Abstract

Expressions are derived, valid within the accuracy of the first Born approximation, for the cross-spectral density and for the spectral intensity of the field that is produced by scattering of radiation of any state of spatial coherence. The results are illustrated by examples that show quantitatively the difference between scattering of laser light and of ambient light. It is suggested that the dependence of the scattered intensity on the degree of spatial coherence of the incident radiation could be utilized to make devices that would discriminate between a laser beam and diffuse light.

© 1988 Optical Society of America

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References

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  1. R. Crane, U.S. patent3,824,018 (July16, 1974).
  2. R. Crane, Opt. Eng. 18, 212 (1979).
  3. E. T. Siebert, U.S. patent4,536,089 (August20, 1985).
  4. W. T. Krohn, M. J. McNally, R. Abreu, U.S. patent4,600,307 (July15, 1986).
  5. E. Wolf, G. S. Agarwal, J. Opt. Soc. Am. A 1, 541 (1984).
    [CrossRef]
  6. See, for example, P. Roman, Advanced Quantum Theory (Addison-Wesley, Reading, Mass., 1965), Sec. 3-2.
  7. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Sec. 4–5.
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Sec. 10.2.
  9. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982); J. Opt. Soc. Am. A 3, 76 (1986), Eq. (3.11).
    [CrossRef]
  10. L. Mandel, E. Wolf, J. Opt. Soc. Am. 66, 529 (1976), Sec. II.
    [CrossRef]

1984 (1)

1982 (1)

1979 (1)

R. Crane, Opt. Eng. 18, 212 (1979).

1976 (1)

L. Mandel, E. Wolf, J. Opt. Soc. Am. 66, 529 (1976), Sec. II.
[CrossRef]

Abreu, R.

W. T. Krohn, M. J. McNally, R. Abreu, U.S. patent4,600,307 (July15, 1986).

Agarwal, G. S.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Sec. 10.2.

Crane, R.

R. Crane, Opt. Eng. 18, 212 (1979).

R. Crane, U.S. patent3,824,018 (July16, 1974).

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Sec. 4–5.

Krohn, W. T.

W. T. Krohn, M. J. McNally, R. Abreu, U.S. patent4,600,307 (July15, 1986).

Mandel, L.

L. Mandel, E. Wolf, J. Opt. Soc. Am. 66, 529 (1976), Sec. II.
[CrossRef]

McNally, M. J.

W. T. Krohn, M. J. McNally, R. Abreu, U.S. patent4,600,307 (July15, 1986).

Roman, P.

See, for example, P. Roman, Advanced Quantum Theory (Addison-Wesley, Reading, Mass., 1965), Sec. 3-2.

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Sec. 4–5.

Siebert, E. T.

E. T. Siebert, U.S. patent4,536,089 (August20, 1985).

Wolf, E.

E. Wolf, G. S. Agarwal, J. Opt. Soc. Am. A 1, 541 (1984).
[CrossRef]

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982); J. Opt. Soc. Am. A 3, 76 (1986), Eq. (3.11).
[CrossRef]

L. Mandel, E. Wolf, J. Opt. Soc. Am. 66, 529 (1976), Sec. II.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Sec. 10.2.

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

R. Crane, Opt. Eng. 18, 212 (1979).

Other (6)

E. T. Siebert, U.S. patent4,536,089 (August20, 1985).

W. T. Krohn, M. J. McNally, R. Abreu, U.S. patent4,600,307 (July15, 1986).

See, for example, P. Roman, Advanced Quantum Theory (Addison-Wesley, Reading, Mass., 1965), Sec. 3-2.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), Sec. 4–5.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Sec. 10.2.

R. Crane, U.S. patent3,824,018 (July16, 1974).

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Figures (1)

Fig. 1
Fig. 1

The ratio f(θ; kσ) = [I(s)]coh./[I(s)]amb. calculated from Eqs. (20) and (22).

