Abstract

The scintillation pattern from a single star can be utilized to provide information on the refractive turbulence along the line of sight. Instruments that provide refractive turbulence parameters are the isoplanometer and the stellar scintillometer. Attention is drawn to the fact that the National Oceanic and Atmospheric Administration theoretical treatment and implementation of the stellar scintillometer is incomplete. The theory is corrected for spectral effects and finite aperture. A comparison is made of simultaneously obtained isoplanometer values and stellar scintillometer-derived values for isoplanatic angle. The measurements are obtained from an electro-optical/meteorological experiment conducted at Pennsylvania State University in April and May 1986. An atmospheric drop-off model is used to extrapolate the scintillometer measurements beyond the heights probed. Agreement between the two instruments is significantly improved after the appropriate corrections are applied to the scintillometer data. These data were obtained during widely varying meteorological conditions that provided the opportunity for comparisons over a wide range of isoplanatic angles (3 to 14 μrad). Over the 5 days that data were obtained, relative percent departures of mean isoplanatic angles derived from the corrected stellar scintillometer are within 10% of the mean isoplanometer isoplanatic angle values. The uncorrected departures range from 16% to 24%.

© 1993 Optical Society of America

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References

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  1. A. Peskoff, “Theory of remote sensing of clear-air turbulence profiles,” J. Opt. Soc. Am. 58, 1032–1040 (1968).
    [CrossRef]
  2. D. L. Fried, “Remote probing of the optical strength of atmospheric turbulence and of wind velocity,” Proc. IEEE 57, 415–430 (1969).
    [CrossRef]
  3. L. C. Shen, “Remote probing of the atmosphere and wind velocity by millimeter waves,” IEEE Trans. Antennas Propag. AP-18, 493–497 (1970).
    [CrossRef]
  4. J. M. Heneghan, A. Ishimaru, “Remote determination of the profiles of the atmospheric structure constant and wind velocity along a line-of-sight path by a statistical inversion procedure,” IEEE Trans. Antennas Propag. AP-22, 457–464 (1974).
    [CrossRef]
  5. G. R. Ochs, T. I. Wang, R. S. Lawrence, S. F. Clifford, “Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations,” Appl. Opt. 15, 2504–2510 (1976).
    [CrossRef] [PubMed]
  6. G. R. Ochs, Ting-I Wang, F. Merren, “Stellar scintillometer model II for measurements of refractive turbulence profiles,” NOAA Tech Mem. ERL WPL-25 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1977).
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    [CrossRef]
  8. F. P. Battles, E. A. Murphy, “Correlations between levels for stellar-scintillometer derived profiles of Cn2,” GL Tech. Rep. GL-TR90-0213, ADA 236927 (Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).
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    [CrossRef]
  11. K. B. Stevens, “Remote measurement of the atmospheric isoplanatic angle and determination of refractive turbulence profiles by direct inversion of the scintillation amplitude covariance function with Tikhonov regularization,” Ph.D. dissertation (Naval Postgraduate School, Monterey, Calif., 1985).
  12. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
    [CrossRef]
  13. Ting-I Wang, Scientific Technology Inc., Gaithersburg, Md. 20877 (personal communication).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
    [CrossRef]
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    [CrossRef] [PubMed]
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  19. S. A. Smith, G. R. Ronick, K. J. Jayaweera, “Poker Flat MST radar observations of shear induced turbulence,” J. Geophys. Res. 88, 5265 (1983).
    [CrossRef]
  20. F. D. Eaton, W. A. Peterson, J. Hines, G. Fernandez, “Isoplanatic angle direct measurements and associated atmospheric conditions,” Appl. Opt. 24, 3264–3273 (1985).
    [CrossRef] [PubMed]
  21. F. B. Battles, E. A. Murphy, J. P. Noonan, “The contributions of atmospheric density to the drop-off rate of Cn2,” Phys. Scr. 37, 151 (1988).
    [CrossRef]
  22. F. D. Eaton, W. A. Peterson, J. R. Hines, G. Fernandez, “Isoplanatic angle direct measurements and associated atmospheric conditions,” Appl. Opt. 24, 3264–3273 (1985).
    [CrossRef] [PubMed]
  23. B. B. Balsley, V. L. Peterson, “Doppler radar measurements of clear air turbulence at 1290 MHz,” J. Appl. Meteorol. 20, 266–274 (1981).
    [CrossRef]

