Abstract

The limitations imposed by atmospheric turbulence in the design of optical surveillance systems with slant optical paths are developed. Image blurring effects which determine scene contrast ratio are separated from spot dancing effects which determine signal-to-noise ratio. The relative position of each turbulent eddy with respect to scene and observer is considered. The effects of turbulence in ground-to-ground, air-to-ground, and ground-to-air optical surveillance systems are compared.

© 1967 Optical Society of America

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References

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  1. H. Hodara, Proc. IEEE 54, 368 (1966).
    [CrossRef]
  2. S. L. Valley, Ed. Handbook of Geophysics (U.S. Air Force, The Macmillan Company, New York, 1957), pp. 2–14.
  3. D. L. Fried, Proc. IEEE 55, 57 (1967).
    [CrossRef]
  4. R. Paulson, E. Ellis, N. Ginsburg, “Atmospheric Optical Noise Measurements,” AFCRL–62–869, August15, 1962.
  5. B. N. Edwards, R. R. Steen, Appl. Opt. 4, 311 (1965).
    [CrossRef]
  6. D. H. Höhn, Appl. Opt. 5, 1433 (1966).
    [CrossRef] [PubMed]
  7. P. Beckmann, Radio Sci. J. Res. NBS/USNC–URSI, 69 D, 629 (1965).
  8. J. Davis, Appl. Opt. 5, 139 (1966).
    [CrossRef] [PubMed]
  9. S. Q. Duntley, W. H. Culver, F. Richey, R. W. Preisendorfer, J. Opt. Soc. Am. 53, 351 (1963).
    [CrossRef]
  10. C. B. Rogers, J. Opt. Soc. Am. 55, 1151 (1965).
    [CrossRef]
  11. C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
    [CrossRef]
  12. H. W. Straub, Appl. Optics 4, 875 (1965).
    [CrossRef]
  13. A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).
  14. D. L. Fried, G. E. Meyers, J. Opt. Soc Am. 55, 740 (1965).
    [CrossRef]
  15. A. Saleh, H. Hodara, Proc. IEEE 55, 1209 (1967).
    [CrossRef]

1967 (2)

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

A. Saleh, H. Hodara, Proc. IEEE 55, 1209 (1967).
[CrossRef]

1966 (5)

C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
[CrossRef]

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).

D. H. Höhn, Appl. Opt. 5, 1433 (1966).
[CrossRef] [PubMed]

J. Davis, Appl. Opt. 5, 139 (1966).
[CrossRef] [PubMed]

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

1965 (5)

C. B. Rogers, J. Opt. Soc. Am. 55, 1151 (1965).
[CrossRef]

P. Beckmann, Radio Sci. J. Res. NBS/USNC–URSI, 69 D, 629 (1965).

B. N. Edwards, R. R. Steen, Appl. Opt. 4, 311 (1965).
[CrossRef]

D. L. Fried, G. E. Meyers, J. Opt. Soc Am. 55, 740 (1965).
[CrossRef]

H. W. Straub, Appl. Optics 4, 875 (1965).
[CrossRef]

1963 (1)

Beckmann, P.

P. Beckmann, Radio Sci. J. Res. NBS/USNC–URSI, 69 D, 629 (1965).

Consortini, A.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).

Coulman, C. E.

Culver, W. H.

Davis, J.

Duntley, S. Q.

Edwards, B. N.

Ellis, E.

R. Paulson, E. Ellis, N. Ginsburg, “Atmospheric Optical Noise Measurements,” AFCRL–62–869, August15, 1962.

Fried, D. L.

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

D. L. Fried, G. E. Meyers, J. Opt. Soc Am. 55, 740 (1965).
[CrossRef]

Ginsburg, N.

R. Paulson, E. Ellis, N. Ginsburg, “Atmospheric Optical Noise Measurements,” AFCRL–62–869, August15, 1962.

Hodara, H.

A. Saleh, H. Hodara, Proc. IEEE 55, 1209 (1967).
[CrossRef]

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

Höhn, D. H.

Meyers, G. E.

D. L. Fried, G. E. Meyers, J. Opt. Soc Am. 55, 740 (1965).
[CrossRef]

Paulson, R.

