Abstract

Holographic correlators can implement many correlations in parallel. For most systems shift invariance limits the number of correlation templates that can be stored in one correlator. This is because the output plane must be divided among the individual templates in the system. When the system is completely shift invariant, the correlation peak from one correlator can shift into an area that has been reserved for a different template; in this case a shifted version of one object might be mistaken for a well-centered version of a different object. We describe a technique for controlling the shift invariance of a correlator system by moving the holographic material away from the Fourier plane.

© 1999 Optical Society of America

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References

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  1. B. Javidi, P. Réfrégier, eds., Optoelectronic Information Processing, Vol. PM54 of the SPIE Monographs and Handbooks Series (SPIE, Bellingham, Wash., 1997).
  2. C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
    [CrossRef]
  3. J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. SPIE825, 128–135 (1987).
    [CrossRef]
  4. D. Psaltis, M. Levene, “Optical neural networks,” in Vol. CR55 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1994), pp. 141–149.
  5. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

1992 (1)

C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
[CrossRef]

Campbell, S.

C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
[CrossRef]

Gu, C.

C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
[CrossRef]

Hong, J.

C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Levene, M.

D. Psaltis, M. Levene, “Optical neural networks,” in Vol. CR55 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1994), pp. 141–149.

Mok, F.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. SPIE825, 128–135 (1987).
[CrossRef]

Psaltis, D.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. SPIE825, 128–135 (1987).
[CrossRef]

D. Psaltis, M. Levene, “Optical neural networks,” in Vol. CR55 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1994), pp. 141–149.

Yu, J.

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. SPIE825, 128–135 (1987).
[CrossRef]

Opt. Commun. (1)

C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
[CrossRef]

Other (4)

J. Yu, F. Mok, D. Psaltis, “Capacity of optical correlators,” in Spatial Light Modulators and Applications II, U. Efron, ed., Proc. SPIE825, 128–135 (1987).
[CrossRef]

D. Psaltis, M. Levene, “Optical neural networks,” in Vol. CR55 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1994), pp. 141–149.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

B. Javidi, P. Réfrégier, eds., Optoelectronic Information Processing, Vol. PM54 of the SPIE Monographs and Handbooks Series (SPIE, Bellingham, Wash., 1997).

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Figures (7)

Fig. 1
Fig. 1

Basic holographic correlator.

Fig. 2
Fig. 2

Experimental correlator setup.

Fig. 3
Fig. 3

Randomly generated image 120 × 120 pixels in size.

Fig. 4
Fig. 4

Correlation strength versus image displacement for (a) in-plane and (b) out-of-plane shifts.

Fig. 5
Fig. 5

(a) In-plane and (b) out-of-plane shift selectivity with the recording material displaced from the Fourier plane.

Fig. 6
Fig. 6

Output of an array of correlators recorded 1 cm from the Fourier plane: (a), (b) centered input images; (c), (d) shifted input images; (e), (f) images recorded at the Fourier plane.

Fig. 7
Fig. 7

Autocorrelation cross sections for (a) Fourier plane and (b) Fresnel zone recordings.

Equations (7)

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

gx, y, z=-- f1x1, y1exp-j kFx1x+y1y× expj k2F2x12+y12zdx1dy1,
gx, y, z=-- f1x1, y1exp-j kFx1x+y1y×expj k2nF2x12+y12z+zc-Lz/2×n-1dx1dy1,
|expjkx sin θ+z cos θ+gx, y, z|2,
Adkd= dx1dy1  dx2dy2f1x1, y1f2x2, y2×volume exp-j k2nF2x12-x22+y12-y22×z+zc-Lz/2n-1×expj kFx1-x2x× expj kFy1-y2y× expjnk sin θ-kdxxexp-jnkdyy×expjnk cos θ-kdzz+zc-Lz/2n-1dxdydz,
Adkd= dx1dy1  dx2dy2f1x1, y1f2x2, y2×exp-j k2nF2x12-x22+y12-y22×zc+zc-Lz/2n-1expjnk cos θ-kdzzc+zc-Lz/2n-1×sincLz2πk2nF2x12-x22+y12-y22+kn cos θ-nkdz×sincLx2πkFx1-x2+kn sin θ-nkdx×sincLy2πkFy1-y2-nkdy,
AdΔx, Δy= f1x1, y1f2x1+Δx, y1+Δy×expjzc+zc-Lc/2n-1α× sincLz2π αdx1dy1,
α=k2nF2x12-x1+Δx2+y12-y1+Δy2+kn cos θ-nkdz, Δx=nFsin θ-kdx/k,  Δy=-nFkdy/k.

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