t = 0 ) tilt ( t = τ ) ] 2 ,

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