Abstract

Stellar scintillations, when appropriately analyzed, yield information about the turbulence throughout the atmosphere. We describe an instrument involving a 36-cm telescope and an on-line minicomputer that provides, after 20 min of observation, the refractive-turbulence profile of the atmosphere. The height resolution is sufficient to divide the atmosphere into about four independent regions. The principal limitation to greater accuracy and resolution is the nonstationary behavior of the atmosphere during the 20-min observing period.

© 1976 Optical Society of America

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References

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  1. A. E. Douglass, Popular Astronomy (1897). Reprinted in Amateur Telescope Making (Book Two) (Scientific American, Inc., New York, 1957), p. 585.
  2. W. H. Pickering, Pop. Astron. 33, 1 (1925).
  3. F. Gifford, A. H. Mikesell, Weather 8, 195 (1953).
  4. W. M. Protheroe, Q. J. R. Meteorol. Soc. 90, 27 (1964).
  5. A. A. Townsend, Q. J. R. Meteorol. Soc. 91, 1 (1965).
  6. J. Vernin, F. Roddier, J. Opt. Soc. Am. 63, 270 (1973).
  7. C. Roddier, F. Roddier, J. Opt. Soc. Am. 63, 661 (1973).
  8. A. Rocca, F. Roddier, J. Vernin, J. Opt. Soc. Am. 64, 1000 (1974).
  9. J. Vernin, F. Roddier, C. R. Acad. Sci. (Paris) 280463 (1975).
  10. A. Peskoff, J. Opt. Soc. Am. 58, 1032 (1968).
  11. A. Peskoff, TRW Systems, Tech. Rept. 99900-6692-R0-00 (1968).
  12. D. L. Fried, Proc. IEEE 57, 415 (1969).
  13. L. C. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).
  14. J. W. Strohbehn, J. Opt. Soc. Am. 60, 948 (1970).
  15. J. W. Strohbehn, Boundary-Layer Meteorol. 3, 476 (1972).
  16. G. R. Ochs, S. F. Clifford, R. S. Lawrence, Ting-i Wang, NOAA Tech. Rept. ERL 397-WPL 30 (Government Printing Office, Wȧshington, D.C., 1974).
  17. Ting-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).
  18. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  19. A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941).
  20. R. E. Hufnagel, in Digest of Topical Meeting on Optical Propagation Through Turbulence (Optical Society of America, Washington, D.C., 1974).
  21. R. E. Hufnagel, Perkin-Elmer Corp.; private communication (1976).

1975

J. Vernin, F. Roddier, C. R. Acad. Sci. (Paris) 280463 (1975).

1974

1973

1972

J. W. Strohbehn, Boundary-Layer Meteorol. 3, 476 (1972).

1970

J. W. Strohbehn, J. Opt. Soc. Am. 60, 948 (1970).

L. C. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).

1969

D. L. Fried, Proc. IEEE 57, 415 (1969).

1968

1965

A. A. Townsend, Q. J. R. Meteorol. Soc. 91, 1 (1965).

1964

W. M. Protheroe, Q. J. R. Meteorol. Soc. 90, 27 (1964).

1953

F. Gifford, A. H. Mikesell, Weather 8, 195 (1953).

1941

A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941).

1925

W. H. Pickering, Pop. Astron. 33, 1 (1925).

1897

A. E. Douglass, Popular Astronomy (1897). Reprinted in Amateur Telescope Making (Book Two) (Scientific American, Inc., New York, 1957), p. 585.

Clifford, S. F.

Ting-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).

G. R. Ochs, S. F. Clifford, R. S. Lawrence, Ting-i Wang, NOAA Tech. Rept. ERL 397-WPL 30 (Government Printing Office, Wȧshington, D.C., 1974).

Douglass, A. E.

A. E. Douglass, Popular Astronomy (1897). Reprinted in Amateur Telescope Making (Book Two) (Scientific American, Inc., New York, 1957), p. 585.

Fried, D. L.

D. L. Fried, Proc. IEEE 57, 415 (1969).

Gifford, F.

F. Gifford, A. H. Mikesell, Weather 8, 195 (1953).

Hufnagel, R. E.

R. E. Hufnagel, Perkin-Elmer Corp.; private communication (1976).

R. E. Hufnagel, in Digest of Topical Meeting on Optical Propagation Through Turbulence (Optical Society of America, Washington, D.C., 1974).

Kolmogorov, A. N.

A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941).

Lawrence, R. S.

