Abstract

Real-time image correlation is achieved by coupling coherent Fourier spectra inside saturable absorbers. Previously described optical correlators using nonlinear susceptibilities are strongly limited by the angular selectivity of Bragg diffraction in thick interaction cells. We overcame these difficulties by a special 3-D arrangement of the interfering beams. High-quality quasi-real-time holographic images, enabling cross-correlation of photographic transparencies free of detection noise, are demonstrated.

© 1980 Optical Society of America

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References

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  1. G. Marie, Philips Res. Rep. 22, 110 (1967).
  2. M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
    [CrossRef]
  3. J. Feinlib, O. S. Oliver, Appl. Opt. 11, 2752 (1972).
    [CrossRef]
  4. H. Eichler, B. Klusowski, Z. Angew. Phys. 28 (6), 306 (1970); H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
    [CrossRef] [PubMed]
  5. Sing H. Lee, K. T. Stalker, Annual Meeting of the Optical Society of America, San Francisco (October1972).
  6. G. Mayer, F. Gires, C. R. Acad. Sci. Paris 258, 2039 (1964).
  7. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [CrossRef]
  8. J. P. Woerdman, Opt. Commun. 2, 212 (1970).
    [CrossRef]
  9. B. Carquille, G. Da Costa, C. Froehly (International Conference, Tokyo, 1974), Jpn. J. Appl. Phys. 14, Suppl. 14, 1 (1975).
  10. See, for example, A. Yariv, Opt. Commun. 25, 23 (1978).
    [CrossRef]
  11. F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
    [CrossRef]
  12. See, for example, N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965); J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  13. P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
    [CrossRef]
  14. G. Bret, F. Gires, C. R. Acad. Sci. Paris 258, 4702 (1964).
  15. P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
    [CrossRef]
  16. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massey, Appl. Opt. 5, 1303 (1966).
    [CrossRef] [PubMed]
  17. Y. Belvaux, Phys. Lett. A 26, 190 (1968); Nouv. Rev. Opt. 6, 137 (1975).
    [CrossRef]
  18. J. P. Prenel, Thesis, U. Besançon (1973).

1978

See, for example, A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

1977

F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
[CrossRef]

1975

B. Carquille, G. Da Costa, C. Froehly (International Conference, Tokyo, 1974), Jpn. J. Appl. Phys. 14, Suppl. 14, 1 (1975).

1972

M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

J. Feinlib, O. S. Oliver, Appl. Opt. 11, 2752 (1972).
[CrossRef]

1970

H. Eichler, B. Klusowski, Z. Angew. Phys. 28 (6), 306 (1970); H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

J. P. Woerdman, Opt. Commun. 2, 212 (1970).
[CrossRef]

1968

Y. Belvaux, Phys. Lett. A 26, 190 (1968); Nouv. Rev. Opt. 6, 137 (1975).
[CrossRef]

1967

G. Marie, Philips Res. Rep. 22, 110 (1967).

1966

1964

G. Bret, F. Gires, C. R. Acad. Sci. Paris 258, 4702 (1964).

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

G. Mayer, F. Gires, C. R. Acad. Sci. Paris 258, 2039 (1964).

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

1961

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Bainier, C.

F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
[CrossRef]

Belvaux, Y.

Y. Belvaux, Phys. Lett. A 26, 190 (1968); Nouv. Rev. Opt. 6, 137 (1975).
[CrossRef]

Bloembergen, N.

See, for example, N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965); J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bret, G.

G. Bret, F. Gires, C. R. Acad. Sci. Paris 258, 4702 (1964).

Carquille, B.

F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
[CrossRef]

B. Carquille, G. Da Costa, C. Froehly (International Conference, Tokyo, 1974), Jpn. J. Appl. Phys. 14, Suppl. 14, 1 (1975).

Da Costa, G.

