Abstract

A novel approach to the inversion of optical scattering data is proposed and investigated. The proposed technique uses only forward scattering data as opposed to the previous research where angle scattering was used. Our method does not use scattering attenuation; in fact, only relative values of the measured signals are important in the suggested technique. Nevertheless, both the scattering coefficient and the scattering particle size may be effectively estimated. The proposed method relies on the fact that, as coherent light travels through a random scattering medium, its coherence deteriorates. The degree of coherence degradation may be described in terms of the mutual intensity function (MIF). The shape of the MIF depends on the scattering particle size and on the scattering coefficient. If a coherent receiver is used to detect forward scattered radiation, its output signal depends on the receiver diameter and on the MIF. Dependence of the receiver output signal on the receiver diameter carries information about the MIF and therefore about the scattering particle size and the scattering coefficient. This information may be extracted by means of the techniques suggested in this paper. Several possible realizations of the proposed device are discussed and analyzed. The results of our study imply that the suggested method can be conveniently implemented. For example, if the technique is used to measure a path-averaged raindrop size, the power needed at the receiver is <1 μW, the propagation path should be of the order of 1 km, and the measurement time required may be of the order of 10 sec. The data processing required is also relatively straightforward and may be handled by a microprocessor. The analysis was performed under the assumption that all the scattering particles have the same size. However, it was also shown that the suggested technique may be generalized to handle an arbitrary large number of groups of scattering particle having distinctly different sizes. Further generalization of the proposed technique to the case of continuous particle size distributions is described in a subsequent paper ( Appl. Opt. 23, 455 ( 1984).

© 1984 Optical Society of America

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References

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  1. M. Z. Hansen, Appl. Opt. 19, 3441 (1980).
    [CrossRef] [PubMed]
  2. M. Z. Hansen, W. H. Evans, Appl. Opt. 19, 3389 (1980).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. G. V. Rosenberg, Atmos. Oceanic Phys. 3, 545 (1967).
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    [CrossRef] [PubMed]
  7. A. de Wolf, Appl. Opt. 17, 1280 (1978).
    [CrossRef] [PubMed]
  8. A. Ishimaru, Appl. Opt. 17, 348 (1978).
    [CrossRef] [PubMed]
  9. R. F. Lutomirski, Appl. Opt. 17, 3915 (1978).
    [CrossRef] [PubMed]
  10. L. G. Kazovsky, N. S. Kopeika, Appl. Opt. 22, 706 (1983).
    [CrossRef] [PubMed]
  11. L. G. Kazovsky, N. S. Kopeika, “The Turbulent Scattering Channel: Effective Heterodyne Receiver Size for Optical Through Millimeter Wavelengths,” in Proceedings, International Conference on Communications, ICC 82, Philadelphia (IEEE, New York, 1982).
  12. Optics Guide 2 (Melles Griot, Inc., Irvine, Calif., 1982), p. 303.
  13. D. L. Fried, Proc. IEEE 55, 57 (1967).
    [CrossRef]
  14. R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).
  15. C. P. Sandback, Ed., Optical Fibre Communication Systems (Wiley, New York, 1980).
  16. R. G. Seippel, Optoelectronics (Prentice-Hall, Reston, Va., 1981).
  17. T. Wang, R. S. Lawrence, M. K. Tsay, Appl. Opt. 19, 3617 (1980).
    [CrossRef] [PubMed]
  18. L. G. Kazovsky, Appl. Opt. 23, 455 (1984).
    [CrossRef] [PubMed]

1984 (1)

1983 (1)

1982 (3)

1980 (3)

1978 (3)

1967 (2)

G. V. Rosenberg, Atmos. Oceanic Phys. 3, 545 (1967).

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

Byer, R. L.

de Wolf, A.

Evans, W. H.

Fried, D. L.

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

Gagliardi, R. M.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).

Hansen, M. Z.

Ishimaru, A.

Karp, S.

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).

Kazovsky, L. G.

