Abstract

Both scattering and turbulence can effect the spatial coherence of short wavelength signals propagating through the open atmosphere. In this paper, the influence of forward scattering on heterodyne receiver performance is investigated, taking into account turbulence. It is shown that the effect of forward scattering is to reduce the effective heterodyne receiver area through spatial coherence degradation. A common approach to scattering as an attenuation phenomenon is not always valid. Generally, this approach underestimates the SNR. The accuracy of the attenuation approach depends on the ratio R of the actual receiver diameter to the scattering particle diameter. If R > 100, scattering is essentially large angle and the typical treatment of scattering as an attenuation effect is indeed justified. However, for small R, forward scattering is primarily small angle, field coherence is noticeably affected by forward scattering, and the attenuation approach is not valid. Further, it is shown that the SNR is improved when the ratio of the scattering particulate size to turbulence coherence diameter decreases. From the practical point of view, the most important result of this study is that small receivers use their area more effectively than large receivers. Thus, an array of several small receivers may perform better than one large receiver with the same total area. The treatment here is particularly relevant for coherent detection through clouds, fog, precipitation, and turbid media in general, including liquid media.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Fried, Proc. IEEE 55, 57 (1967).
    [CrossRef]
  2. R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), pp. 173–201.
  3. J. R. Clark, J. R. Baird, R. S. Rearden, Appl. Opt. 15, 314 (1976).
    [CrossRef] [PubMed]
  4. P. Bruscaglioni, G. Milloni, G. Zaccanti, Opt. Acta 27, 1229 (1980).
    [CrossRef]
  5. G. C. Mooradian, M. Geller, P. H. Levine, L. B. Stotts, D. H. Stephens, Appl. Opt. 19, 11 (1980).
    [CrossRef] [PubMed]
  6. A. Ishimaru, Opt. Eng. 20, 63 (1981).
    [CrossRef]
  7. J. H. Shapiro, C. Warde, Opt. Eng. 20, 76 (1981).
    [CrossRef]
  8. D. J. Laws, S. A. Parsons, “The Relation of Raindrop Size to Intensity,” Trans. Am. Geophys. Union, pp. 452–460 (1943).
  9. V. N. Kelkar, Indian J. Meteorol. Geophys. 4, 583 (1961).
  10. G. E. Weibel, H. O. Dressel, Proc. IEEE 55, 497 (1967).
    [CrossRef]
  11. S. L. Goddard, IEEE Trans. Antennas Propag. AP-18, 530 (1970).
    [CrossRef]
  12. Y. Furuhama, T. Ihara, IEEE Trans. Antennas Propag. AP-29, 275 (1981).
    [CrossRef]
  13. R. K. Crane, “Microwave Scattering Parameters for New England Rain,” MIT, Lexington, Mass., 1966, AD-647798.
  14. R. F. Lutomirski, Appl. Opt. 17, 3915 (1978).
    [CrossRef] [PubMed]
  15. D. A. deWolf, Appl. Opt. 17, 1280 (1978).
    [CrossRef]
  16. D. E. Setzer, Bell Syst. Tech. J. 49, 1873 (1970).
  17. H. T. Yura, Appl. Opt. 10, 114 (1971).
    [CrossRef] [PubMed]
  18. A. Ishimaru, Appl. Opt. 17, 348 (1978).
    [CrossRef] [PubMed]
  19. G. V. Rozenberg, Atmos. Ocean Phys. 3, 930 (1967).
  20. R. L. Olsen, Radio Sci. 16, 761 (1981).
    [CrossRef]
  21. F. Fedi, “Atmospheric Effects on Electromagnetic-Wave Free Propagation at Frequencies Above 19 GHz,” in Proceedings, European Microwave Conference 2, Brussels, Belgium (1973).
  22. N. S. Kopeika, S. Solomon, Y. Gencay, J. Opt. Soc. Am. 71, 892 (1981).
    [CrossRef]
  23. N. S. Kopeika, J. Opt. Soc. Am. 72, 1092 (1982).
    [CrossRef]
  24. G. R. Ochs, R. R. Bergman, J. R. Snyder, J. Opt. Soc. Am. 59, 231 (1969).
    [CrossRef]
  25. M. C. Thompson, F. E. Marier, K. C. Allen, IEEE Trans. Antennas Propag. AP-28, 278 (1980).
    [CrossRef]
  26. S. F. Clifford, J. W. Strohbehn, IEEE Trans. Antennas Propag. AP-18, 264 (1970).
    [CrossRef]