B. Carquille, G. Da Costa, C. Froehly (International Conference, Tokyo, 1974), Jpn. J. Appl. Phys. 14, Suppl. 14, 1 (1975).

Donjon, J.

M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Eichler, H.

H. Eichler, B. Klusowski, Z. Angew. Phys. 28 (6), 306 (1970); H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

Feinlib, J.

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Froehly, C.

B. Carquille, G. Da Costa, C. Froehly (International Conference, Tokyo, 1974), Jpn. J. Appl. Phys. 14, Suppl. 14, 1 (1975).

Gires, F.

G. Bret, F. Gires, C. R. Acad. Sci. Paris 258, 4702 (1964).

G. Mayer, F. Gires, C. R. Acad. Sci. Paris 258, 2039 (1964).

Grenot, M.

M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Guignard, M.

F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Klusowski, B.

H. Eichler, B. Klusowski, Z. Angew. Phys. 28 (6), 306 (1970); H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

Kozma, A.

Lee, Sing H.

Sing H. Lee, K. T. Stalker, Annual Meeting of the Optical Society of America, San Francisco (October1972).

Leith, E. N.

Maker, P. D.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Marie, G.

M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

G. Marie, Philips Res. Rep. 22, 110 (1967).

Marks, J.

Massey, N.

Mayer, G.

G. Mayer, F. Gires, C. R. Acad. Sci. Paris 258, 2039 (1964).

Oliver, O. S.

Pergrale, J.

M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Prenel, J. P.

J. P. Prenel, Thesis, U. Besançon (1973).

Savage, C. M.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Stalker, K. T.

Sing H. Lee, K. T. Stalker, Annual Meeting of the Optical Society of America, San Francisco (October1972).

Terhune, R. W.

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Upatnieks, J.

Vienot, F.

F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Woerdman, J. P.

J. P. Woerdman, Opt. Commun. 2, 212 (1970).
[CrossRef]

Yariv, A.

See, for example, A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Grenot, J. Pergrale, J. Donjon, G. Marie, Appl. Phys. Lett. 21, 83 (1972).
[CrossRef]

C. R. Acad. Sci. Paris

G. Bret, F. Gires, C. R. Acad. Sci. Paris 258, 4702 (1964).

G. Mayer, F. Gires, C. R. Acad. Sci. Paris 258, 2039 (1964).

Jpn. J. Appl. Phys.

B. Carquille, G. Da Costa, C. Froehly (International Conference, Tokyo, 1974), Jpn. J. Appl. Phys. 14, Suppl. 14, 1 (1975).

Opt. Acta

F. Vienot, C. Bainier, B. Carquille, M. Guignard, Opt. Acta 24, 811 (1977).
[CrossRef]

Opt. Commun.

See, for example, A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

J. P. Woerdman, Opt. Commun. 2, 212 (1970).
[CrossRef]

Philips Res. Rep.

G. Marie, Philips Res. Rep. 22, 110 (1967).

Phys. Lett. A

Y. Belvaux, Phys. Lett. A 26, 190 (1968); Nouv. Rev. Opt. 6, 137 (1975).
[CrossRef]

Phys. Rev. Lett.

P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

P. D. Maker, R. W. Terhune, C. M. Savage, Phys. Rev. Lett. 12, 507 (1964).
[CrossRef]

Z. Angew. Phys.

H. Eichler, B. Klusowski, Z. Angew. Phys. 28 (6), 306 (1970); H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

Other

Sing H. Lee, K. T. Stalker, Annual Meeting of the Optical Society of America, San Francisco (October1972).

See, for example, N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965); J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

J. P. Prenel, Thesis, U. Besançon (1973).

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Figures (11)

Fig. 1
Fig. 1

Experimental device for image coupling: (a) arrangement for observation of the induced slit (image of a slit in the nonlinear medium); (b) arrangement for observation of the far-field diffraction pattern of the induced slit. ∑0, powerful laser beam; ∑1, weak laser beam; E, nonlinear screen; F, real slit; F′, slit induced in the nonlinear medium; F″, image of F′ on photographic film; L3, lens imaging the far-field diffraction pattern.