Equations (22)

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[ 2 + k 2 n 2 ( r ) ] U ( s ) ( r ) = 0 ,
U ( s ) ( r , ω ) = D F ( r , ω ) U ( r , ω ) G ( r , r ; ω ) d 3 r ,
F ( r , ω ) = 1 4 π k 2 [ n 2 ( r , ω ) - 1 ]
G ( r , r ; ω ) = exp ( i k r - r ) r - r
U ( s ) ( r , ω ) = D F ( r , ω ) U ( i ) ( r , ω ) G ( r , r ; ω ) d 3 r .
W ( i ) ( r 1 , r 2 , ω ) = - Γ ( i ) ( r 1 , r 2 , τ ) exp ( i ω τ ) d τ ,
Γ ( i ) ( r 1 , r 2 , τ ) = V ( i ) * ( r 1 , t ) V ( i ) ( r 2 , t + τ )
W ( i ) ( r 1 , r 2 , ω ) = U ( i ) * ( r 1 , ω ) U ( i ) ( r 2 , ω ) ω .
W ( s ) ( r 1 , r 2 , ω ) = U ( s ) * ( r 1 , ω ) U ( s ) ( r 2 , ω ) ω .
W ( s ) ( r 1 , r 2 , ω ) = D D F * ( r 1 , ω ) F ( r 2 , ω ) W ( i ) ( r 1 , r 2 , ω ) × G * ( r 1 , r 1 ; ω ) G ( r 2 , r 2 ; ω ) d 3 r 1 d 3 r 2 .
I ( s ) ( r , ω ) = D D F * ( r 1 , ω ) F ( r 2 , ω ) W ( i ) ( r 1 , r 2 , ω ) × G * ( r , r 1 ; ω ) G ( r , r 2 ; ω ) d 3 r 1 d 3 r 2 .
μ ( i ) ( r 1 , r 2 , ω ) = W ( i ) ( r 1 , r 2 , ω ) I ( i ) ( r 1 , ω ) I ( i ) ( r 2 , ω ) .
I ( s ) ( r , ω ) = D D F * ( r 1 , ω ) F ( r 2 , ω ) μ ( i ) ( r 1 , r 2 , ω ) × I ( i ) ( r 1 , ω ) I ( i ) ( r 2 , ω ) G * ( r , r 1 ; ω ) × G ( r , r 2 , ω ) d 3 r 1 d 3 r 2 .
G ( r u , r ; ω ) ~ exp ( i k r ) r exp ( - i k u · r )             as k r ,
I ( s ) ( r u , ω ) = 1 r 2 D D F * ( r 1 , ω ) F ( r 2 , ω ) × μ ( i ) ( r 1 , r 2 , ω ) I ( i ) ( r 1 , ω ) I ( i ) ( r 2 , ω ) × exp [ - i k u · ( r 2 - r 1 ) ] d 3 r 1 d 3 r 2 .
C F ( r 1 , r 2 , ω ) = F * ( r 1 , ω ) F ( r 2 , ω ) F .
I ( s ) ( r u , ω ) = 1 r 2 D D C F ( r 1 , r 2 , ω ) × μ ( i ) ( r 1 , r 2 , ω ) I ( i ) ( r 1 , ω ) I ( i ) ( r 2 , ω ) × exp [ - i k u · ( r 2 - r 1 ) ] d 3 r 1 d 3 r 2 .
C F ( r 1 , r 2 , ω ) = A ( σ 2 π ) 3 exp [ - r 2 - r 1 2 / 2 σ 2 ] ,
W ( i ) ( r 1 , r 2 , ω ) = I ( i ) ( ω ) exp [ i k s 0 · ( r 2 - r 1 ) ] .
[ I ( s ) ( r u , ω ) ] coh . = A V r 2 I ( i ) ( ω ) exp [ - 2 ( k σ ) 2 sin 2 ( θ / 2 ) ] ,
W ( i ) ( r 1 , r 2 , ω ) = I ( i ) ( ω ) sin k r 2 - r 1 k r 2 - r 1 .
[ I ( s ) ( r u , ω ) ] amb . = A V r 2 1 2 ( k σ ) 2 I ( i ) ( ω ) { 1 - exp [ - 2 ( k σ ) 2 ] } .

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