Abstract

Performance limitations of optical detector arrays (ODA) are evaluated taking into account background radiation, quantum noise, and internal noises of the photodetector as well as the impact of the atmosphere on the optical wave propagation. It is shown that the accuracy of the ODA-based angle estimator rapidly decreases when the range exceeds a certain limit. Thus, it is possible to define the maximum range of the ODA. Behavior of the maximum range as a function of wavelength and of target radiation energy is investigated. Large maximum ranges are obtained at important wavelengths of 0.63, 3.83, and 10.6 μm. It is shown that the ODA performance is limited by the quantum noise for the small-target radiation energy and by the atmospheric turbulence and attenuation for the large-target radiation energy.

© 1983 Optical Society of America

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References

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  1. R. C. Harney, R. J. Hull, Proc. Soc. Photo-Opt. Instrum. Eng. 227, 162 (1980).
  2. J. H. Shapiro, B. A. Capron, R. C. Harney, Appl. Opt. 20, 3292 (1981).
    [CrossRef] [PubMed]
  3. P. A. Forrester, K. F. Hulme, Opt. Quantum Electron. 13, 259 (1981).
    [CrossRef]
  4. J. D. Mulholland, Scientific Applications of Lunar Laser Range-Finding (Reidel, Dordrecht, 1977).
    [CrossRef]
  5. J. D. E. Beynon, Radio Electron. Eng. 49, 493 (1979).
    [CrossRef]
  6. D. J. Purll, Radio Electron. Eng. 49, 498 (1979).
    [CrossRef]
  7. D. Fink, S. N. Vodopla, Appl. Opt. 15, 453 (1976).
    [CrossRef] [PubMed]
  8. J. H. Churnside, C. M. McIntyre, Appl. Opt. 18, 2315 (1979).
    [CrossRef] [PubMed]
  9. S. R. Robinson, IEEE Trans. Commun. Technol. COM-25, 900 (1979).
  10. L. G. Kazovsky, Signal Process. 3, 345 (1981).
    [CrossRef]
  11. L. G. Kazovsky, Opt. Quantum Electron. 13, 421 (1981).
    [CrossRef]
  12. L. G. Kazovsky, “Azimuth measurement by means of optical detector arrays,” IEEE Trans. Instrum. Meas. IM-31, 60 (1982).
    [CrossRef]
  13. L. G. Kazovsky, Transmission of Information in the Optical Wave Band (Wiley, New York, 1978).
  14. W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).
  15. J. A. Jamieson et al., Infrared Physics and Engineering (McGraw-Hill, New York, 1963).
  16. W. L. Wolfe, Ed. Handbook of Military Infrared Technology, (Office of Naval Research, Washington, D.C., 1976).
  17. N. S. Kopeika, J. Bordogna, Proc. IEEE 58, 1571 (1970).
    [CrossRef]
  18. H. Van-Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968).

1982 (1)

L. G. Kazovsky, “Azimuth measurement by means of optical detector arrays,” IEEE Trans. Instrum. Meas. IM-31, 60 (1982).
[CrossRef]

1981 (4)

J. H. Shapiro, B. A. Capron, R. C. Harney, Appl. Opt. 20, 3292 (1981).
[CrossRef] [PubMed]

P. A. Forrester, K. F. Hulme, Opt. Quantum Electron. 13, 259 (1981).
[CrossRef]

L. G. Kazovsky, Signal Process. 3, 345 (1981).
[CrossRef]

L. G. Kazovsky, Opt. Quantum Electron. 13, 421 (1981).
[CrossRef]

1980 (1)

R. C. Harney, R. J. Hull, Proc. Soc. Photo-Opt. Instrum. Eng. 227, 162 (1980).

1979 (4)

J. H. Churnside, C. M. McIntyre, Appl. Opt. 18, 2315 (1979).
[CrossRef] [PubMed]

S. R. Robinson, IEEE Trans. Commun. Technol. COM-25, 900 (1979).

J. D. E. Beynon, Radio Electron. Eng. 49, 493 (1979).
[CrossRef]

D. J. Purll, Radio Electron. Eng. 49, 498 (1979).
[CrossRef]

1976 (1)

1970 (1)

N. S. Kopeika, J. Bordogna, Proc. IEEE 58, 1571 (1970).
[CrossRef]

Beynon, J. D. E.