R. Paulson, E. Ellis, N. Ginsburg, “Atmospheric Optical Noise Measurements,” AFCRL–62–869, August15, 1962.

Preisendorfer, R. W.

Richey, F.

Rogers, C. B.

Ronchi, L.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).

Saleh, A.

A. Saleh, H. Hodara, Proc. IEEE 55, 1209 (1967).
[CrossRef]

Scheggi, A. M.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).

Steen, R. R.

Straub, H. W.

H. W. Straub, Appl. Optics 4, 875 (1965).
[CrossRef]

Toraldi di Francia, G.

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).

Appl. Opt. (3)

Appl. Optics (1)

H. W. Straub, Appl. Optics 4, 875 (1965).
[CrossRef]

J. Opt. Soc Am. (1)

D. L. Fried, G. E. Meyers, J. Opt. Soc Am. 55, 740 (1965).
[CrossRef]

J. Opt. Soc. Am. (3)

Proc. IEEE (3)

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

A. Saleh, H. Hodara, Proc. IEEE 55, 1209 (1967).
[CrossRef]

Radio Sci. (1)

A. Consortini, L. Ronchi, A. M. Scheggi, G. Toraldi di Francia, Radio Sci. 1, 523 (1966).

Radio Sci. J. Res. NBS/USNC–URSI (1)

P. Beckmann, Radio Sci. J. Res. NBS/USNC–URSI, 69 D, 629 (1965).

Other (2)

R. Paulson, E. Ellis, N. Ginsburg, “Atmospheric Optical Noise Measurements,” AFCRL–62–869, August15, 1962.

S. L. Valley, Ed. Handbook of Geophysics (U.S. Air Force, The Macmillan Company, New York, 1957), pp. 2–14.

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Figures (3)

Fig. 1
Fig. 1

Atmospheric effects in active optical surveillance system.

Fig. 2
Fig. 2

Image blur radius ss′ and spot dancing radius oo′ relative to positions of scene s′, observer o′, and turbulent eddy.

Fig. 3
Fig. 3

Reduction of time-averaged scene contrast ratio by atmospheric turbulence. The bar thickness (in subtended radians) is specified in terms of the turbulence optical state A and range R. Co———Inherent contrast ratio, Cr– – – – Gaussian distribution of radiance,9 Cr— – —Uniform radiance [Eq. (16)].

Tables (2)

Tables Icon

Table I Radii of Blur Circle and Spot Dancing Circle for Different Optical Paths of Length R = 1 km

Tables Icon

Table II Intensity Fluctuation at Receiver of Aperture Diameter D for Slant Optical Paths of Length R = 1 km

Equations (34)