1990

1988

J. H. Churnside, R. J. Lataitis, R. S. Lawrence, “Localized measurements of refractive turbulence using spatial filtering of scintillations,” Appl. Opt. 27, 2199–2213 (1988).
[CrossRef] [PubMed]

F. B. Battles, E. A. Murphy, J. P. Noonan, “The contributions of atmospheric density to the drop-off rate of Cn2,” Phys. Scr. 37, 151 (1988).
[CrossRef]

1985

1983

S. A. Smith, G. R. Ronick, K. J. Jayaweera, “Poker Flat MST radar observations of shear induced turbulence,” J. Geophys. Res. 88, 5265 (1983).
[CrossRef]

1982

1981

B. B. Balsley, V. L. Peterson, “Doppler radar measurements of clear air turbulence at 1290 MHz,” J. Appl. Meteorol. 20, 266–274 (1981).
[CrossRef]

1979

1977

R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
[CrossRef]

1976

1974

J. M. Heneghan, A. Ishimaru, “Remote determination of the profiles of the atmospheric structure constant and wind velocity along a line-of-sight path by a statistical inversion procedure,” IEEE Trans. Antennas Propag. AP-22, 457–464 (1974).
[CrossRef]

1970

L. C. Shen, “Remote probing of the atmosphere and wind velocity by millimeter waves,” IEEE Trans. Antennas Propag. AP-18, 493–497 (1970).
[CrossRef]

1969

D. L. Fried, “Remote probing of the optical strength of atmospheric turbulence and of wind velocity,” Proc. IEEE 57, 415–430 (1969).
[CrossRef]

1968

Balsley, B. B.

B. B. Balsley, V. L. Peterson, “Doppler radar measurements of clear air turbulence at 1290 MHz,” J. Appl. Meteorol. 20, 266–274 (1981).
[CrossRef]

Battles, F. B.

F. B. Battles, E. A. Murphy, J. P. Noonan, “The contributions of atmospheric density to the drop-off rate of Cn2,” Phys. Scr. 37, 151 (1988).
[CrossRef]

Battles, F. P.

F. P. Battles, E. A. Murphy, “Correlations between levels for stellar-scintillometer derived profiles of Cn2,” GL Tech. Rep. GL-TR90-0213, ADA 236927 (Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Beecher, E. A.

E. A. Beecher, “Analysis of temperature and velocity micro turbulence parameters from aircraft data and relationship to atmospheric refractive index structure,” M. S. thesis (Pennsylvania State University, University Park, Pa., 1988).

Brown, J. H.

Chonacky, N.

Churnside, J. H.

Clifford, S. F.

Deuel, R. W.

Earl Good, R.

Eaton, F. D.

Fernandez, G.

Fried, D. L.

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

D. L. Fried, “Remote probing of the optical strength of atmospheric turbulence and of wind velocity,” Proc. IEEE 57, 415–430 (1969).
[CrossRef]

Heneghan, J. M.

J. M. Heneghan, A. Ishimaru, “Remote determination of the profiles of the atmospheric structure constant and wind velocity along a line-of-sight path by a statistical inversion procedure,” IEEE Trans. Antennas Propag. AP-22, 457–464 (1974).
[CrossRef]

Hines, J.

Hines, J. R.

Hogge, C. B.

Honeycutt, R. R.

R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
[CrossRef]

Ishimaru, A.

J. M. Heneghan, A. Ishimaru, “Remote determination of the profiles of the atmospheric structure constant and wind velocity along a line-of-sight path by a statistical inversion procedure,” IEEE Trans. Antennas Propag. AP-22, 457–464 (1974).
[CrossRef]

Jayaweera, K. J.