G. R. Ochs, S. F. Clifford, R. S. Lawrence, Ting-i Wang, NOAA Tech. Rept. ERL 397-WPL 30 (Government Printing Office, Wȧshington, D.C., 1974).

Mikesell, A. H.

F. Gifford, A. H. Mikesell, Weather 8, 195 (1953).

Ochs, G. R.

Ting-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).

G. R. Ochs, S. F. Clifford, R. S. Lawrence, Ting-i Wang, NOAA Tech. Rept. ERL 397-WPL 30 (Government Printing Office, Wȧshington, D.C., 1974).

Peskoff, A.

A. Peskoff, J. Opt. Soc. Am. 58, 1032 (1968).

A. Peskoff, TRW Systems, Tech. Rept. 99900-6692-R0-00 (1968).

Pickering, W. H.

W. H. Pickering, Pop. Astron. 33, 1 (1925).

Protheroe, W. M.

W. M. Protheroe, Q. J. R. Meteorol. Soc. 90, 27 (1964).

Rocca, A.

Roddier, C.

Roddier, F.

Shen, L. C.

L. C. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).

Strohbehn, J. W.

J. W. Strohbehn, Boundary-Layer Meteorol. 3, 476 (1972).

J. W. Strohbehn, J. Opt. Soc. Am. 60, 948 (1970).

Tatarskii, V. I.

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

Townsend, A. A.

A. A. Townsend, Q. J. R. Meteorol. Soc. 91, 1 (1965).

Vernin, J.

Wang, Ting-i

Ting-i Wang, S. F. Clifford, G. R. Ochs, Appl. Opt. 13, 2602 (1974).

G. R. Ochs, S. F. Clifford, R. S. Lawrence, Ting-i Wang, NOAA Tech. Rept. ERL 397-WPL 30 (Government Printing Office, Wȧshington, D.C., 1974).

Appl. Opt.

Boundary-Layer Meteorol.

J. W. Strohbehn, Boundary-Layer Meteorol. 3, 476 (1972).

C. R. Acad. Sci. (Paris)

J. Vernin, F. Roddier, C. R. Acad. Sci. (Paris) 280463 (1975).

Dokl. Akad. Nauk SSSR

A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941).

IEEE Trans. Antennas Propag.

L. C. Shen, IEEE Trans. Antennas Propag. AP-18, 493 (1970).

J. Opt. Soc. Am.

Pop. Astron.

W. H. Pickering, Pop. Astron. 33, 1 (1925).

Popular Astronomy

A. E. Douglass, Popular Astronomy (1897). Reprinted in Amateur Telescope Making (Book Two) (Scientific American, Inc., New York, 1957), p. 585.

Proc. IEEE

D. L. Fried, Proc. IEEE 57, 415 (1969).

Q. J. R. Meteorol. Soc.

W. M. Protheroe, Q. J. R. Meteorol. Soc. 90, 27 (1964).

A. A. Townsend, Q. J. R. Meteorol. Soc. 91, 1 (1965).

Weather

F. Gifford, A. H. Mikesell, Weather 8, 195 (1953).

Other

A. Peskoff, TRW Systems, Tech. Rept. 99900-6692-R0-00 (1968).

R. E. Hufnagel, in Digest of Topical Meeting on Optical Propagation Through Turbulence (Optical Society of America, Washington, D.C., 1974).

R. E. Hufnagel, Perkin-Elmer Corp.; private communication (1976).

G. R. Ochs, S. F. Clifford, R. S. Lawrence, Ting-i Wang, NOAA Tech. Rept. ERL 397-WPL 30 (Government Printing Office, Wȧshington, D.C., 1974).

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

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Figures (11)

Fig. 1
Fig. 1

Weighting function of an infinite linear array of detectors observing the scintillations of a monochromatic plane wave source. The relative weight is shown as a function of normalized height x = πzλ2/d, where z is the height of the turbulence and d is the spatial wavelength of the array of detectors.

Fig. 2
Fig. 2

Weighting function of a finite linear array of detectors (array length = 35.6 cm) observing stellar scintillations for various spatial wavelengths d. The finite bandwidth of the light source has been included.

Fig. 3
Fig. 3

Composite path-weighting functions obtained by linearly combining weighting functions at three different spatial wavelengths (see text and Table I for details).

Fig. 4
Fig. 4

The telescope and the attached instrument box.

Fig. 5
Fig. 5

Schematic of the optical spatial filter and the electronics.