Fig. 2
Fig. 2

(a) Slit image F″; (b) far-field diffraction pattern.

Fig. 3
Fig. 3

(a) Diffraction phenomena occurring in a sinusoidally stratified thick pupil. (b) Schematic representation of +1 diffraction order in the case of periodical sequence of parallel identical beam splitters equivalent to the physical situation in (a).

Fig. 4
Fig. 4

Arrangement for holographic image coupling: NL, nonlinear optical material; S0 reference source (wave ∑0); S1, powerful amplitude repartition (wave ∑1); S2 weak amplitude repartition (wave ∑2); T, transparency stratification induced by interference of (∑1) with (∑0); ( Σ 0 ) , ( Σ 1 ), transmitted waves; ( Σ 2 ) , ( Σ 2 ) diffracted waves; α: angular aperture of beam coming from S2.

Fig. 5
Fig. 5

The experimental setup that nearly satisfies the Bragg condition: S0, S1, S2, quasi-monochromatic light sources; S 0 , S 1 , S 2 , S 2 , transmitted and diffracted amplitude repartitions; L: lens imaging plane P onto plane P′.

Fig. 6
Fig. 6

Photographs recorded with a holographic image-coupling arrangement closely satisfying the Bragg condition. Direct images (lower trace) and holographic images (upper trace).

Fig. 7
Fig. 7

Effect of Bragg selectivity on holographic images: the deviation with respect to the Bragg angle is ~1.5°.

Fig. 8
Fig. 8

Modulation transfer function of a 1-mm thick nonlinear hologram (cryptocyanine solution; average laser power: 10 MW/cm2); N denotes spatial frequencies in mm−1.

Fig. 9
Fig. 9

Experimental setup of a quasi-real-time correlator: the whole optical arrangement is clearly shown. A prismatic beam splitter B.S. divides the pulsed laser beam into three parts; telescope systems T1, T2 secure entrance pupils P1, P2 from any damage; lens L1 images spectra on the nonlinear screen; strioscopic filter S.F. suppresses zero spatial frequency, preventing the nonlinear slab from breakdown and improving the selectivity of the correlation operation. Lens L2 yields the correlation function onto photographic film Ph.

Fig. 10
Fig. 10

Some experimental results after correlation of photographic transparencies made on Kodak Recordak AHU microfilm developed in Dektol Kodak developer; the size of the transparencies is 12 × 12 mm2. The photographic recordings of the correlation images are displayed on high sensitivity emulsion: Ilford HP4 600 ASA developed in D-11 Kodak developer.

Fig. 11
Fig. 11

Optical correlator to be placed at the output of a Quantel passively Q-switched ruby laser.

Equations (11)

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χ _ _ _ and χ _ _ _ _
E ( t , Z ) = E 0 cos ( 2 π ν 0 t - k 0 Z ) .
Δ i = Δ i = λ b = λ e sin i = 2 a e = 2 e N
Δ N 2 / ( e i ) = 20 mm - 1 ,
( Δ N ) 2 400 mm - 2 .
K 4 × 10 2 × 9 × 10 4 = 36 × 10 6 degrees of freedom ,
F ( N x , N y ) = F . T . [ f ( x , y ) ] ,
A ( N x , N y ) = a · exp ( - j 2 π λ θ N x ) + F ( N x , N y )
E ( N x , N y ) = a 2 + F 2 + a · exp ( + j 2 π λ θ N x ) · F ( N x , N y ) + a · exp ( - j 2 π λ θ N x ) · F * ( N x , N y )
F . T . [ G ( N x , N y ) · F * ( N x , N y ) ] = g ( x , y ) f * ( - x , - y ) ,
K = a 2 · Δ N x · Δ N y ,

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