1982 (1)

1981 (5)

N. S. Kopeika, S. Solomon, Y. Gencay, J. Opt. Soc. Am. 71, 892 (1981).
[CrossRef]

A. Ishimaru, Opt. Eng. 20, 63 (1981).
[CrossRef]

J. H. Shapiro, C. Warde, Opt. Eng. 20, 76 (1981).
[CrossRef]

Y. Furuhama, T. Ihara, IEEE Trans. Antennas Propag. AP-29, 275 (1981).
[CrossRef]

R. L. Olsen, Radio Sci. 16, 761 (1981).
[CrossRef]

1980 (3)

M. C. Thompson, F. E. Marier, K. C. Allen, IEEE Trans. Antennas Propag. AP-28, 278 (1980).
[CrossRef]

P. Bruscaglioni, G. Milloni, G. Zaccanti, Opt. Acta 27, 1229 (1980).
[CrossRef]

G. C. Mooradian, M. Geller, P. H. Levine, L. B. Stotts, D. H. Stephens, Appl. Opt. 19, 11 (1980).
[CrossRef] [PubMed]

1978 (3)

1976 (1)

1971 (1)

1970 (3)

S. L. Goddard, IEEE Trans. Antennas Propag. AP-18, 530 (1970).
[CrossRef]

S. F. Clifford, J. W. Strohbehn, IEEE Trans. Antennas Propag. AP-18, 264 (1970).
[CrossRef]

D. E. Setzer, Bell Syst. Tech. J. 49, 1873 (1970).

1969 (1)

1967 (3)

G. V. Rozenberg, Atmos. Ocean Phys. 3, 930 (1967).

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

G. E. Weibel, H. O. Dressel, Proc. IEEE 55, 497 (1967).
[CrossRef]

1961 (1)

V. N. Kelkar, Indian J. Meteorol. Geophys. 4, 583 (1961).

1943 (1)

D. J. Laws, S. A. Parsons, “The Relation of Raindrop Size to Intensity,” Trans. Am. Geophys. Union, pp. 452–460 (1943).

Allen, K. C.

M. C. Thompson, F. E. Marier, K. C. Allen, IEEE Trans. Antennas Propag. AP-28, 278 (1980).
[CrossRef]

Baird, J. R.

Bergman, R. R.

Bruscaglioni, P.

P. Bruscaglioni, G. Milloni, G. Zaccanti, Opt. Acta 27, 1229 (1980).
[CrossRef]

Clark, J. R.

Clifford, S. F.

S. F. Clifford, J. W. Strohbehn, IEEE Trans. Antennas Propag. AP-18, 264 (1970).
[CrossRef]

Crane, R. K.

R. K. Crane, “Microwave Scattering Parameters for New England Rain,” MIT, Lexington, Mass., 1966, AD-647798.

deWolf, D. A.

Dressel, H. O.

G. E. Weibel, H. O. Dressel, Proc. IEEE 55, 497 (1967).
[CrossRef]

Fedi, F.

F. Fedi, “Atmospheric Effects on Electromagnetic-Wave Free Propagation at Frequencies Above 19 GHz,” in Proceedings, European Microwave Conference 2, Brussels, Belgium (1973).

Fried, D.

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

Furuhama, Y.

Y. Furuhama, T. Ihara, IEEE Trans. Antennas Propag. AP-29, 275 (1981).
[CrossRef]

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), pp. 173–201.

Geller, M.

Gencay, Y.

Goddard, S. L.

S. L. Goddard, IEEE Trans. Antennas Propag. AP-18, 530 (1970).
[CrossRef]

Ihara, T.

Y. Furuhama, T. Ihara, IEEE Trans. Antennas Propag. AP-29, 275 (1981).
[CrossRef]

Ishimaru, A.

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), pp. 173–201.

Kelkar, V. N.

V. N. Kelkar, Indian J. Meteorol. Geophys. 4, 583 (1961).

Kopeika, N. S.