L. G. Kazovsky, Appl. Opt. 23, 455 (1984).
[CrossRef] [PubMed]

L. G. Kazovsky, N. S. Kopeika, Appl. Opt. 22, 706 (1983).
[CrossRef] [PubMed]

L. G. Kazovsky, N. S. Kopeika, “The Turbulent Scattering Channel: Effective Heterodyne Receiver Size for Optical Through Millimeter Wavelengths,” in Proceedings, International Conference on Communications, ICC 82, Philadelphia (IEEE, New York, 1982).

Kopeika, N. S.

L. G. Kazovsky, N. S. Kopeika, Appl. Opt. 22, 706 (1983).
[CrossRef] [PubMed]

L. G. Kazovsky, N. S. Kopeika, “The Turbulent Scattering Channel: Effective Heterodyne Receiver Size for Optical Through Millimeter Wavelengths,” in Proceedings, International Conference on Communications, ICC 82, Philadelphia (IEEE, New York, 1982).

Lawrence, R. S.

Lutomirski, R. F.

Miller, J. R.

O’Neil, N. T.

Raskin, V.

Rosenberg, G. V.

G. V. Rosenberg, Atmos. Oceanic Phys. 3, 545 (1967).

Seippel, R. G.

R. G. Seippel, Optoelectronics (Prentice-Hall, Reston, Va., 1981).

Tsay, M. K.

Wang, T.

Wolfe, D. C.

Appl. Opt. (11)

Atmos. Oceanic Phys. (1)

G. V. Rosenberg, Atmos. Oceanic Phys. 3, 545 (1967).

Proc. IEEE (1)

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

Other (5)

R. M. Gagliardi, S. Karp, Optical Communications (Wiley, New York, 1976).

C. P. Sandback, Ed., Optical Fibre Communication Systems (Wiley, New York, 1980).

R. G. Seippel, Optoelectronics (Prentice-Hall, Reston, Va., 1981).

L. G. Kazovsky, N. S. Kopeika, “The Turbulent Scattering Channel: Effective Heterodyne Receiver Size for Optical Through Millimeter Wavelengths,” in Proceedings, International Conference on Communications, ICC 82, Philadelphia (IEEE, New York, 1982).

Optics Guide 2 (Melles Griot, Inc., Irvine, Calif., 1982), p. 303.

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Figures (8)

Fig. 1
Fig. 1

Block diagram of the proposed device.

Fig. 2
Fig. 2

Alternative method to control the active receiver area; several detectors with different active areas can be used. Switching to a different detector diameter is accomplished by rotating the disk so that the scattered light falls on the detector with the appropriate diameter.

Fig. 3
Fig. 3

Alternative method to control the active receiver area; a composite detector is used. The detector consists of several nonoverlapping rings and a small central circle. The active detector area is controlled by combining the output current of the central circle with the output currents of several rings. Electronic switches are controlled by the central processor of Fig. 1.

Fig. 4
Fig. 4

Mutual intensity function (MIF) vs ρ. All the scattering particles are assumed to be the same size.

Fig. 5
Fig. 5

Yield Y,dB vs the normalized diaphragm diameter Δ ≜ D/a. All the scattering particles are assumed to be the same size.

Fig. 6
Fig. 6

Log Δ0 vs S a Z. Δ0 is the value of Δ at which condition (15) is satisfied; S a Z is the scattering attenuation.

Fig. 7
Fig. 7

Mutual intensity function (MIF) vs ρ. The scattering medium includes two different types of scatterer.

Fig. 8
Fig. 8

Yield Y,dB vs the normalized diaphragm diameter Δ ≜ D/a1. The scattering medium includes two different types of scatterer.

Equations (38)

