Abstract

A theoretical model for the edge image waviness effect is developed for the ground-to-ground imaging scheme and validated by use of IR imagery data collected at the White Sands Missile Range. It is shown that angle-of-arrival (AA) angular anisoplanatism causes the phenomenon of edge image waviness and that the AA correlation scale, not the isoplanatic angle, characterizes the edge image waviness scale. The latter scale is determined by the angular size of the imager and a normalized atmospheric outer scale, and it does not depend on the strength of turbulence along the path. Spherical divergence of the light waves increases the edge waviness scale. A procedure for estimating the atmospheric and camera-noise components of the edge image motion is developed and implemented. A technique for mitigation of the edge image waviness that relies on averaging the effects of AA anisoplanatism on the image is presented and validated. The edge waviness variance is reduced by a factor of 2–3. The time history and temporal power spectrum of the edge image motion are obtained. These data confirm that the observed edge image motion is caused by turbulence.

© 2001 Optical Society of America

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References

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1999 (2)

1998 (1)

1997 (2)

1995 (2)

1994 (1)

1993 (1)

1991 (1)

1982 (1)

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 63, 207–211 (1976).
[CrossRef]

Agabi, A.

Avila, R.

Barducci, A.

A. Barducci, I. Pippi, “Object recognition by edge analysis: a case study,” Opt. Eng. 38, 284–294 (1999).
[CrossRef]

Belen’kii, M. S.

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental validation of a technique to measure tilt from a laser guide star,” Opt. Lett. 24, 637–639 (1999).
[CrossRef]

M. S. Belen’kii, “Principle of equivalency of the phase difference and off-axis tilt sensing technique with a laser guide star,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 280–292 (1996).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Measurements of tilt angular anisoplanatism,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 481–487 (1997).
[CrossRef]

M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 206–217 (1996).
[CrossRef]

M. S. Belen’kii, “Full-aperture tilt measurement technique with a laser guide star,” in Atmospheric Propagation and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE2471, 289–300 (1995).
[CrossRef]

Borgnino, J.

Brown, J. M.

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental validation of a technique to measure tilt from a laser guide star,” Opt. Lett. 24, 637–639 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Measurements of tilt angular anisoplanatism,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 481–487 (1997).
[CrossRef]

Clifford, S. F.

S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 2.
[CrossRef]

Dror, I.

Ellerbroek, B. L.

Fried, D. L.

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
[CrossRef]

D. L. Fried, “Varieties of anisoplanatism,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. SPIE75, 20–29 (1976).
[CrossRef]

Fugate, R. Q.

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental validation of a technique to measure tilt from a laser guide star,” Opt. Lett. 24, 637–639 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Measurements of tilt angular anisoplanatism,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 481–487 (1997).
[CrossRef]

He, L.

L. He, J. Wu, “Application of the staring-edge tracking in laser radar,” in Free-Space Laser Communication Technologies IX, G. S. Mecherle, ed., Proc. SPIE2990, 190–197 (1997).
[CrossRef]

Hu, P. H.

Karis, S. J.

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental validation of a technique to measure tilt from a laser guide star,” Opt. Lett. 24, 637–639 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Measurements of tilt angular anisoplanatism,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 481–487 (1997).
[CrossRef]

Kopeika, N. S.

Ma, S.

Martin, F.

Mills, S. P.

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 63, 207–211 (1976).
[CrossRef]

Pippi, I.

A. Barducci, I. Pippi, “Object recognition by edge analysis: a case study,” Opt. Eng. 38, 284–294 (1999).
[CrossRef]

Roggemann, M. C.

Sasiela, R. J.

Shelton, J. D.

Stone, J.

Takato, N.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (McGraw-Hill, New York, 1961).

Welsh, B. M.

Whiteley, M. R.

Winker, D. M.

Wu, J.

L. He, J. Wu, “Application of the staring-edge tracking in laser radar,” in Free-Space Laser Communication Technologies IX, G. S. Mecherle, ed., Proc. SPIE2990, 190–197 (1997).
[CrossRef]

Yamaguchi, I.