S. A. Smith, G. R. Ronick, K. J. Jayaweera, “Poker Flat MST radar observations of shear induced turbulence,” J. Geophys. Res. 88, 5265 (1983).
[CrossRef]

Krause-Polstorff, J.

Lataitis, R. J.

Lawrence, R. S.

Loos, G. C.

Loriot, G. B.

Merren, F.

G. R. Ochs, Ting-I Wang, F. Merren, “Stellar scintillometer model II for measurements of refractive turbulence profiles,” NOAA Tech Mem. ERL WPL-25 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1977).

Murphy, E. A.

F. B. Battles, E. A. Murphy, J. P. Noonan, “The contributions of atmospheric density to the drop-off rate of Cn2,” Phys. Scr. 37, 151 (1988).
[CrossRef]

F. P. Battles, E. A. Murphy, “Correlations between levels for stellar-scintillometer derived profiles of Cn2,” GL Tech. Rep. GL-TR90-0213, ADA 236927 (Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Noonan, J. P.

F. B. Battles, E. A. Murphy, J. P. Noonan, “The contributions of atmospheric density to the drop-off rate of Cn2,” Phys. Scr. 37, 151 (1988).
[CrossRef]

Ochs, G. R.

G. R. Ochs, T. I. Wang, R. S. Lawrence, S. F. Clifford, “Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations,” Appl. Opt. 15, 2504–2510 (1976).
[CrossRef] [PubMed]

G. R. Ochs, Ting-I Wang, F. Merren, “Stellar scintillometer model II for measurements of refractive turbulence profiles,” NOAA Tech Mem. ERL WPL-25 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1977).

Peskoff, A.

Peterson, V. L.

B. B. Balsley, V. L. Peterson, “Doppler radar measurements of clear air turbulence at 1290 MHz,” J. Appl. Meteorol. 20, 266–274 (1981).
[CrossRef]

Peterson, W. A.

Quesda, A. F.

Ramsey, L. W.

R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
[CrossRef]

Ridgway, S. T.

R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
[CrossRef]

Ronick, G. R.

S. A. Smith, G. R. Ronick, K. J. Jayaweera, “Poker Flat MST radar observations of shear induced turbulence,” J. Geophys. Res. 88, 5265 (1983).
[CrossRef]

Shen, L. C.

L. C. Shen, “Remote probing of the atmosphere and wind velocity by millimeter waves,” IEEE Trans. Antennas Propag. AP-18, 493–497 (1970).
[CrossRef]

Smith, S. A.

S. A. Smith, G. R. Ronick, K. J. Jayaweera, “Poker Flat MST radar observations of shear induced turbulence,” J. Geophys. Res. 88, 5265 (1983).
[CrossRef]

Stevens, K. B.

K. B. Stevens, “Remote measurement of the atmospheric isoplanatic angle and determination of refractive turbulence profiles by direct inversion of the scintillation amplitude covariance function with Tikhonov regularization,” Ph.D. dissertation (Naval Postgraduate School, Monterey, Calif., 1985).

Walters, D. L.

J. Krause-Polstorff, D. L. Walters, “Refractive turbulence profiling using an orbiting light source,” Appl. Opt. 29, 1877–1885 (1990).
[CrossRef] [PubMed]

D. L. Walters, “Saturation and the zenith angle dependence of the atmospheric isoplanatic angle,” in Adaptive Optics, J. E. Ludman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.551, 38–41 (1985).

Wang, T. I.

Wang, Ting-I

G. R. Ochs, Ting-I Wang, F. Merren, “Stellar scintillometer model II for measurements of refractive turbulence profiles,” NOAA Tech Mem. ERL WPL-25 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1977).

Ting-I Wang, Scientific Technology Inc., Gaithersburg, Md. 20877 (personal communication).

Warren, W. H.

R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
[CrossRef]

Watkins, B. J.