J. D. E. Beynon, Radio Electron. Eng. 49, 493 (1979).
[CrossRef]

Bordogna, J.

N. S. Kopeika, J. Bordogna, Proc. IEEE 58, 1571 (1970).
[CrossRef]

Capron, B. A.

Churnside, J. H.

Fink, D.

Forrester, P. A.

P. A. Forrester, K. F. Hulme, Opt. Quantum Electron. 13, 259 (1981).
[CrossRef]

Harney, R. C.

J. H. Shapiro, B. A. Capron, R. C. Harney, Appl. Opt. 20, 3292 (1981).
[CrossRef] [PubMed]

R. C. Harney, R. J. Hull, Proc. Soc. Photo-Opt. Instrum. Eng. 227, 162 (1980).

Hull, R. J.

R. C. Harney, R. J. Hull, Proc. Soc. Photo-Opt. Instrum. Eng. 227, 162 (1980).

Hulme, K. F.

P. A. Forrester, K. F. Hulme, Opt. Quantum Electron. 13, 259 (1981).
[CrossRef]

Jamieson, J. A.

J. A. Jamieson et al., Infrared Physics and Engineering (McGraw-Hill, New York, 1963).

Kazovsky, L. G.

L. G. Kazovsky, “Azimuth measurement by means of optical detector arrays,” IEEE Trans. Instrum. Meas. IM-31, 60 (1982).
[CrossRef]

L. G. Kazovsky, Signal Process. 3, 345 (1981).
[CrossRef]

L. G. Kazovsky, Opt. Quantum Electron. 13, 421 (1981).
[CrossRef]

L. G. Kazovsky, Transmission of Information in the Optical Wave Band (Wiley, New York, 1978).

Kopeika, N. S.

N. S. Kopeika, J. Bordogna, Proc. IEEE 58, 1571 (1970).
[CrossRef]

McIntyre, C. M.

Mulholland, J. D.

J. D. Mulholland, Scientific Applications of Lunar Laser Range-Finding (Reidel, Dordrecht, 1977).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).

Purll, D. J.

D. J. Purll, Radio Electron. Eng. 49, 498 (1979).
[CrossRef]

Robinson, S. R.

S. R. Robinson, IEEE Trans. Commun. Technol. COM-25, 900 (1979).

Shapiro, J. H.

Van-Trees, H.

H. Van-Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968).

Vodopla, S. N.

Appl. Opt. (3)

IEEE Trans. Commun. Technol. (1)

S. R. Robinson, IEEE Trans. Commun. Technol. COM-25, 900 (1979).

IEEE Trans. Instrum. Meas. (1)

L. G. Kazovsky, “Azimuth measurement by means of optical detector arrays,” IEEE Trans. Instrum. Meas. IM-31, 60 (1982).
[CrossRef]

Opt. Quantum Electron. (2)

L. G. Kazovsky, Opt. Quantum Electron. 13, 421 (1981).
[CrossRef]

P. A. Forrester, K. F. Hulme, Opt. Quantum Electron. 13, 259 (1981).
[CrossRef]

Proc. IEEE (1)

N. S. Kopeika, J. Bordogna, Proc. IEEE 58, 1571 (1970).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. C. Harney, R. J. Hull, Proc. Soc. Photo-Opt. Instrum. Eng. 227, 162 (1980).

Radio Electron. Eng. (2)

J. D. E. Beynon, Radio Electron. Eng. 49, 493 (1979).
[CrossRef]

D. J. Purll, Radio Electron. Eng. 49, 498 (1979).
[CrossRef]

Signal Process. (1)

L. G. Kazovsky, Signal Process. 3, 345 (1981).
[CrossRef]

Other (6)

J. D. Mulholland, Scientific Applications of Lunar Laser Range-Finding (Reidel, Dordrecht, 1977).
[CrossRef]

H. Van-Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968).

L. G. Kazovsky, Transmission of Information in the Optical Wave Band (Wiley, New York, 1978).

W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).