Ziad, A.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
[CrossRef]

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 63, 207–211 (1976).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Eng. (1)

A. Barducci, I. Pippi, “Object recognition by edge analysis: a case study,” Opt. Eng. 38, 284–294 (1999).
[CrossRef]

Opt. Lett. (1)

Other (8)

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Measurements of tilt angular anisoplanatism,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 481–487 (1997).
[CrossRef]

L. He, J. Wu, “Application of the staring-edge tracking in laser radar,” in Free-Space Laser Communication Technologies IX, G. S. Mecherle, ed., Proc. SPIE2990, 190–197 (1997).
[CrossRef]

D. L. Fried, “Varieties of anisoplanatism,” in Imaging through the Atmosphere, J. C. Wyant, ed., Proc. SPIE75, 20–29 (1976).
[CrossRef]

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (McGraw-Hill, New York, 1961).

M. S. Belen’kii, “Principle of equivalency of the phase difference and off-axis tilt sensing technique with a laser guide star,” in Image Propagation through the Atmosphere, J. C. Dainty, L. R. Bissonnette, eds., Proc. SPIE2828, 280–292 (1996).
[CrossRef]

M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 206–217 (1996).
[CrossRef]

M. S. Belen’kii, “Full-aperture tilt measurement technique with a laser guide star,” in Atmospheric Propagation and Remote Sensing IV, J. C. Dainty, ed., Proc. SPIE2471, 289–300 (1995).
[CrossRef]

S. F. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer, New York, 1978), Chap. 2.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Angular correlation coefficient for the lateral AA for the ground-to-ground imaging scheme.

Fig. 2
Fig. 2

Sample scene obtained with the I-525 imager.

Fig. 3
Fig. 3

Three consecutive frames of the target board edge image recorded at 14:30.

Fig. 4
Fig. 4

Mean edge position and edge standard deviation for the data set recorded at 12:45.

Fig. 5
Fig. 5

Edge structure functions recorded at various times of day.

Fig. 6
Fig. 6

Comparison of the measured and predicted edge structure functions.

Fig. 7
Fig. 7

Edge averaging functions corrected for camera noise for four sets of measured data and the predicted averaging function.

Fig. 8
Fig. 8

Time history of the integrated edge position for low and high turbulence.

Fig. 9
Fig. 9

Temporal power spectrum of the integrated edge motion and the theoretical prediction described by -2/3 power law. PSD, power spectral density.

Tables (2)

Tables Icon

Table 1 Estimates of the Atmospheric and Camera Noise Components of Edge Motion

Tables Icon

Table 2 Comparison of Measured Standard Deviation of Integrated Edge σθ R and Prediction σθ R C

Equations (20)

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

θi=2.91k20L Cn2zz5/3dz-3/5,
θi=3/82.91k2Cn2L8/3-3/5.
ϕnκ=0.00969Cn2κ2+1/L02-11/6,
bx,yθ=0LdξCn2ξQξ/L0dκ2γκ2+1-11/6J22κ/κJ0AκJ2Aκ0LdξCn2ξQξ/L0dκ2γκ2+1-11/6J22κ/κ,
σA2=3.04D-1/3fγ0L Cn2x1-x/L5/3dx.
σA2=1.14Cn2LD-1/3fL0/D=0.18λ2r0-5/3D-1/3fL0/L,
θc=αL0/DθD,
σθR2=σA2θR20θRdθ10θRdθ2byθ1-θ2.
G=σθR2σA2=1θR0θR byθ/θc1-θ/θRdθ,
IFOV=2 arctanω/2L=12.7 μrad,
ui=ēi=1Nj=1N ei, j,
σi=1N-1j=1Nei, j-ui21/2.
Dθ=Eθ0-Eθ0+θ2¯,
Dθ=i=1M-kEi-Ei+k2/M-k¯,
DNθ=Dθ/2σA2=1-byθ.
σA=DN2451 μrad1/20.932,
σN=σ2-σA2.
eθR=1θR0θR eθdθ=1ni=1n ei,
σθRC2=σA2GθR+σN2,
G*θR=GθR-σN2σA21-σN2σA2-1.

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