Appl. Opt.

Astrophys. J.

R. R. Honeycutt, L. W. Ramsey, W. H. Warren, S. T. Ridgway, “Spectrophotometry of cool angular-diameter stars,” Astrophys. J. 215, 584–596 (1977).
[CrossRef]

IEEE Trans. Antennas Propag.

L. C. Shen, “Remote probing of the atmosphere and wind velocity by millimeter waves,” IEEE Trans. Antennas Propag. AP-18, 493–497 (1970).
[CrossRef]

J. M. Heneghan, A. Ishimaru, “Remote determination of the profiles of the atmospheric structure constant and wind velocity along a line-of-sight path by a statistical inversion procedure,” IEEE Trans. Antennas Propag. AP-22, 457–464 (1974).
[CrossRef]

J. Appl. Meteorol.

B. B. Balsley, V. L. Peterson, “Doppler radar measurements of clear air turbulence at 1290 MHz,” J. Appl. Meteorol. 20, 266–274 (1981).
[CrossRef]

J. Geophys. Res.

S. A. Smith, G. R. Ronick, K. J. Jayaweera, “Poker Flat MST radar observations of shear induced turbulence,” J. Geophys. Res. 88, 5265 (1983).
[CrossRef]

J. Opt. Soc. Am.

Phys. Scr.

F. B. Battles, E. A. Murphy, J. P. Noonan, “The contributions of atmospheric density to the drop-off rate of Cn2,” Phys. Scr. 37, 151 (1988).
[CrossRef]

Proc. IEEE

D. L. Fried, “Remote probing of the optical strength of atmospheric turbulence and of wind velocity,” Proc. IEEE 57, 415–430 (1969).
[CrossRef]

Other

D. L. Walters, “Saturation and the zenith angle dependence of the atmospheric isoplanatic angle,” in Adaptive Optics, J. E. Ludman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.551, 38–41 (1985).

G. R. Ochs, Ting-I Wang, F. Merren, “Stellar scintillometer model II for measurements of refractive turbulence profiles,” NOAA Tech Mem. ERL WPL-25 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1977).

F. P. Battles, E. A. Murphy, “Correlations between levels for stellar-scintillometer derived profiles of Cn2,” GL Tech. Rep. GL-TR90-0213, ADA 236927 (Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

E. A. Beecher, “Analysis of temperature and velocity micro turbulence parameters from aircraft data and relationship to atmospheric refractive index structure,” M. S. thesis (Pennsylvania State University, University Park, Pa., 1988).

K. B. Stevens, “Remote measurement of the atmospheric isoplanatic angle and determination of refractive turbulence profiles by direct inversion of the scintillation amplitude covariance function with Tikhonov regularization,” Ph.D. dissertation (Naval Postgraduate School, Monterey, Calif., 1985).

Ting-I Wang, Scientific Technology Inc., Gaithersburg, Md. 20877 (personal communication).

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Figures (13)

Fig 1
Fig 1

Plot of corrected scintillometer composite weighting functions for seven ranges. Note the oscillatory character of the first five weighting functions. The source is Arcturus.

Fig. 2
Fig. 2

Plot of corrected scintillometer composite weighting functions for seven ranges. The source is Regulus. Note the difference in the position of the peaks.

Fig. 3
Fig. 3

Plot of uncorrected scintillometer composite weighting functions for seven ranges. These are the original NOAA functions and include no source.

Fig. 4
Fig. 4

Isoplanatic angles for 30 April 1986. Uncorrected scintillometer values were used.

Fig. 5
Fig. 5

Isoplanatic angles for 2 May 1986. Uncorrected scintillometer values were used.

Fig. 6
Fig. 6

Isoplanatic angles for 3 May 1986. Uncorrected scintillometer values were used.

Fig. 7
Fig. 7

Isoplanatic angles for 5 May 1986. Uncorrected scintillometer values were used.

Fig. 8
Fig. 8

Isoplanatic angles for 6 May 1986. Uncorrected scintillometer values were used.