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Δ n n - 1 = - Δ u u = - Δ T T | isobaric = Δ p p | isothermal .
Δ n 2 ¯ = 10 - 12 exp ( - h / 3.2 ) ,
Δ n ( r ) Δ n ( r + ρ ) Δ n 2 ( r ) = Δ n ( r ) Δ n ( r + L c ) Δ n 2 ( r ) = 0.5 ,
Δ n ( t ) Δ n ( t + τ ) ¯ Δ n 2 ( t ) ¯ = Δ n ( t ) Δ n ( t + T c ) ¯ Δ n 2 ( t ) ¯ = 0.5 ,
Δ n 2 ( r ) = Δ n 2 ( t ) ¯ .
L c = ( 4 h ) 1 2 ,
L c R ( λ / c )             or             L c ( R λ ) 1 2 .
sin θ 0 = ( 1 + Δ n ) sin ( θ 0 + Δ θ i ) ( 1 + n ) × ( sin θ 0 + Δ θ i cos θ 0 ) - Δ θ i cos θ 0 Δ n
Δ θ i = - Δ n tan θ 0 = - Δ n L c z / L c t ,
Δ θ i 2 ¯ = Δ n 2 ¯ ( L c z / L c t ) 2 = Δ n 2 ¯ ( L c z / L c x ) 2 + Δ n 2 ¯ ( L c z / L c y ) 2 ,
s s 2 = i Δ θ i 2 ¯ z i 2 0 R Δ θ i 2 ¯ ( z 2 / L c z ) d z , for R L c z ,
o o 2 = i Δ θ i 2 ( R - z i ) 2 0 R Δ θ i 2 ¯ ( R - z ) 2 ( 1 / L c z ) d z , for R L c z .
Δ θ 2 image blurring 1 2 = ( s s 2 ) 1 2 ( 1 / R ) .
Δ θ 2 spot dancing 1 2 = ( o o 2 ) 1 2 ( 1 / R ) .
( Δ θ 2 ) 1 2 = ( Δ θ i 2 ¯ R / 3 L c z ) 1 2 = ( 2 A R ) 1 2 ,
( Δ θ 2 ) 1 2 = ( 2 Δ n 2 ¯ R / 3 L c ) 1 2 .
C r / C 0 ( 1 + Δ θ 2 1 2 / ψ ) - 2 = ( 1 + ( 2 A R ) 1 2 ψ ) - 2 , circular targets ,
C r / C 0 ( 1 + Δ θ 2 1 2 / ψ ) - 1 = ( 1 + ( 2 A R ) 1 2 ψ ) - 1 , infinite bar targets .
Δ θ 2 1 2 image blurring = ( 1 / R ) [ h 1 R 2 Δ n 2 ¯ h 2 ( 1 / L c ) d h ] 1 2 = ( 1 / R ) [ h 1 R 2 × 10 - 12 exp ( - h / 3200 ) h 2 ( 1 4 h ) 1 2 d h ] 1 2 .
Δ θ 2 1 2 image blurring = ( 1 / R ) [ h 1 R 2 Δ n 2 ¯ ( R - h ) 2 ( 1 / L c ) d h ] 1 2 = ( 1 / R ) [ h 1 R 2 × 10 - 12 exp ( - h / 3200 ) ( R - h ) 2 ( 1 / 4 h ) 1 2 d h ] 1 2 .
Δ φ 1 Δ φ 2 ¯ / Δ φ 2 ¯ = Δ n 1 Δ n 2 ¯ / Δ n 2 ¯ 0.9 ,
Δ φ 2 ¯ = ( 2 π D / λ ) 2 4 Δ θ 2 spot dancing π 2 .
D ( λ / 4 ) ( Δ θ 2 spot dancing ) - 1 2 .
Δ φ i 2 ¯ = ( 2 π L c z / λ ) 2 Δ n 2 ¯ .
Δ φ 2 = i ( 2 π L c z / λ ) 2 Δ n 2 ¯ = ( 2 π / λ ) 2 0 R L c z Δ n 2 ¯ d z .
Δ f 2 1 2 = ( d φ / d t ) 2 1 2 [ Δ φ 2 T c 2 ] 1 2 = [ ( 2 π / λ T c ) 2 0 R Δ n 2 ¯ L c z d z ] 1 2 .
1 + Δ S / S = ( 1 + Δ I / I ) - 1 .
Δ S / S - Δ I / I .
Δ S / S scene = π [ R ψ + R ( Δ θ 2 spot dancing 1 2 ) ] 2 - π ( R ψ ) 2 π ( R ψ ) 2 = 2 / ψ Δ θ 2 spot dancing 1 2 + 1 / ψ 2 Δ θ 2 spot dancing .
Δ S / S receiver = π [ D / 2 - R ( Δ θ 2 spot dancing 1 2 ) ] 2 - π D 2 / 4 π D 2 / 4 = ( 4 R / D ) Δ θ 2 spot dancing 1 2 + ( 2 R / D ) 2 Δ θ 2 spot dancing .
( S / N ) photo - detection = [ ( I / Δ I ) scene 2 + ( I / Δ I receiver ) 2 ] - 1 2 .
( S / N ) heterodyne = ( m 2 / 2 ) [ ( I / Δ I ) scene 2 + ( I / Δ I ) 2 receiver ] - 1 2 .
Δ Φ i 2 ¯ ( 1 1     6 ) Δ θ i 4 ¯ sin 2 2 Φ ,
Δ Φ 2 = i Δ Φ i 2 ¯ 0 R Δ Φ i 2 ¯ ( 1 / L c z ) d z , R L c z .

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