Laws, D. J.

D. J. Laws, S. A. Parsons, “The Relation of Raindrop Size to Intensity,” Trans. Am. Geophys. Union, pp. 452–460 (1943).

Levine, P. H.

Lutomirski, R. F.

Marier, F. E.

M. C. Thompson, F. E. Marier, K. C. Allen, IEEE Trans. Antennas Propag. AP-28, 278 (1980).
[CrossRef]

Milloni, G.

P. Bruscaglioni, G. Milloni, G. Zaccanti, Opt. Acta 27, 1229 (1980).
[CrossRef]

Mooradian, G. C.

Ochs, G. R.

Olsen, R. L.

R. L. Olsen, Radio Sci. 16, 761 (1981).
[CrossRef]

Parsons, S. A.

D. J. Laws, S. A. Parsons, “The Relation of Raindrop Size to Intensity,” Trans. Am. Geophys. Union, pp. 452–460 (1943).

Rearden, R. S.

Rozenberg, G. V.

G. V. Rozenberg, Atmos. Ocean Phys. 3, 930 (1967).

Setzer, D. E.

D. E. Setzer, Bell Syst. Tech. J. 49, 1873 (1970).

Shapiro, J. H.

J. H. Shapiro, C. Warde, Opt. Eng. 20, 76 (1981).
[CrossRef]

Snyder, J. R.

Solomon, S.

Stephens, D. H.

Stotts, L. B.

Strohbehn, J. W.

S. F. Clifford, J. W. Strohbehn, IEEE Trans. Antennas Propag. AP-18, 264 (1970).
[CrossRef]

Thompson, M. C.

M. C. Thompson, F. E. Marier, K. C. Allen, IEEE Trans. Antennas Propag. AP-28, 278 (1980).
[CrossRef]

Warde, C.

J. H. Shapiro, C. Warde, Opt. Eng. 20, 76 (1981).
[CrossRef]

Weibel, G. E.

G. E. Weibel, H. O. Dressel, Proc. IEEE 55, 497 (1967).
[CrossRef]

Yura, H. T.

Zaccanti, G.

P. Bruscaglioni, G. Milloni, G. Zaccanti, Opt. Acta 27, 1229 (1980).
[CrossRef]

Appl. Opt. (6)

Atmos. Ocean Phys. (1)

G. V. Rozenberg, Atmos. Ocean Phys. 3, 930 (1967).

Bell Syst. Tech. J. (1)

D. E. Setzer, Bell Syst. Tech. J. 49, 1873 (1970).

IEEE Trans. Antennas Propag. (4)

M. C. Thompson, F. E. Marier, K. C. Allen, IEEE Trans. Antennas Propag. AP-28, 278 (1980).
[CrossRef]

S. F. Clifford, J. W. Strohbehn, IEEE Trans. Antennas Propag. AP-18, 264 (1970).
[CrossRef]

S. L. Goddard, IEEE Trans. Antennas Propag. AP-18, 530 (1970).
[CrossRef]

Y. Furuhama, T. Ihara, IEEE Trans. Antennas Propag. AP-29, 275 (1981).
[CrossRef]

Indian J. Meteorol. Geophys. (1)

V. N. Kelkar, Indian J. Meteorol. Geophys. 4, 583 (1961).

J. Opt. Soc. Am. (3)

Opt. Acta (1)

P. Bruscaglioni, G. Milloni, G. Zaccanti, Opt. Acta 27, 1229 (1980).
[CrossRef]

Opt. Eng. (2)

A. Ishimaru, Opt. Eng. 20, 63 (1981).
[CrossRef]

J. H. Shapiro, C. Warde, Opt. Eng. 20, 76 (1981).
[CrossRef]

Proc. IEEE (2)

G. E. Weibel, H. O. Dressel, Proc. IEEE 55, 497 (1967).
[CrossRef]

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

Radio Sci. (1)

R. L. Olsen, Radio Sci. 16, 761 (1981).
[CrossRef]

Trans. Am. Geophys. Union (1)

D. J. Laws, S. A. Parsons, “The Relation of Raindrop Size to Intensity,” Trans. Am. Geophys. Union, pp. 452–460 (1943).

Other (3)

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976), pp. 173–201.

