Abstract

A pupil plane imaging system, consisting of a camera and optics that image the entrance pupil of a telescope, measures scintillation induced by atmospheric turbulence. Algorithms are developed to estimate the distribution of turbulence from scintillation assuming the well known relationship between scintillation scale size and the range of turbulence layer. The algorithms were exercised using a 75  cm pupil within a 1 meter telescope located at North Oscura Peak in New Mexico, based on light from a source 52 .6   km away. Estimates of the Cn2 profile over the path are derived using coarse range bins. From the Cn2 profile, an estimate of Fried's transverse coherence length was computed and compared with that from other sensors. The algorithm is tested in several ways. Error sources are discussed, including the intrinsic insensitivity of the technique to turbulence near the pupil.

© 2007 Optical Society of America

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References

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  1. W. M. Protheroe, "The motion and structure of stellar shadow-band patterns," Q. J. R. Meteorol. Soc. 90, 27-30 (1964).
    [CrossRef]
  2. A. Peskoff, "Theory of remote sensing of clear-air turbulence profiles," J. Opt. Soc. Am. 58, 1032-1040 (1968).
    [CrossRef]
  3. D. L. Fried, "Remote probing of the optical strength of atmospheric turbulence and of wind velocity," Proc. IEEE 57, 415-420 (1969).
    [CrossRef]
  4. J. W. Strohbehn, "Remote sensing of clear air turbulence," J. Opt. Soc. Am. 60, 948-950 (1970).
    [CrossRef]
  5. A. Rocca, F. Roddier, and J. Vernin, "Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillation," J. Opt. Soc. Am. 64, 1000-1004 (1974).
    [CrossRef]
  6. S. F. Clifford, G. R. Ochs, and T. Wang, "Optical wind sensing by observing the scintillations of a random scene," Appl. Opt. 14, 2844-2850 (1975).
    [PubMed]
  7. G. R. Ochs, Ting-i Wang, R. S. Lawrence, and S. F. Clifford, "Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations," Appl. Opt. 15, 2504-2510 (1976).
    [CrossRef] [PubMed]
  8. J. L. Caccia, M. Azouit, and J. Vernin, "Wind and Cn2 profiling by single star scintillation analysis," Appl. Opt. 26, 1288-1294 (1987).
    [CrossRef] [PubMed]
  9. S. F. Clifford and J. H. Churnside, "Refractive turbulence profiling using synthetic aperture spatial filtering of scintillation," Appl. Opt. 26, 1295-1303 (1987).
    [CrossRef] [PubMed]
  10. J. H. Churnside and S. F. Clifford, "Refractive turbulence profiling using stellar scintillation and radar wind profiles," Appl. Opt. 27, 4884-4890 (1988).
    [CrossRef] [PubMed]
  11. J. H. Churnside, R. J. Lataitis, and R. S. Lawrence, "Measurements of refractive turbulence using spatial filtering of scintillation," Appl. Opt. 27, 2199-2209 (1988).
    [CrossRef] [PubMed]
  12. R. Holmes, "Passive optical wind profilometer," U.S. patent 5,469,250 (filed 17 May 1993, granted 21 November 1995).
  13. S. G. Hanson, J. H. Churnside, and J. J. Wilson, "Remote sensing of wind velocity and strength of refractive turbulence using a two-spatial-filter receiver," Appl. Opt. 33, 5859-5868 (1994).
    [CrossRef] [PubMed]
  14. S. F. Clifford, "The classical theory of wave propagation in a turbulent medium," in Laser Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, 1978), Fig. 2.5.
  15. W. M. Hughes and R. B. Holmes, 3357 Chasen Drive, Cameron Park, CA 95682, submitted a manuscript to Applied Optics called "Pupil-plane imager for scintillometry over long horizontal paths."
  16. F. Eaton and R. Butts, Air Force Research Laboratories, AFRL/DEBA, Bldg. 401, 3550 Aberdeen Ave. SE, Kirtland AFB, NM 87117 (personal communication, 1999).
  17. S. F. Clifford and H. T. Yura, "Equivalence of two theories of strong optical scintillation," J. Opt. Soc. Am. 64, 1641-1644 (1974).
    [CrossRef]
  18. J. H. Churnside, R. J. Hill, G. Conforti, and A. Consortini, "Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere," Appl. Opt. 28, 4126-4132 (1989).
    [CrossRef] [PubMed]
  19. T. Wang, G. R. Ochs, and S. F. Clifford, "A saturation-resistant optical scintillometer to measure Cn 2," J. Opt. Soc. Am. 68, 334-338 (1978).
    [CrossRef]
  20. G. R. Ochs, S. F. Clifford, and Ting-i Wang, "Laser wind sensing: the effects of saturation of scintillation," Appl. Opt. 15, 403-408 (1976).
    [CrossRef] [PubMed]
  21. R. J. Hill and R. G. Frehlich, "Probability distribution of irradiance for the onset of strong scintillation," J. Opt. Soc. Am. 14, 1530-1540 (1997).
    [CrossRef]

