Abstract

We analyze the correlation pattern and the cross-talk noise of optical correlators, using multiplexed volume holograms as matched filters. Our results show that sidelobes of the correlation patterns are suppressed in such an optical system; therefore the signal-to-noise ratio in pattern recognition is significantly higher than that in a planar holographic correlator system. We consider both angle- and wavelength-multiplexed holograms and compare the results for various thicknesses of volume holographic media. Our results show that the degree of sidelobe suppression depends on the thickness of the holographic medium and the angle between the object beam and the reference beam during recording. When the correlation patterns obtained with the transmission holograms in angle multiplexing are compared with the reflection holograms in wavelength multiplexing, it is seen that the sidelobes decrease much faster with the increase of thickness with angle multiplexing than with wavelength multiplexing. In addition, we demonstrate the effect of sidelobe suppression, and our experimental result is in good qualitative agreement with theoretical predictions.

© 1995 Optical Society of America

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  1. D. Brady, D. Psaltis, “Information capacity of 3-D holographic data storage,” Opt. Quantum Electron. 25, S597–S610 (1993).
    [CrossRef]
  2. G. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef] [PubMed]
  3. A. Yariv, “Interpage and interpixel cross talk in orthogonal (wavelength-multiplexed) holograms,” Opt. Lett. 18, 652–654 (1993).
    [CrossRef] [PubMed]
  4. J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [CrossRef] [PubMed]
  5. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  6. Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543 (1962).
  7. D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
    [CrossRef]
  8. J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
    [CrossRef]
  9. E. G. Ramberg, “Holographic information storage,” RCA Rev. 33, 5–53 (1972).
  10. G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7.
  11. F. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–607 (1991).
    [CrossRef] [PubMed]
  12. C. Gu, J. Hong, S. Campbell, “2-D shift-invariant volume holographic correlator,” Opt. Commun. 88, 309–314 (1992).
    [CrossRef]
  13. F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
    [CrossRef]
  14. F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThII4.
  15. C. Gu, J. Hong, I. McMichael, R. Saxena, F. Mok, “Crosstalk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  16. H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
    [CrossRef]
  17. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  18. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 57–96.
  20. K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
    [CrossRef] [PubMed]

1994 (1)

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (3)

1991 (2)

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

F. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–607 (1991).
[CrossRef] [PubMed]

1989 (1)

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

1988 (1)

1972 (2)

E. G. Ramberg, “Holographic information storage,” RCA Rev. 33, 5–53 (1972).

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

1971 (1)

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

1963 (1)

1962 (1)

Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543 (1962).

Amodei, J. J.

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Bashaw, M.

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Brady, D.

D. Brady, D. Psaltis, “Information capacity of 3-D holographic data storage,” Opt. Quantum Electron. 25, S597–S610 (1993).
[CrossRef]

D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

Burr, G. W.

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7.

Campbell, S.

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

Curtis, K.

Denisyuk, Y. N.

Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543 (1962).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 57–96.

Gu, C.

Gu, X.-G.

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

Heanue, J.

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Hesselink, L.

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Hong, J.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. Mok, “Crosstalk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
[CrossRef]

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), pp. 427–432.

Lee, H.

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

Leyva, V.

Mayers, A. W.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

McMichael, I.

Mok, F.

C. Gu, J. Hong, I. McMichael, R. Saxena, F. Mok, “Crosstalk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
[CrossRef]

F. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–607 (1991).
[CrossRef] [PubMed]

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThII4.

Mok, F. H.

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7.

Phillips, W.

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

Psaltis, D.

D. Brady, D. Psaltis, “Information capacity of 3-D holographic data storage,” Opt. Quantum Electron. 25, S597–S610 (1993).
[CrossRef]

K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
[CrossRef] [PubMed]

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
[CrossRef]

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7.

Rajan, S.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Rakuljic, G.

Ramberg, E. G.

E. G. Ramberg, “Holographic information storage,” RCA Rev. 33, 5–53 (1972).

Saxena, R.

Staebler, D. L.

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Stoll, H. M.

F. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–607 (1991).
[CrossRef] [PubMed]

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThII4.

Tackitt, M.

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThII4.

Tackitt, M. C.

van Heerden, P. J.

Wagner, K.

Wu, S.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Yariv, A.

Yu, F. T. S.

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

J. Appl. Phys. (1)

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

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

F. T. S. Yu, S. Wu, A. W. Mayers, S. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun. 81, 343–347 (1991).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

D. Brady, D. Psaltis, “Information capacity of 3-D holographic data storage,” Opt. Quantum Electron. 25, S597–S610 (1993).
[CrossRef]

RCA Rev. (1)

E. G. Ramberg, “Holographic information storage,” RCA Rev. 33, 5–53 (1972).

Science (1)

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Sov. Phys. Dokl. (1)

Y. N. Denisyuk, “Photographic reconstruction of the optical properties of an object in its own scattered radiation field,” Sov. Phys. Dokl. 7, 543 (1962).

Other (4)

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 57–96.

F. Mok, M. Tackitt, H. M. Stoll, “Massively parallel optical template matcher/correlator,” Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThII4.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of an optical correlator system in which multiple holograms are stored in a thick recording medium located in the Fourier domain.

Fig. 2
Fig. 2

Object pattern used in our simulation and experiment.

Fig. 3
Fig. 3

(a) Autocorrelation pattern of Fig. 2. (b), (c), (d), (e) Output pattern of the volume holographic correlator g(xc, yc) calculated by use of relations (8) and (12), with thickness t = 0.005 cm, t = 0.05 cm, t = 0.5 cm, t = 5 cm, respectively. Units of the vertical axis are arbitrary.

