Abstract

In this paper, we will illustrate a new technique by which the hologram image speckle can be reduced by spatially random sampling of the hologram aperture. The sampling procedure can be performed by a movable random mask. If the sampling function is made to be uncorrelated in subsequent spatial sampling, the speckle effect in the hologram image can be eliminated. However, an optimum sampling function may be difficult to obtain, which remains to be seen. This speckle reduction technique can be achieved only by some trade-off of the holographic resolution. A simple experimental confirmation of this technique is illustrated. Since one of the most severely limiting factors in applications of holography may be the speckle effect, this proposed technique should be added, together with the other existent techniques, to remedy this limiting factor.

© 1973 Optical Society of America

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References

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  1. J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).
  2. B. M. Oliver, Proc. IEEE 51, 220 (1963).
    [Crossref]
  3. L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).
  4. H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, Appl. Opt. 7, 2301 (1968).
    [Crossref] [PubMed]
  5. D. Gabor, IBM J. Res. Dev. 14, 509 (1970).
    [Crossref]
  6. H. J. Caulfield, Opt. Commun. 3, 323 (1971).
    [Crossref]
  7. R. F. van Ligten, Appl. Opt. 12, 255 (1973).
    [Crossref] [PubMed]
  8. A. D. Gara, private communication.
  9. F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography, (MIT Press, Cambridge, Mass., 1973).

1973 (1)

1971 (1)

H. J. Caulfield, Opt. Commun. 3, 323 (1971).
[Crossref]

1970 (1)

D. Gabor, IBM J. Res. Dev. 14, 509 (1970).
[Crossref]

1968 (1)

1967 (1)

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

1963 (1)

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[Crossref]

1962 (1)

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Caulfield, H. J.

H. J. Caulfield, Opt. Commun. 3, 323 (1971).
[Crossref]

Enloe, L. H.

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

Gabor, D.

D. Gabor, IBM J. Res. Dev. 14, 509 (1970).
[Crossref]

Gara, A. D.

A. D. Gara, private communication.

Gerritsen, H. J.

Gordon, E. I.

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Hannan, W. J.

Oliver, B. M.

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[Crossref]

Ramberg, E. G.

Rigden, J. D.

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

van Ligten, R. F.

Yu, F. T. S.

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography, (MIT Press, Cambridge, Mass., 1973).

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

IBM J. Res. Dev. (1)

D. Gabor, IBM J. Res. Dev. 14, 509 (1970).
[Crossref]

Opt. Commun. (1)

H. J. Caulfield, Opt. Commun. 3, 323 (1971).
[Crossref]

Proc. IEEE (1)

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[Crossref]

Proc. IRE (1)

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Other (2)

A. D. Gara, private communication.

F. T. S. Yu, Introduction to Diffraction, Information Processing, and Holography, (MIT Press, Cambridge, Mass., 1973).

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Figures (5)

Fig. 1
Fig. 1

An off-axis wavefront recording. O, diffuse object; P. photographic plate; v, oblique reference wave.

Fig. 2
Fig. 2

Schematic diagram of speckle reduction by random spatial sampling. f(x,y), the sampling function; H, hologram; v, monochromatic illumination; P, photographic plate.

Fig. 3
Fig. 3

A rotating circular sampler for the experiment.

Fig. 4
Fig. 4

Real hologram image by spatial sampling technique; area magnification, 60×.

Fig. 5
Fig. 5

Conventional real hologram image without the sampling technique; area magnification, 60×.

Equations (14)

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u ( x , y ) = n = 1 N a n r n exp ( i k r n ) ,
u ( x , y ) 1 R n = 1 N a n exp [ i k ( R - ζ n ) ] exp { i k 2 R [ ( x - ξ n ) 2 + ( y - η n ) 2 } ,
I ( ρ ; k ) = ( u + v ) ( u + v ) * = b 2 + 1 R 2 i = 1 N j = 1 N a i a j cos { k [ ϕ i ( x , y ) - ϕ j ( x , y ) ] } + 2 b R n = 1 N a n cos { k [ x sin θ + ϕ n ( x , y ) ] } , i j ,
T ( ρ ; k ) = K I ( ρ ; k ) ,
E r ( σ ; k ) = K - L y 2 L y 2 - L x 2 L x 2 n = 1 N a n exp [ i k ϕ n ( x , y ) ] E l + ( σ - ρ ; k ) d x d y ,
f ( x , y ; t ) = { 1 , over the open aperture , 0 , otherwise ,
u ( x , y ; t ) = K f ( x , y ; t ) ,
E ( σ ; t ; k ) = f ( x , y ; t ) T ( x , y ) E l + ( σ - ρ ; k ) d x d y ,
E r ( σ ; t ; k ) = C O * ( σ ; k ) N * ( σ ; t ; k ) ,
I ( σ ; t ; k ) = K O ( σ ; k ) 2 N ( σ ; t ; k ) 2 .
E ( α , β ) = 0 T I ( σ ; t ; k ) d t = K 0 ( σ ; k ) 2 0 T N ( σ ; t ; k ) 2 d t ,
T f ( ρ ; t ) f ( ρ ; t + τ ) d t 0 , > 0 ,
T N ( σ ; t ; k ) 2 d t K 1 .
E ( α , β ) K 2 0 ( σ ; k ) 2 ;

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