1997 (1)

R. J. Hill and R. G. Frehlich, "Probability distribution of irradiance for the onset of strong scintillation," J. Opt. Soc. Am. 14, 1530-1540 (1997).
[CrossRef]

1994 (1)

1989 (1)

1988 (2)

1987 (2)

1978 (1)

1976 (2)

1975 (1)

1974 (2)

1970 (1)

1969 (1)

D. L. Fried, "Remote probing of the optical strength of atmospheric turbulence and of wind velocity," Proc. IEEE 57, 415-420 (1969).
[CrossRef]

1968 (1)

1964 (1)

W. M. Protheroe, "The motion and structure of stellar shadow-band patterns," Q. J. R. Meteorol. Soc. 90, 27-30 (1964).
[CrossRef]

Appl. Opt. (9)

S. F. Clifford, G. R. Ochs, and T. Wang, "Optical wind sensing by observing the scintillations of a random scene," Appl. Opt. 14, 2844-2850 (1975).
[PubMed]

G. R. Ochs, Ting-i Wang, R. S. Lawrence, and S. F. Clifford, "Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations," Appl. Opt. 15, 2504-2510 (1976).
[CrossRef] [PubMed]

J. L. Caccia, M. Azouit, and J. Vernin, "Wind and Cn2 profiling by single star scintillation analysis," Appl. Opt. 26, 1288-1294 (1987).
[CrossRef] [PubMed]

S. F. Clifford and J. H. Churnside, "Refractive turbulence profiling using synthetic aperture spatial filtering of scintillation," Appl. Opt. 26, 1295-1303 (1987).
[CrossRef] [PubMed]

J. H. Churnside and S. F. Clifford, "Refractive turbulence profiling using stellar scintillation and radar wind profiles," Appl. Opt. 27, 4884-4890 (1988).
[CrossRef] [PubMed]

J. H. Churnside, R. J. Lataitis, and R. S. Lawrence, "Measurements of refractive turbulence using spatial filtering of scintillation," Appl. Opt. 27, 2199-2209 (1988).
[CrossRef] [PubMed]

S. G. Hanson, J. H. Churnside, and J. J. Wilson, "Remote sensing of wind velocity and strength of refractive turbulence using a two-spatial-filter receiver," Appl. Opt. 33, 5859-5868 (1994).
[CrossRef] [PubMed]

J. H. Churnside, R. J. Hill, G. Conforti, and A. Consortini, "Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere," Appl. Opt. 28, 4126-4132 (1989).
[CrossRef] [PubMed]

G. R. Ochs, S. F. Clifford, and Ting-i Wang, "Laser wind sensing: the effects of saturation of scintillation," Appl. Opt. 15, 403-408 (1976).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (6)

Proc. IEEE (1)

D. L. Fried, "Remote probing of the optical strength of atmospheric turbulence and of wind velocity," Proc. IEEE 57, 415-420 (1969).
[CrossRef]

Q. J. R. Meteorol. Soc. (1)

W. M. Protheroe, "The motion and structure of stellar shadow-band patterns," Q. J. R. Meteorol. Soc. 90, 27-30 (1964).
[CrossRef]

Other (4)

S. F. Clifford, "The classical theory of wave propagation in a turbulent medium," in Laser Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, 1978), Fig. 2.5.

