Abstract

This paper describes a new optical technique for measuring the refractive-index structure parameter Cn2. By using relatively large incoherent transmitting and receiving optics, the scintillometer maintains its calibration and path-weighting function throughout the range of observed refractive turbulence values, even to the case of saturated scintillation.

© 1978 Optical Society of America

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References

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  1. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  2. V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation, IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).
  3. R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
    [Crossref]
  4. A. N. Kolmogorov, Dokl. Akad. Nauk, SSSR 30, 299 (1941).
  5. S. F. Clifford, G. R. Ochs, and R. S. Lawrence, J. Opt. Soc. Am. 64, 148 (1974).
    [Crossref]
  6. S. F. Clifford and H. T. Yura, J. Opt. Soc. Am. 64, 1641 (1974).
    [Crossref]
  7. G. R. Ochs, S. F. Clifford, and Ting-i Wang, Appl. Opt. 15, 403 (1976).
    [Crossref] [PubMed]
  8. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
    [Crossref]

1976 (1)

1974 (2)

1970 (1)

1969 (1)

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

1941 (1)

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

Clifford, S. F.

Harp, J. C.

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

Kolmogorov, A. N.

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

Lawrence, R. S.

Lee, R. W.

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

Ochs, G. R.

Tatarskii, V. I.

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

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation, IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).

Wang, Ting-i

Yura, H. T.

Appl. Opt. (1)

Dokl. Akad. Nauk, SSSR (1)

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

J. Opt. Soc. Am. (3)

Proc. IEEE (1)

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

Other (2)

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

V. I. Tatarskii, The Effect of the Turbulent Atmosphere on Wave Propagation, IPST Catalog 5319 (National Technical Information Service, Springfield, Va., 1971).

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Figures (8)

FIG. 1
FIG. 1

The effect of the microscale on the weighting function of a point transmitter and detector system.

FIG. 2
FIG. 2

The effect of saturation of scintillation on the weighting function of a point transmitter and detector system, where σ T 2 = 0.124 k 7 / 6 L 11 / 6 C n 2.

FIG. 3
FIG. 3

The effect of the microscale on a finite transmitter and detector system [Dt = Dr = 4(λL)1/2].

FIG. 4
FIG. 4

The path-weighting function for different receiving aperture diameters.

FIG. 5
FIG. 5

The C n 2 weighting versus the eddy size normalized to the receiver aperture size. Solid-line: for single detector. Dashed-line: for two equal-aperture tangent detectors.

FIG. 6
FIG. 6

Measurements of C n 2 ( m - 2 / 3 ) obtained from the saturation-resistant optical scintillometer vs C n 2 derived from a differential thermometer placed at the center of a 500 m optical path 1.5 m above the ground. Each point is a 5 min average. Transmitting and receiving apertures were 15 cm in diameter; the differential thermometers were separated 20 cm in the vertical direction.

FIG. 7
FIG. 7

Comparison of C n 2 ( m - 2 / 3 ) measurements made with the saturation-resistant optical scintillometer and with a laser scintillometer on a 500 m optical path 1.5 m above the ground. Each point is a 5 min average. The differential saturation-resistant system used 15 cm diameter optics; the laser system used a spherical wave front which irradiated a 1-mm-diam receiving aperture.

FIG. 8
FIG. 8

Comparison of differential saturation-resistant optical scintillometers of different path lengths and aperture diameters. Each point is a 1 h average and all paths are 1.5 m above the ground. The solid line represents data obtained from the system using 15 cm apertures on a 500 m path. The dotted line data to the left of the break in the graph was obtained using 7.5 cm apertures on a parallel 500 m path; to the right of the break, the dotted line data is from 7.5 cm apertures on a 250 m path also parallel to the 500 m path. The data averages differ by less than 5%.

Equations (26)

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σ T 2 = 4 π 2 k 2 0 L d z 0 d K K Φ ( K ) × sin 2 ( K 2 z ( L - z ) 2 k L ) ,
Φ ( K ) = 0.033 C n 2 ( z ) K - 11 / 3 .
σ T 2 = 0.124 k 7 / 6 L 11 / 6 C ¯ n 2 ,
σ T 2 = 0 L d z C n 2 ( z ) W ( z ) ,
W ( z ) = 4 π 2 k 2 0 d K K Φ ( K ) sin 2 ( K 2 z ( L - z ) 2 k L ) .
Φ ( K ) = 0.033 C n 2 ( z ) K - 11 / 3 exp ( - K 2 / K m 2 ) ,
C χ ( ρ ) = 2.94 0 1 d u σ T 2 ( u ) [ u ( 1 - u ) ] 5 / 6 0 d y y - 11 / 6 sin 2 y × exp { - σ T 2 [ u ( 1 - u ) ] 5 / 6 F ( y ) } J 0 { [ 4 π y u / ( 1 - u ) ] 1 / 2 ρ } ,
F ( y ) = 7.02 y 5 / 6 0.7 y d ξ ξ - 8 / 3 [ 1 - J 0 ( ξ ) ] .
C χ ( ρ ) = 0 1 d u C n 2 ( u ) W ( u ) ,
W ( u ) = 0.365 k 7 / 6 L 11 / 6 [ u ( 1 - u ) ] 5 / 6 × 0 d y g ( u , y ) J 0 { [ 4 π y u / ( 1 - u ) ] 1 / 2 ρ } ,
g ( u , y ) = y - 11 / 6 sin 2 y exp { - σ T 2 [ u ( 1 - u ) ] 5 / 6 F ( y ) } .
g ( u , y ) = g ( u , y ) ( 2 J 1 { [ π y u / ( 1 - u ) ] 1 / 2 α r } [ π y u / ( 1 - u ) ] 1 / 2 α r ) 2 × ( 2 J 1 { [ π y ( 1 - u ) / u ] 1 / 2 α t } [ π y ( 1 - u ) / u ] 1 / 2 α t ) 2 ,
g ( u , y ) = y - 11 / 6 sin 2 y A ,
A exp ( - F ( y ) F ( y s ) ) ( 2 J 1 [ ( y / y r ) 1 / 2 ] ( y / y r ) 1 / 2 ) 2 × ( 2 J 1 [ ( y / y t ) 1 / 2 ] ( y / y t ) 1 / 2 ) 2 ,
y r ( 1 - u ) / α r 2 π u ,
y t u / [ α t 2 π ( 1 - u ) ] ,
F ( y s ) { σ T 2 [ u ( 1 - u ) ] 5 / 6 } - 1 .
F ( y ) { 7.9 y 5 / 6 if y 1 7.9 y - 5 / 6 if y 1 .
0.084 ( σ T 2 ) - 6 / 5 u - 1 ( 1 - u ) - 1 > ( 1 - u ) / ( α r 2 π u )
0.084 ( σ T 2 ) - 6 / 5 u - 1 ( 1 - u ) - 1 > u / [ α t 2 π ( 1 - u ) ] ,
α r > 1.95 ( σ T 2 ) 3 / 5 ( 1 - u )
α t > 1.95 ( σ T 2 ) 3 / 5 u .
α r + α t > 1.95 ( σ T 2 ) 3 / 5 .
C ¯ n 2 = C σ χ 2 D t 7 / 3 L - 3 ,
C n 2 = 0.689 ( I A - I B ) 2 Ī 2 D 7 / 3 L - 3 ,
C n 2 = C 4 ( I - Ī ) 2 ( Ī ) 2 D 7 / 3 L - 3 .