J. A. Jamieson et al., Infrared Physics and Engineering (McGraw-Hill, New York, 1963).

W. L. Wolfe, Ed. Handbook of Military Infrared Technology, (Office of Naval Research, Washington, D.C., 1976).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the method of estimation of a target azimuth by means of an array of optical detectors.

Fig. 2
Fig. 2

Spectral characteristics of optical wave atmospheric transmission.

Fig. 3
Fig. 3

Angular accuracy of the ODA vs target range for conditions of weak (·····), intermediate (—), and strong (----) turbulence.

Fig. 4
Fig. 4

Spectral characteristics of maximum range for weak (·····), intermediate (—), and strong (---) turbulence.

Fig. 5
Fig. 5

Maximum range as a function of target radiation energy for weak (·····), intermediate (—), and strong (----) turbulence; (a) λ = 0.63 μm; (b) λ = 3.83 μm; (c) λ = 10.6 μm.

Equations (26)

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P ( k n | θ , E n ) = [ α ( E n + E b ) ] k n k n ! exp [ α ( E n + E b ) ] ,
E n = S I ϒ y ,
y = { cos ( ψ n θ ) π / 2 Φ , | ψ n θ | Φ 0 , | ψ n θ | Φ ,
ψ n = Δ ( n 1 ) / ( N 1 ) Δ / 2 , n = 1 , 2 , N ,
σ 2 E [ ( θ ˆ θ ) 2 ] / Δ 2 ,
σ 2 ( I ) σ l b 2 ( I ) ,
σ l b 2 ( I ) = 1 k t Δ 2 [ n = 1 N ρ y ˙ 2 1 + ρ y ] 1 ,
k t α I S ϒ ,
y ˙ y / θ ,
ρ k t / α E B .
σ l b 2 = 4 ϕ 2 π 2 k t Δ 2 [ n = a b ρ sin 2 ( ψ n θ ) π / 2 Φ 1 + ρ cos ( ψ n θ ) π / 2 Φ ] 1 ,
a G [ 0.5 Δ + θ Φ Δ ( N 1 ) + 1 ] ,
b G [ 0.5 Δ + θ + Φ Δ ( N 1 ) ] .
Φ = Δ / ( N 1 ) .
Φ = Δ / N .
σ l b 2 = 4 π 2 k t N 2 [ n = a a + 1 ρ 2 sin 2 ( ψ n θ ) π / 2 Φ 1 + ρ cos ( ψ n θ ) π / 2 Φ ] 1 .
A ( I ) σ 1 ( I ) = π N ρ 2 [ k t n = a a + 1 sin 2 ( ψ n θ ) π / 2 Φ 1 + ρ cos ( Φ n θ ) π / 2 Φ ] 1 / 2 .
θ = 0.
A ( I ) = π N ρ 2 ( k t 1 + ρ 2 ) 1 / 2 .
f ( I ) = 1 σ ln I 2 π I exp { 1 2 σ ln I 2 ln [ I I ¯ exp ( σ ln I 2 / 2 ) ] } , I > 0 ,
σ ln I 2 = 2.24 ( 2 π λ ) 7 / 6 0 L C n 2 ( z ) ( L z ) 5 / 6 d z ,
σ ln I 2 = 1.22 C n 2 ( 2 π λ ) 7 / 6 L 11 / 6 ,
Weak turbulence , C n = 8 × 10 9 m 1 / 3 , Intermediate turbulence , C n = 4 × 10 8 m 1 / 3 , Strong turbulence , C n = 5 × 10 7 m 1 / 3 .
τ a = exp ( α a L ) ,
I ¯ = I 0 τ a = I 0 exp [ α a ( λ ) · L ] ,
A ¯ = 0 A ( I ) f ( I ) d I ,

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