W. M. Hughes and R. B. Holmes, 3357 Chasen Drive, Cameron Park, CA 95682, submitted a manuscript to Applied Optics called "Pupil-plane imager for scintillometry over long horizontal paths."

F. Eaton and R. Butts, Air Force Research Laboratories, AFRL/DEBA, Bldg. 401, 3550 Aberdeen Ave. SE, Kirtland AFB, NM 87117 (personal communication, 1999).

R. Holmes, "Passive optical wind profilometer," U.S. patent 5,469,250 (filed 17 May 1993, granted 21 November 1995).

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Figures (9)

Fig. 1
Fig. 1

Schematic of NOP beam train. See text for explanation of the figure.

Fig. 2
Fig. 2

(Color online) Comparison of estimates of r 0 based on range partitions 1 and 2. Horizontal scale:PPI-based r 0 ( cm ) using partition 2. Vertical scale:PPI-based r 0 ( cm ) using partition 1.

Fig. 3
Fig. 3

(Color online) Normalized fit error as a function of process noise for a ( 1.0 , 51.6 ) km range partition, using data set s2224sa1202.

Fig. 4
Fig. 4

Comparison of estimates of r 0 based on the wavefront sensor (WFS) and on the pupil plane imager (PPI), with optimized partitions. Open-loop WFS (diamonds), closed-loop WFS (squares), and average of closed and open loop results (triangles). The average slope is 0.84; the average relative root-mean-square error is 0.39.

Fig. 5
Fig. 5

Estimated C n 2 profile with partition 1 versus data set. Estimate for the 0.5   km bin, closest to receiver (top, dashed curve), estimate for the 52 .1   km bin, furthest from receiver (bottom, solid curve).

Fig. 6
Fig. 6

Estimated C n 2 profile with partition 2 versus data set. Estimate for the 17.5   km bin, closest to receiver (top, dashed curve), estimate for the 35.1   km bin, furthest from receiver (bottom, solid curve).

Fig. 7
Fig. 7

Measured (solid) and fitted (dashed) power spectral density of the log-amplitude fluctuations for data set 2224, from Salinas beacon, day 202. The scintillation per bin is the ring-averaged mean-square variation of log amplitude.

Fig. 8
Fig. 8

Scintillation PSD from simulation (dashed) and from measured data (solid) for data set 02343, day 211. The scintillation per bin is the ring-averaged mean-square log amplitude.

Fig. 9
Fig. 9

Simulated (dashed) and estimated (dotted) scintillation PSD's. The estimated (fit) is produced using partition 1. The scintillation per bin is the ring-averaged mean-square log amplitude.

Equations (8)

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χ ( k ) 2 = i = 1 , N C n 2 ( z i ) Δ z i Φ ( k ) S ( k , z i ) ,
k χ ( k ) 2 i C n 2 ( z i ) Δ z i Φ ( k ) S ( k , z i ) 2 ,
k χ ( k ) + ε ( k ) 2 i C n 2 ( z i ) Δ z i [ Φ ( k ) S ( k , z i ) + ε p ( k , z i ) ] 2 ,
k { ( χ ( k ) 2 + σ 2 ) 2 2 ( χ ( k ) 2 + σ 2 ) i ζ i Φ ( k ) × S ( k , z i ) + i j ζ i ζ j [ Φ ( k ) S ( k , z i ) Φ ( k ) S ( k , z j ) + σ p 2 δ ( z i z j ) ] } ,
k χ ( k ) 2 M Φ ( k ) S ( k , z i ) = j [ k Φ ( k ) S ( k , z i ) × Φ ( k ) S ( k , z j ) + σ p 2 δ ( z i z j ) ] ζ j , j M i j ζ j ,
for   i = 1 , … ,  N .
r 0 = [ 0.424 k 0 2 i ζ i ( 1 z i / L ) 5 / 3 ] 3 / 5 ,
P 1 = { 0.5 , 52.1 }   km , P 2 = { 17.5 , 35.1 }   km .

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