R. K. Crane, “Microwave Scattering Parameters for New England Rain,” MIT, Lexington, Mass., 1966, AD-647798.

F. Fedi, “Atmospheric Effects on Electromagnetic-Wave Free Propagation at Frequencies Above 19 GHz,” in Proceedings, European Microwave Conference 2, Brussels, Belgium (1973).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Heterodyne efficiency as a function of normalized receiver diameter for the random scatter nonturbulent channel. Heterodyne efficiency is defined as effective heterodyne receiver area normalized to the actual receiver area, and the receiver diameter is normalized to the particle radius.

Fig. 2
Fig. 2

Same as Fig. 1 but for a random scatter turbulent channel. The ratio ρt/a is equal to 10.

Fig. 3
Fig. 3

Sarne as Fig. 2, but ρt/a = 103.

Fig. 4
Fig. 4

Same as Fig. 2, but ρt/a = 105.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

R actual receiver diameter scattering particulate diameter .
a ( t , r ) = s ( t , r ) + b ( t ) .
F ( t 1 , t 2 , r 1 , r 2 ) E [ s ( t 1 , r 1 ) · s * ( t 2 , r 2 ) ] / I s ,
F ( t 1 , t 2 , r 1 , r 2 ) = R ( t 1 , t 2 ) · M ( r 1 , r 2 ) ,
M s ( ρ ) = { exp [ ( ρ a ) 2 S a z ] , ρ a exp ( S a z ) , ρ 2 a S a z 1 ,
M s ( ρ ) = { exp [ ( ρ a ) 2 S a z ] , ρ a exp ( S a z ) , ρ a S a z 1.
SNR = 2 η I s A r e ( h ν + 2 η N o b ) · 2 B s ,
A r e A r A r M ( r 1 , r 2 ) w 0 ( r 1 ) w 0 * ( r 2 ) d r 1 d r 2 .
A r e = 2 π 0 d M ( ρ ) R 0 ( ρ ) ρ d ρ ,
A r e = 4 d 2 0 a { exp [ ( ρ a ) 2 S a z ] } [ d 2 cos 1 ( ρ d ) ρ ( d 2 ρ 2 ) 1 / 2 ] ρ d p + 4 d 2 exp ( S a z ) a d [ d 2 cos 1 ( ρ d ) ρ ( d 2 ρ 2 ) 1 / 2 ] ρ d ρ .
A r e = 4 d 2 { 0 Δ 1 [ exp ( Δ 2 x 2 S a z ) ] [ x cos 1 x x 2 ( 1 x 2 ) 1 / 2 ] d x + exp ( S a z ) · [ Δ 2 1 8 Δ 4 ( Δ 2 + 2 ) + ( 1 8 1 2 Δ 2 ) arccos 1 Δ ] } .
Y A r e / A r ,
M t ( ρ ) = exp [ ( ρ / ρ t ) 5 / 3 ] ,
ρ t = ( 0.5 k 2 C n 2 z ) 3 / 5 ,
M ( ρ ) = { exp [ ( ρ a ) 2 S a z ] · exp [ ( ρ ρ t ) 5 / 3 ] , ρ a exp ( S a z ) exp [ ( ρ ρ t ) 5 / 3 ] , ρ > a .
A r e = 4 d 2 { 0 a { exp [ ( ρ a ) 2 S a z ( ρ ρ t ) 5 / 3 ] } [ d 2 cos 1 ( ρ d ) ρ ( d 2 ρ 2 ) 1 / 2 ] ρ d ρ + exp ( S a z ) a d { exp [ ( ρ ρ t ) 5 / 3 ] } [ d 2 cos 1 ( ρ d ) ρ ( d 2 ρ 2 ) 1 / 2 ] ρ d ρ } .
A r e A r = 16 π { 0 Δ 1 { exp [ x 2 Δ 2 S a z ( x · Δ · a ρ t ) 5 / 3 ] } · [ x cos 1 x x 2 ( 1 x 2 ) 1 / 2 ] d x + exp ( S a z ) Δ 1 1 { exp [ ( x Δ a ρ t ) 5 / 3 ] } · [ x cos 1 x x 2 ( 1 x 2 ) 1 / 2 ] d x } } .

Metrics