Fig. 4
Fig. 4

NSR at various peak positions calculated according to relations (14) and (15), with θ = 90°, t = 0.1 cm, and M = 1000.

Fig. 5
Fig. 5

Maximum NSR as a function of M (the total number of stored holograms is N = 2M + 1) in the case of angle multiplexing with θ = 90° and t = 0.5 cm.

Fig. 6
Fig. 6

Output pattern of the wavelength-multiplexing volume holographic correlator g(xc, yc) with thickness (a) t = 0.05 cm, (b) t = 0.2 cm, (c) t = 0.5 cm, (d) t = 1 cm.

Fig. 7
Fig. 7

NSR at various peak wavelengths calculated according to relations (17), with θ = 180°, t = 0.5 cm, and M = 1000.

Fig. 8
Fig. 8

NSR as a function of M (the total number of stored holograms is N = 2M + 1) in the case of wavelength multiplexing with θ = 180° and t = 0.5 cm; the values are taken at i = 0.

Fig. 9
Fig. 9

Experimental setup.

Fig. 10
Fig. 10

Experimental result of the suppressed correlation pattern taken at the output plane of the volume holographic correlator.

Equations (17)

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Δ m = M M R m S m * + c . c . ,
E ( r ) S + k 0 2 4 π exp ( i k r ) r d r exp ( i k d · r ) S Δ ( r ) ,
R m = exp ( i k m · r ) .
k m x = 2 π λ x m f = 0 , k m y = 2 π λ y m f cos θ 2 π λ [ 1 1 2 ( y m f ) 2 ] sin θ , k m z = 2 π λ y m f sin θ + 2 π λ [ 1 1 2 ( y m f ) 2 ] cos θ ,
S m ( r ) = exp ( 2 i k f + i k n Δ 0 ) i λ f exp ( i k z ) × d x 0 d y 0 f m ( x 0 , y 0 ) exp [ i 2 π λ f ( x x 0 + y y 0 ) ] × exp [ i π λ f z f ( x 0 2 + y 0 2 ) ] ,
k d x = 2 π λ x c f , k d y = 2 π λ y c f cos θ 2 π λ ( 1 x c 2 2 f 2 y c 2 2 f 2 ) sin θ , k d z = 2 π λ y c f sin θ + 2 π λ ( 1 x c 2 2 f 2 y c 2 2 f 2 ) cos θ .
g ( x c , y c ) m = M M d x 0 d y 0 d x 1 d y 1 f ( x 0 , y 0 ) f m * ( x 1 , y 1 ) × V sinc [ a 2 π ( k m x k d x + 2 π λ x 1 x 0 f ) ] × sinc [ b 2 π ( k m y k d y + 2 π λ y 1 y 0 f ) ] × sinc [ t 2 π ( k m z k d z + π λ x 1 2 x 0 2 + y 1 2 y 0 2 f 2 ) ] ,
g ( x c , y c ) m = M M d x 0 d y 0 f ( x 0 , y 0 ) f m * ( x 0 + ξ , y 0 + η ) × t sinc { t 2 π [ k m z k d z + π λ ξ ( 2 x 0 + ξ ) + η ( 2 y 0 + η ) f 2 ] } ,
ξ = λ f 2 π ( k d x k m x ) , η = λ f 2 π ( k d y k m y ) .
g ( x c , y c ) m = M M d x 0 d y 0 f ( x 0 , y 0 ) f m * ( x 0 + ξ , y 0 + η ) .
k m z k d z + π λ ξ ( 2 x 0 + ξ ) + η ( 2 y 0 + η ) f 2 = 0 .
ξ = x c , η = cos θ ( y c + y m ) + sin θ x c 2 + y c 2 y m 2 2 f , k m z k d z = 2 π λ sin θ y c + y m f + 2 π λ cos θ x c 2 + y c 2 y m 2 2 f 2 .
g ( x c , y c ) m = M M d x 0 d y 0 f ( x 0 , y 0 ) × f m * ( x 0 + x c , y 0 + x c 2 + y c 2 y m 2 2 f ) × t sinc { t λ [ y c + y m f + x c ( 2 x 0 + x c ) 2 f 2 + y 0 ( x c 2 + y c 2 y m 2 2 f 3 ] } .
Signal d x 0 d y 0 f ( x 0 , y 0 ) f i * ( x 0 , y 0 ) .
Noise m i d x 0 d y 0 f ( x 0 , y 0 ) f m * ( x 0 , y 0 + y i 2 y m 2 2 f ) × t sinc { t λ [ y i + y m f + y 0 ( y i 2 y m 2 ) 2 f 3 ] } .
g ( x c , y c ) m = M M d x 0 d y 0 f ( x 0 , y 0 ) × f m * [ λ m λ ( x 0 + x c ) , λ m λ ( y 0 + y c ) ] × t sinc { 2 t ( 1 λ 1 λ m ) + t 2 λ [ λ m λ ( x 0 + x c ) 2 + ( y 0 + y c ) 2 f 2 x c 2 + x 0 2 + y c 2 + y 0 2 f 2 ] } .
Signal d x 0 d y 0 f ( x 0 , y 0 ) f i * ( x 0 , y 0 ) , Noise m i d x 0 d y 0 f ( x 0 , y 0 ) × f m * ( λ m λ i x 0 , λ m λ i y 0 ) × t sinc [ 2 t ( 1 λ i 1 λ m ) + t 2 λ i ( λ m λ i x 0 2 + y 0 2 f 2 x 0 2 + y 0 2 f 2 ) ] .

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