Abstract

We present three new interferometers, which are based on interference between combinations of image-bearing optical fields and their redirected phase-conjugate reflections in two- and three-dimensional configurations. Our interferometers can be used to implement mathematical operations on images, including the Hartley transform.

© 1992 Optical Society of America

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References

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  1. E. Wolf, Progress in Optics (Elsevier, Amsterdam, 1987), Vol. 24, pp. 132 and 458, and references therein.
    [CrossRef]
  2. J. Villasenor, R. N. Bracewell, Nature (London) 330, 735 (1987).
    [CrossRef]
  3. R. V. L. Hartley, Proc. Inst. Radio Eng. 30, 144 (1942).
  4. R. N. Bracewell, J. Opt. Soc. Am. 73, 1832 (1983).
    [CrossRef]
  5. R. N. Bracewell, Proc. IEEE 72, 1010 (1984).
    [CrossRef]
  6. R. N. Bracewell, H. Bartelt, A. W Lohmann, N. Streibl, Appl. Opt. 24, 1401 (1985).
    [CrossRef] [PubMed]
  7. Y. Li, G. Eichmann, Opt. Commun. 56, 150 (1985).
    [CrossRef]
  8. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  9. Y. Fainman, E. Lenz, J. Shamir, Appl. Opt. 20, 158 (1981).
    [CrossRef] [PubMed]

1987 (1)

J. Villasenor, R. N. Bracewell, Nature (London) 330, 735 (1987).
[CrossRef]

1985 (2)

1984 (1)

R. N. Bracewell, Proc. IEEE 72, 1010 (1984).
[CrossRef]

1983 (1)

1982 (1)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

1981 (1)

1942 (1)

R. V. L. Hartley, Proc. Inst. Radio Eng. 30, 144 (1942).

Bartelt, H.

Bracewell, R. N.

Cronin-Golomb, M.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Eichmann, G.

Y. Li, G. Eichmann, Opt. Commun. 56, 150 (1985).
[CrossRef]

Fainman, Y.

Fischer, B.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Hartley, R. V. L.

R. V. L. Hartley, Proc. Inst. Radio Eng. 30, 144 (1942).

Lenz, E.

Li, Y.

Y. Li, G. Eichmann, Opt. Commun. 56, 150 (1985).
[CrossRef]

Lohmann, A. W

Shamir, J.

Streibl, N.

Villasenor, J.

J. Villasenor, R. N. Bracewell, Nature (London) 330, 735 (1987).
[CrossRef]

White, J. O.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Wolf, E.

E. Wolf, Progress in Optics (Elsevier, Amsterdam, 1987), Vol. 24, pp. 132 and 458, and references therein.
[CrossRef]

Yariv, A.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (London) (1)

J. Villasenor, R. N. Bracewell, Nature (London) 330, 735 (1987).
[CrossRef]

Opt. Commun. (1)

Y. Li, G. Eichmann, Opt. Commun. 56, 150 (1985).
[CrossRef]

Proc. IEEE (1)

R. N. Bracewell, Proc. IEEE 72, 1010 (1984).
[CrossRef]

Proc. Inst. Radio Eng. (1)

R. V. L. Hartley, Proc. Inst. Radio Eng. 30, 144 (1942).

Other (1)

E. Wolf, Progress in Optics (Elsevier, Amsterdam, 1987), Vol. 24, pp. 132 and 458, and references therein.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Scheme of the three-dimensional periscopic H interferometer. The input and output functions are f(x, y, 0) and O(u, υ), respectively.

Fig. 2
Fig. 2

Experimental results obtained with the interferometer shown in Fig. 1. (a) The object plane of lens L for an input image of the letter R. (b) The H transform of a displaced circular slit obtained at the focal plane of lens L.

Fig. 3
Fig. 3

Scheme of the S interferometer.

Fig. 4
Fig. 4

Experimental results obtained at the object plane of the lens at the output of the S interferometer of Fig. 3 for an input image of the letter R.

Fig. 5
Fig. 5

Scheme of the Y interferometer. The dashed line and the additional PCM are optional.

Equations (10)

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H ( u , υ , z ) = f ( x , y , z ) cas [ 2 π ( u x + υ y ) ] d x d y ,
O ( u , υ ) = F ( u , υ ) + exp ( i φ ) F ( u , υ ) ,
O ( u , υ ) = exp ( i π / 4 ) 2 H ( u , υ ) .
f e ( x , y , z ) 0 . 5 [ f ( x , y , z ) + f ( x , y , z ) ] , f o ( x , y , z ) 0 . 5 [ f ( x , y , z ) f ( x , y , z ) ] ,
S ( u , υ ) = F * ( u , υ ) + exp ( i φ ) F ( u , υ ) .
S ( u , υ ) = 2 exp ( i φ / 2 ) [ F 1 ( u , υ ) cos ( φ / 2 ) + F 2 ( u , υ ) sin ( φ / 2 ) ] .
f ( x , y ) = f R ( x , y ) exp [ i θ ( x , y ) ] ,
f * ( x , y ) + exp ( i φ ) f ( x , y ) = 2 f R ( x , y ) exp ( i φ / 2 ) × cos [ θ ( x , y ) + φ / 2 ] ,
Y ˆ ( u , υ ) = F * ( u , υ ) + exp ( i φ ) F * ( u , υ ) .
Y ( u , υ ) = f ( x , y , z ) cas [ 2 π ( u x υ y ) ] d x d y = 2 exp ( i π / 4 ) Y ˆ ( u , υ ) .

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