Abstract

A new technique for modifying the coherence of a light field is described theoretically, and experimental confirmation is presented. A hologram of a coherently illuminated spatially random diffuser and a reference plane wave is recorded. When the processed hologram is placed back into position and the diffuser is illuminated by partially coherent light, the coherent reference plane wave is reconstructed by the hologram. Thus this optical system can be used to separate a coherent component from partially coherent illumination.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. H. Carter and E. Wolf, “Coherence properties of Lambertian and non-Lambertian sources,” J. Opt. Soc. Am. 65, 1067–1071 (1975).
    [Crossref]
  2. W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
    [Crossref]
  3. F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
    [Crossref]
  4. P. DeSantis and et al., “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
    [Crossref]
  5. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 139–142.
  6. D. Courjon and J. Bulabois, “Modifications of the coherence properties of a light beam: applications in optical processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 194, 129–134 (1979).
  7. L. H. Enloe, “Noise-like structure in the image of diffusely reflecting objects in coherent illumination,” Bell Syst. Tech. J. 46, 1479–1489 (1967).
    [Crossref]
  8. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

1979 (3)

F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
[Crossref]

P. DeSantis and et al., “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

D. Courjon and J. Bulabois, “Modifications of the coherence properties of a light beam: applications in optical processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 194, 129–134 (1979).

1975 (1)

1967 (1)

L. H. Enloe, “Noise-like structure in the image of diffusely reflecting objects in coherent illumination,” Bell Syst. Tech. J. 46, 1479–1489 (1967).
[Crossref]

1964 (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

Bulabois, J.

D. Courjon and J. Bulabois, “Modifications of the coherence properties of a light beam: applications in optical processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 194, 129–134 (1979).

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 139–142.

Carter, W. H.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 139–142.

Courjon, D.

D. Courjon and J. Bulabois, “Modifications of the coherence properties of a light beam: applications in optical processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 194, 129–134 (1979).

DeSantis, P.

P. DeSantis and et al., “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

Enloe, L. H.

L. H. Enloe, “Noise-like structure in the image of diffusely reflecting objects in coherent illumination,” Bell Syst. Tech. J. 46, 1479–1489 (1967).
[Crossref]

Gori, F.

F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
[Crossref]

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 139–142.

Martienssen, W.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Spiller, E.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Wolf, E.

Am. J. Phys. (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Bell Syst. Tech. J. (1)

L. H. Enloe, “Noise-like structure in the image of diffusely reflecting objects in coherent illumination,” Bell Syst. Tech. J. 46, 1479–1489 (1967).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

F. Gori, “Lau effect and coherence theory,” Opt. Commun. 31, 4–8 (1979).
[Crossref]

P. DeSantis and et al., “An example of a Collett–Wolf source,” Opt. Commun. 29, 256–260 (1979).
[Crossref]

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

D. Courjon and J. Bulabois, “Modifications of the coherence properties of a light beam: applications in optical processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 194, 129–134 (1979).

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1975).

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 139–142.

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

Diagrams of the optical systems for (a) recording and (b) reconstructing the hologram.

Fig. 2
Fig. 2

Experimental setups for (a) recording and (b) reconstructing the hologram.

Fig. 3
Fig. 3

Diagram of the mechanical holder that keeps the hologram in place in a simplified lensless setup in which DD′ ≃ 10 cm.

Fig. 4
Fig. 4

Photograph of the far-field intensity reconstructed from the hologram and showing an image of the point M′ surrounded by a weak halo.