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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 ( ρ ) = { exp [ - ( ρ a ) 2 S a Z ] , ρ a exp ( - S a Z ) , ρ a             S a Z 1 ,
i ¯ = η A O A ¯ S · [ π 0 D ρ d ρ K O ( ρ ) M ( ρ ) ] 1 / 2 ,
K O ( ρ ) = { 1 2 [ D 2 arccos ρ D - ρ ( D 2 - ρ 2 ) 1 / 2 ] , ρ D , 0 , ρ D .
i ¯ = η A O A ¯ S 2 · π D 2 4 · 4 π · { 0 Δ - 1 [ arccos x - x ( 1 - x 2 ) 1 / 2 ] · exp [ - x 2 Δ 2 S a Z ] x d x + exp ( - S a Z ) · [ ( Δ 2 + 2 ) 8 Δ 4 Δ 2 - 1 + ( 1 8 - 1 2 Δ 2 ) arccos 1 Δ ] } 1 / 2 if Δ 1 ,
i ¯ = η A O A ¯ S 2 · π D 2 4 · 4 π · { 0 1 [ arccos x - x ( 1 - x 2 ) 1 / 2 ] · exp ( - x 2 Δ 2 S a Z ) x d x } 1 / 2             if Δ 1 ,
Y K · i ¯ / S = K · i ¯ / D 2 ,
K 4 2 / ( π η A o A ¯ S ) .
Y = 4 π { 0 Δ - 1 [ arccos x - x ( 1 - x 2 ) 1 / 2 ] · exp [ - x 2 · Δ 2 · S a Z ] · x d x + exp ( - S a Z ) × [ ( Δ 2 + 2 ) 8 Δ 4 Δ 2 - 1 + ( 1 8 - 1 2 Δ 2 ) arccos 1 Δ ] } 1 / 2             if Δ > 1 ,
Y = 4 π { 0 1 [ arccos x - x · ( 1 - x 2 ) 1 / 2 ] · exp ( - x 2 Δ 2 S a Z ) x d x } 1 / 2             if Δ < 1.
Y , dB = 20 log Y .
Y , dB Δ 1 - Y , dB Δ 1 = 20 log exp ( S a Z / 2 ) = S a Z · 10 log e = 4.34 · S a Z .
Y , dB Δ 1 - Y , dB Δ 1 = 20 log i ¯ min D max 2 / i ¯ max D min 2 ,
D min a D max .
S a Z = 4.6 log i min D max 2 / i ¯ max D min 2 .
Y , dB = Y min , dB + 3 dB .
log Δ 0 = 0.206 · S a Z ,
Δ 0 = exp ( 0.474 · S a Z ) = exp ( S a Z / 2.1 ) .
Y , dB = Y min , dB + 3 dB .
a = D 0 / Δ 0 .
N = e η S A 0 2 ,
S N = i ¯ 2 N = η e · 1 2 · A S 2 · S min · [ Y D min ] 2 ,
S N = η e · A ¯ s 2 2 · S min = R e · I S · S min = R e · P min ,
P beam = P min · ( D max / D min ) 2 .
M ( ρ ) = M 1 ( ρ ) · M 2 ( ρ ) ,
M ( ρ ) = { exp [ - ( ρ a 1 ) 2 S a 1 Z - ( ρ a 2 ) 2 S a 2 Z ] , ρ a 1 , exp [ - S a 1 Z - ( ρ a 2 ) 2 S a 2 Z ] , a 1 ρ a 2 , exp [ - S a 1 Z - S a 2 Z ] , ρ a 2 .
Y = 4 π [ 0 1 f 1 ( x ) · f 2 ( x ) · x d x ] 1 / 2 ,
f 1 ( x ) { exp [ - x 2 Δ 2 S a 1 Z - x 2 Δ 2 S a 2 Z / a 2 n 2 ] , x · Δ 1 , exp [ - S a 1 Z - x 2 Δ 2 S a 2 Z / a 2 n 2 ] , 1 x · Δ a 2 n , exp [ - S a 1 Z - S a 2 Z ] , x · Δ a 2 n ,
f 2 ( x ) arccos x - x 1 - x 2 ,
a 2 n a 2 / a 1 .
Y , dB Δ 1 - Y , dB plateau = 20 log exp ( S a 1 Z / 2 ) = 4.34 · S a 1 Z ,
Y , dB plateau - Y , dB Δ 1 = 20 log exp ( S a 2 Z / 2 ) = 4.34 · S a 2 Z .
Y , dB = Y plateau , dB + 3 dB .
Y , dB = Y min , dB + 3 dB .
a 1 = D 1 / Δ 1 ,
a 2 = D 2 / Δ 2 .
a 2 a 1 .

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