Abstract

When light radiating from a distant object passes through extended turbulence, the light is scintillated. Such scintillated light may be received by an optical system and passed to a camera in the focal plane, and used to track an object. Such trackers often use centroid trackers. Then a laser or other light may be projected back toward the object, steered by the centroid measured on the tracker. The presence of scintillation on the tracker return will cause a jitter error in the pointing of projected light, if the projected light’s intensity differs from that of the incoming scintillation pattern. This error is caused by a lack of full-field conjugation of the tilt component of the received return. This error is considered, for horizontal path conditions, as a difference between centroid tilt and gradient tilt. The estimated error is typically not large, and is estimated by both simulation and analytic means, and these are found to agree for conditions of interest. The possibility of means for correction of this error is discussed briefly.

© 2009 Optical Society of America

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References

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  1. G. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A 11, 358-367 (1994).
    [CrossRef]
  2. S. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer-Verlag, 1978), Eqs. 2.70-2.83, for example.
  3. B. Ya. Zel'dovich, in Principles of Phase Conjugation, B.Ya.Zel'dovich, N.F.Pilipetsky, and V.V.Shkunov, eds., (Springer-Verlag, 1985) Chap. 1 and 2.
  4. M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
    [CrossRef]
  5. V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation,” National Science Foundation Technical Report TT-68-50464 (National Technical Information Service, 1968).
  6. H. T. Yura and M. T. Tavis, “Centroid anisoplanatism,” J. Opt. Soc. Am. A 2, 765-773 (1985).
    [CrossRef]
  7. J. H. Churnside, M. T. Tavis, H. T. Yura, and G. T. Tyler, “Zernike-polynomial expansion of turbulence-induced centroid anisoplanatism,” Opt. Lett. 10, 258-260 (1985).
    [CrossRef] [PubMed]
  8. M. T. Tavis and H. T. Yura, “Scintillation effects on centroid anisoplanatism,” J. Opt. Soc. Am. A 4, 57-59 (1987).
    [CrossRef]
  9. Jeffrey D. Barchers, David L. Fried, and Donald J. Link, “Evaluation of the performance of Hartmann sensors in strong scintillation,” Appl. Opt. 41, 1012-1021 (2002).
    [CrossRef] [PubMed]
  10. R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics (SPIE, 2004), p. 19.
    [CrossRef]

2002 (1)

1994 (1)

1987 (1)

1985 (2)

1984 (1)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Barchers, Jeffrey D.

Churnside, J. H.

Clifford, S.

S. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer-Verlag, 1978), Eqs. 2.70-2.83, for example.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Frazier, B. W.

R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics (SPIE, 2004), p. 19.
[CrossRef]

Fried, David L.

Link, Donald J.

Tatarskii, V. I.

V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation,” National Science Foundation Technical Report TT-68-50464 (National Technical Information Service, 1968).

Tavis, M. T.

Tyler, G.

Tyler, G. T.

Tyson, R. K.

R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics (SPIE, 2004), p. 19.
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Ya. Zel'dovich, B.

B. Ya. Zel'dovich, in Principles of Phase Conjugation, B.Ya.Zel'dovich, N.F.Pilipetsky, and V.V.Shkunov, eds., (Springer-Verlag, 1985) Chap. 1 and 2.

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

Yura, H. T.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12-30 (1984).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Lett. (1)

Other (4)

R. K. Tyson and B. W. Frazier, Field Guide to Adaptive Optics (SPIE, 2004), p. 19.
[CrossRef]

S. Clifford, “The classical theory of wave propagation in a turbulent medium,” in Laser Propagation in the Atmosphere, J.W.Strohbehn, ed. (Springer-Verlag, 1978), Eqs. 2.70-2.83, for example.

B. Ya. Zel'dovich, in Principles of Phase Conjugation, B.Ya.Zel'dovich, N.F.Pilipetsky, and V.V.Shkunov, eds., (Springer-Verlag, 1985) Chap. 1 and 2.

V. I. Tatarskii, “The effects of the turbulent atmosphere on wave propagation,” National Science Foundation Technical Report TT-68-50464 (National Technical Information Service, 1968).

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Figures (2)

Fig. 1
Fig. 1

Exemplary sensing and correction of jitter for projection of light to a distant object. (a) Distant object, (b) turbulence, (c) resulting scintillation of incoming light, (d) primary aperture, (e) steering mirror, (f) beamsplitter for projected and incoming light, (g) focusing lens, (h) focal-plane camera, (i) projected laser beam, and (j) intensity profile of projected beam.

Fig. 2
Fig. 2

Scintillation-induced jitter error (1-sigma, 2-axis, normalized by λ D ) versus spherical-wave log-amplitude variance for 50 km path with uniform turbulence strength. Specific results include 1.06 μ m wavelength, 2 m diameter aperture (solid curve with squares); 1.06 μ m , 1 m (solid red curve, no symbol); 1.06 μ m , 0.5 m (solid curve, crosses); 1.06 μ m , 0.25 m (dotted curve, no symbol); 0.532 μ m , 0.5 m (solid curve, circles); 2.12 μ m , 0.5 m (solid curve, plusses); wave-optics simulation with 1.06 μ m and 1 m , seed 1 (up-pointing triangles); wave-optics simulation with 1.06 μ m and 1 m , seed 2 (down-pointing triangles).

Equations (6)

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T in = d θ 2 θ d x 2 exp [ i ϕ ( x ) + χ ( x ) ] exp ( i k o θ x ) 2 S = ( 1 k o ) d x 2 ϕ ( x ) exp [ 2 χ ( x ) ] I in S ,
T out = ( 1 k o ) d x 2 ϕ ( x ) exp [ 2 χ o ( x ) ] A .
σ T 2 = T in T out 2 ,
σ T 2 = ( 1 A k o ) 2 d x 2 ϕ ( x ) { exp [ 2 χ ( x ) ] exp [ 2 χ o ( x ) ] } 2 .
σ T 2 = ( 1 A k o ) 2 d x 1 2 d x 2 2 ϕ ( x 1 ) ϕ ( x 2 ) × { exp [ 2 χ ( x 1 ) ] exp [ 2 χ o ( x 1 ) ] } { exp [ 2 χ ( x 2 ) ] exp [ 2 χ o ( x 2 ) ] } .
{ exp [ 2 χ ( x 1 ) ] exp [ 2 χ o ( x 1 ) ] } { exp [ 2 χ ( x 2 ) ] exp [ 2 χ o ( x 2 ) ] } = exp [ 4 C χ ( x 1 x 2 ) ] exp [ 2 χ o ( x 1 ) ] exp [ 2 χ o ( x 2 ) ] + exp [ 2 χ o ( x 1 ) + 2 χ o ( x 2 ) ] .

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