Fig. 6
Fig. 6

Typical optically measured Cn2 vertical profiles at Boulder, Colorado. Each curve is the average of the measurements of a single evening. The dashed line represents the statistical average profile of Hufnagel’s latest model.

Fig. 7
Fig. 7

More measurements of Cn2 profiles at Boulder, Colorado. Each curve is the average of the measurements of a single evening. The dashed line represents the statistical average of Hufnagel’s latest model.

Fig. 8
Fig. 8

Typical variation of the vertical Cn2 profile in a single evening.

Fig. 9
Fig. 9

A comparison between direct measurements of the whole aperture log-amplitude variance and calculations based on the measured Cn2 profiles.

Fig. 10
Fig. 10

Rawisonde measurements of wind speed, wind direction, and temperature taken at Denver.

Fig. 11
Fig. 11

Comparison of optical measurements (x) and the Hufnagel model (smooth curves) that results from using the wind speed profiles measured by the rawinsonde.

Tables (1)

Tables Icon

Table I The Peak Altitudes and Relative Inverse Areas [see Eq. (14)] of Each of the Seven Weighting Functions W1 shown in Fig. 3

Equations (17)

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σ I f 2 = - D / 2 D / 2 I ( x ) cos ( 2 π x / d ) d x - D / 2 D / 2 I ( x ) cos ( 2 π x / d ) d x - D / 2 D / 2 I ¯ d x - D / 2 D / 2 I ¯ d x ,
σ I f 2 = D - 2 - D / 2 D / 2 d x - D / 2 D / 2 d x cos ( 2 π x / d ) × cos ( 2 π x / d ) C I ( x - x ) .
C I ( x - x ) = I ( x ) I ( x ) / I ¯ 2 = 0.528 π 2 k 2 0 d z C n 2 ( z ) 0 d K K - 8 / 3 sin 2 [ K 2 z / ( 2 k ) ] × J 0 [ K ( x - x ) ] ,
Φ n ( K ) = 0.033 C n 2 K - 11 / 3 ; L 0 - 1 K l 0 - 1 ,
σ I f 2 = ( 1 / D ) 0 D d ξ C I ( ξ ) { sin [ K 0 ( D - ξ ) ] K 0 D + ( 1 - ξ / D ) cos ( K 0 ξ ) } ,
J 0 ( K ξ ) = π - 1 - d K ( K 2 - K 2 ) - 1 / 2 × exp ( i K ξ ) ; 0 < K < K .
σ I f 2 = 0.264 π k 2 0 d z C n 2 ( z ) 0 d K × { sin [ ( K 0 - K ) D / 2 ] ( K 0 - K ) D / 2 + sin [ ( K 0 + K ) D / 2 ] ( K 0 + K ) D / 2 } 2 × K d K K - 8 / 3 ( K 2 - K 2 ) - 1 / 2 sin 2 [ K 2 z / ( 2 k ) ] .
σ I f 2 = 0 d z C n 2 ( z ) W ( z ) ,
W ( z ) = ( 0.528 π 2 k 2 / D ) × 0 d y β [ sin [ π β ( y - 1 ) ] π β ( y - 1 ) + sin [ π β ( y + 1 ) ] π β ( y + 1 ) ] 2 × ( K 0 y ) - 8 / 3 W 0 ( x y 2 ) ,
W 0 ( x ) = 0 d u ( 1 + u 2 ) - 11 / 6 sin 2 [ x ( 1 + u 2 ) ] .
W ( z ) = ( π / 2 ) - 1 / 2 σ λ - 1 { 1 + Φ [ λ 0 / ( 2 σ λ ) ] } - 1 × 0 d λ W ( z ) exp [ - ( λ - λ 0 ) 2 / 2 σ λ 2 ] ,
W c ( z ) = i = 1 N R i K i 8 / 3 W ( z , d i ) ,
C n 2 = B i = 1 N R i K i 8 / 3 σ I f 2 ( d i ) ,
B = 1.87 × 10 - 13 [ 0 d z W c ( z ) ] - 1 .
σ I f 2 = [ ( I 1 I ¯ 1 - I 2 I ¯ 2 ) 2 ¯ ] 1 / 2 .
σ I f { [ ln ( I ¯ 1 + I 1 ) - ln ( I ¯ 2 + I 2 ) ] 2 } ¯ 1 / 2
σ χ 2 = 0.132 π 2 k 2 0 d z C n 2 ( z ) 0 d K K - 8 / 3 sin 2 ( K 2 z / 2 k ) × [ 2 J 1 ( K D / 2 ) K D / 2 ] 2 ,

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