Fig. 9
Fig. 9

Isoplanatic angles for 30 April 1986. Corrected scintillometer values were used.

Fig. 10
Fig. 10

Isoplanatic angles for 2 May 1986. Corrected scintillometer values were used.

Fig. 11
Fig. 11

Isoplanatic angles for 3 May 1986. Corrected scintillometer values were used.

Fig. 12
Fig. 12

Isoplanatic angles for 5 May 1986. Corrected scintillometer values were used.

Fig. 13
Fig. 13

Isoplanatic angles for 6 May 1986. Corrected scintillometer values were used.

Tables (3)

Tables Icon

Table 1 Area Ratios of Original Weighting Function To Revised Weighting Functions

Tables Icon

Table 2 Comparison of Scintillometer Data To Isoplanometedr Data a

Tables Icon

Table 3 Correlation of Scintillometer Data To Isoplanometer Data

Equations (15)

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f R ( x , y ) = cyl [ ( x 2 + y 2 ) 1 / 2 r ] cos ( K R x ) cos ( K R y ) / π r 2 ,
F R ( K x , K y ) = ½ ( J 1 c { r [ ( K x K R ) 2 + ( K y K R ) 2 ] 1 / 2 } + J 1 c { r [ ( K x K R ) 2 + ( K y + K R ) 2 ] 1 / 2 } + J 1 c { r [ ( K x + K R ) 2 + ( K y K R ) 2 ] 1 / 2 } + J 1 c { r [ ( K x + K R ) 2 + ( K y + K R ) 2 ] 1 / 2 } ) ,
σ χ f 2 = 0.132 π 2 k 2 0 d z C n 2 ( z ) × d 2 K K 11 / 3 sin 2 ( K 2 z / 2 k ) | F R ( K ) | 2 ,
σ χ f 2 = 0 d z C n 2 ( z ) W ( z ) ,
W ( z ) = 0.132 π 2 k 2 d 2 K K 11 / 3 sin 2 ( K 2 z / 2 k ) | F R ( K ) | 2 .
W ( z ) = λ c d λ W ( z , λ ) S ( λ ) exp [ ( λ λ 0 ) 2 / 2 σ λ 2 ] λ c d λ S ( λ ) exp [ ( λ λ 0 ) 2 / 2 σ λ 2 ] .
σ s 2 / S 2 = 16 π 2 ( 0.033 k 2 ) 0 l C n 2 ( z ) d z × 0 d K K 8 / 3 I ( K ) sin 2 ( K 2 z 2 k ) ,
θ 0 5 / 3 = 2.905 k 2 sec 8 / 3 ϕ 0 l d z C n 2 ( z ) z 5 / 3 ,
W ( z ) = 0 d K K 8 / 3 I ( K ) sin 2 ( K 2 z 2 k ) ,
θ 0 5 / 3 = A σ s 2 / S 2 ,
W ( z ) = 1 ( 1 1 2 + 2 2 3 2 ) 2 0 K 8 / 3 dK sin 2 ( K 2 z 2 k ) × { 2 2 [ 2 J 1 ( 2 KD / 2 ) 2 KD / 2 ] 1 2 [ 2 J 1 ( 1 KD / 2 ) 1 KD / 2 ] + [ 2 J 1 ( KD / 2 ) KD / 2 ] 3 2 [ 2 J 1 ( 3 KD / 2 ) 3 KD / 2 ] } 2 ,
θ 0 = 5.8 × 10 4 λ 1.2 I 3 / 5 ,
I = I scint + I a + I b = 0 z 1 z 5 / 3 C n 2 ( z ) d z + z 1 z 7 z 5 / 3 C n 2 ( z ) d z + z 7 z 5 / 3 C n 2 ( z ) d z .
C n 2 ( z ) = C n 2 ( z 1 ) ( z / z 1 ) 2 / 3 ,
C n 2 ( z ) = C n 2 ( z 7 ) exp [ a ( z z 7 ) ] ,

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