Equations (27)

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

U ( ξ ) = n = 1 N a n δ 2 ( ξ - ξ n ) ,
U 0 ( x ) = + - U ( ξ ) exp ( i k ξ · x f ) d 2 ξ ,
U 0 ( x ) = n = 1 N a n exp ( i k ξ n · x f ) .
U r ( x ) = A ( x ) exp ( i k x sin θ ) .
E U r ( x ) + U 0 ( x ) 2 ,
S ( x ) = C { A ( x ) 2 + | n = 1 N a n exp ( i k ξ n · x f ) | 2 + A ( x ) n = 1 N a n * exp [ i k ( x sin θ - ξ n · x f ) ] + c . c . } .
S ( x ) = C E ,
0 S 1.
W ( ξ 1 , ξ 2 ) = n = 1 N a n ( t ) δ 2 ( ξ 1 - ξ n ) × m = 1 N a * m ( t ) δ 2 ( ξ 2 - ξ m ) .
W ( ξ 1 , ξ 2 ) = δ 2 ( ξ 1 - ξ 2 ) n = 1 N a n ( t ) 2 δ 2 ( ξ 1 - ξ n ) .
a n 2 = a n ( t ) 2 .
W ( ξ 1 , ξ 2 ) = δ 2 ( ξ 1 - ξ 2 ) n = 1 N a n 2 δ 2 ( ξ 1 - ξ n ) .
W 0 ( x 1 , x 2 ) = + - W ( ξ 1 , ξ 2 ) × exp [ i k ( ξ 1 · x 1 f - ξ 2 · x 2 f ) ] d 2 ξ 1 d 2 ξ 2 .
W 0 ( x 1 , x 2 ) = n = 1 N a n 2 exp [ i l ξ n · ( x 1 - x 2 f ) ] .
W ( x 1 , x 2 ) = W 0 ( x 1 , x 2 ) S ( x 1 ) S * ( x 2 ) .
W ( x 1 , x 2 ) = C 2 n = 1 N a n 2 exp [ i k ξ n · ( x 1 - x 2 f ) ] × A ( x 1 ) m = 1 N a m * exp [ i k ( x 1 sin θ - ξ m · x 1 f ) ] × A * ( x 2 ) l = 1 N a l * exp [ - i k ( x 2 sin θ - ξ l · x 2 f ) ] ,
J ( s ) = ( 2 π k ) 2 cos 2 θ W ˜ 12 ( k s , - k s ) ,
W ˜ ( k s , - k s ) = 1 λ 4 + - W ( x 1 , x 2 ) × exp [ - i k s · ( x 1 - x 2 ) ] d 2 x 1 d 2 x 2 .
W ˜ ( k s , - k s ) = C 2 λ 4 × + - n , m , l N a n 2 a m * a l exp [ i k ( x 1 - x 2 ) sin θ ] × A ( x 1 ) A * ( x 2 ) exp [ i k ( x 1 - x 2 f ) · ξ n ] × exp [ - i k ( x 1 · ξ m f - x 2 · ξ l f ) ] × exp [ - i k ( x 1 - x 2 ) · s ] d 2 x 1 d 2 x 2 .
W ˜ ( k s , - k s ) = | C 2 n , m , l N a n 2 a m * a l A ˜ ( s - - ξ n + ξ m - τ sin θ ) × A ˜ * ( s - ξ n + ξ l - τ sin θ ) ,
A ˜ ( u ) = 1 λ 2 + - A ( x ) exp ( - i k x · u ) d 2 x
A ˜ ( u ) ~ A δ 2 ( u ) ,
W ˜ ( k s , - k s ) = C 2 A 2 n , m N a n 2 a m 2 δ 2 ( s - τ sin θ - ξ n + ξ m ) ,
J ( s ) = ( 2 π k ) 2 cos 2 θ C 2 A 2 × n , m a n 2 a m 2 δ 2 [ s - τ sin θ + ( ξ m - ξ n ) ] .
J ( s ) = ( 2 π k ) 2 cos 2 θ C 2 A 2 N a 4 δ 2 ( s - τ sin θ ) ,
W ( x 1 , x 2 ) = ( n = 1 N a n 2 ) A ( x 1 ) A * ( x 2 ) exp [ i k ( x 1 - x 2 ) sin θ ] + W ( x 1 , x 2 ) .
μ ( x 1 , x 2 ) = W ( x 1 , x 2 ) [ W ( x 1 , x 1 ) W ( x 2 , x 2 ) ] 2 = exp [ i k ( x 1 - x 2 ) sin θ + i arg ( W ) ] .