Abstract

Experimental results are given that show that a random phase shifter (RPS) is effective in reducing speckle noise caused by optical defects in coherent imaging systems, including holographic imaging systems. Here the RPS is composed of many tiny transparent blocks, each of which gives a definite phase shift such as O or π to the transmitting light; and the distribution of the phase shift is two-dimensionally random. The optical defects are scattering centers such as scratches or dust on lenses or on the hologram medium in the case of holographic imaging systems.

© 1975 Optical Society of America

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References

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  1. D. Gabor, SPIE Seminar Proc. 25, 129 (1971).
    [Crossref]
  2. H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, Appl. Opt. 7, 2301 (1968).
    [Crossref] [PubMed]
  3. E. N. Leith, J. Upatnieks, Appl. Opt. 7, 2085 (1968).
    [Crossref] [PubMed]
  4. A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).
  5. C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
    [Crossref] [PubMed]
  6. Y. Takeda, Y. Oshida, Y. Miyamura, Appl. Opt. 11, 818 (1972).
    [Crossref] [PubMed]
  7. Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
    [Crossref]
  8. Y. Tsunoda, Y. Takeda, Trans. Inst. Electron. Commun. Eng. Jap. 56-C, 299 (1973).
  9. M. Matsumura, Jap. J. Appl. Phys. 13, 562 (1974).
  10. T. Winthrop, C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).
    [Crossref]

1974 (1)

M. Matsumura, Jap. J. Appl. Phys. 13, 562 (1974).

1973 (2)

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

Y. Tsunoda, Y. Takeda, Trans. Inst. Electron. Commun. Eng. Jap. 56-C, 299 (1973).

1972 (2)

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Y. Takeda, Y. Oshida, Y. Miyamura, Appl. Opt. 11, 818 (1972).
[Crossref] [PubMed]

1971 (1)

D. Gabor, SPIE Seminar Proc. 25, 129 (1971).
[Crossref]

1970 (1)

1968 (2)

1965 (1)

Burckhardt, C. B.

Firester, A. H.

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Fox, E. C.

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Gabor, D.

D. Gabor, SPIE Seminar Proc. 25, 129 (1971).
[Crossref]

Gayeski, T.

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Gerritsen, H. J.

Hannan, W. J.

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, Appl. Opt. 7, 2301 (1968).
[Crossref] [PubMed]

Leith, E. N.

Lurie, M.

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Matsumura, M.

M. Matsumura, Jap. J. Appl. Phys. 13, 562 (1974).

Miyamura, Y.

Oshida, Y.

Ramberg, E. G.

Takeda, Y.

Y. Tsunoda, Y. Takeda, Trans. Inst. Electron. Commun. Eng. Jap. 56-C, 299 (1973).

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

Y. Takeda, Y. Oshida, Y. Miyamura, Appl. Opt. 11, 818 (1972).
[Crossref] [PubMed]

Tsunoda, Y.

Y. Tsunoda, Y. Takeda, Trans. Inst. Electron. Commun. Eng. Jap. 56-C, 299 (1973).

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

Upatnieks, J.

Winthrop, T.

Worthington, C. R.

Appl. Opt. (4)

J. Appl. Phys. (1)

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

J. Opt. Soc. Am. (1)

Jap. J. Appl. Phys. (1)

M. Matsumura, Jap. J. Appl. Phys. 13, 562 (1974).

RCA Rev. (1)

A. H. Firester, E. C. Fox, T. Gayeski, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

SPIE Seminar Proc. (1)

D. Gabor, SPIE Seminar Proc. 25, 129 (1971).
[Crossref]

Trans. Inst. Electron. Commun. Eng. Jap. (1)

Y. Tsunoda, Y. Takeda, Trans. Inst. Electron. Commun. Eng. Jap. 56-C, 299 (1973).

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Figures (13)

Fig. 1
Fig. 1

Experimental setup. RPS, random phase shifter; O, object; L1, L2, lenses; I, image of object O; P1, P2, P3, glass plate; A, aperture.

Fig. 2
Fig. 2

Image I when P1 and P3 are inserted, but P2 is removed.

Fig. 3
Fig. 3

Image I when P1, P2, and P3 are all inserted.

Fig. 4
Fig. 4

Image I when the RPS A is used.

Fig. 5
Fig. 5

Image I when the RPS B is used.

Fig. 6
Fig. 6

Image I when the RPS C is used.

Fig. 7
Fig. 7

Image I when the same mask as the RPS A is used in contact with the object O and is illuminated by a uniphase beam.

Fig. 8
Fig. 8

Explanation of speckle noise production when the noise source is located far away from the focal plane.

Fig. 9
Fig. 9

Speckle noise pattern. (a) ϕ(x,y) = O; (b) ϕ(x,y) = O or π.

Fig. 10
Fig. 10

Explanation of speckle noise production when the noise source is located near or at the focal plane.

Fig. 11
Fig. 11

Image I for the MOB method at m = ½.

Fig. 12
Fig. 12

Image I for the MOB method at m = ⅓.

Fig. 13
Fig. 13

Spectra for (a) the RPS method and (b) the MOB method; (a) and (b) correspond to Fig. 4 and Figs. 11 or 12.

Tables (1)

Tables Icon

Table I Types of RPS Used in the Experiment

Equations (12)

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U A = A exp i ( { [ k ( x 2 + y 2 ) ] / ( 2 z ) } + φ A ) ,
U B = B exp i ( { [ k ( x 2 + y 2 ) ] / ( 2 R B ) } + φ B ( x , y ) ) ,
G = | U A + U B | 2 = A 2 + B 2 + 2 A B cos { 1 2 ( x 2 + y 2 ) × [ ( 1 / R B ) ( 1 / z ) ] + φ B ( x , y ) φ A } .
1 2 [ ( 1 / R B ) ( 1 / z ) ] ( x 2 + y 2 ) + φ B ( x , y ) φ A = 2 m λ;
1 2 [ ( 1 / R B ) ( 1 / z ) ] ( x 2 + y 2 ) + φ B ( x , y ) φ A = ( 2 m 1 ) λ,
z = [ ( 2 p 2 ) / λ ] × m ,
m = N / n ,
m p > d o ,
d H ( RPS ) = ( 2 λ f 1 ) / [ p o ( RPS ) d o ( RPS ) ] ,
d H ( MOB ) = ( 2 λ f 1 ) / [ p o ( MOB ) d o ( MOB ) ] ,
d o ( RPS ) / d o ( MOB ) 1 / m .
d H ( RPS ) / d H ( MOB ) = m .

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