Abstract

The cross talk between holograms multiplexed with Walsh–Hadamard phase codes is analyzed. Each hologram is stored with a reference beam that consists of N phase-coded plane waves. The signal-to-noise ratio (SNR) is calculated for a recording schedule for which the center of each stored image coincides with the nulls of the selectivity function for the adjacent plane-wave components of the reference beam. The SNR characteristics for phase coding with Walsh–Hadamard phase codes are then compared with the SNR for angle and wavelength multiplexing.

© 1993 Optical Society of America

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References

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  1. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  2. G. A. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef] [PubMed]
  3. C. Denz, G. Pauliat, G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
    [CrossRef]
  4. J. Trisnadi, S. Redfield, “Practical verification of hologram multiplexing without beam movement,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 362–371 (1992).
    [CrossRef]
  5. J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1088–1090 (1990).
    [CrossRef] [PubMed]
  6. C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, “Cross-talk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  7. K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
    [CrossRef] [PubMed]
  8. C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Potentialities and limitations of hologram multiplexing by using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–96.
  10. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.

1993 (2)

1992 (3)

1991 (1)

C. Denz, G. Pauliat, G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

1990 (1)

Curtis, K.

Denz, C.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Potentialities and limitations of hologram multiplexing by using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Fainman, Y.

Ford, J. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–96.

Gu, C.

Hong, J.

Jackson, J. D.

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

Lee, S. H.

Leyva, V.

McMichael, I.

Mok, F. H.

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Potentialities and limitations of hologram multiplexing by using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Psaltis, D.

Rakuljic, G. A.

Redfield, S.

J. Trisnadi, S. Redfield, “Practical verification of hologram multiplexing without beam movement,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 362–371 (1992).
[CrossRef]

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Potentialities and limitations of hologram multiplexing by using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Saxena, R.

Trisnadi, J.

J. Trisnadi, S. Redfield, “Practical verification of hologram multiplexing without beam movement,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 362–371 (1992).
[CrossRef]

Tschudi, T.

Yariv, A.

Appl. Opt. (1)

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

Opt. Commun. (1)

C. Denz, G. Pauliat, G. Roosen, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Opt. Lett. (4)

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–96.

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

J. Trisnadi, S. Redfield, “Practical verification of hologram multiplexing without beam movement,” in Photonics for Computers, Neural Networks, and Memories, S. T. Kowel, W. J. Miceli, J. A. Neff, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1773, 362–371 (1992).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Recording and readout geometry for ϕ multiplexing.

Fig. 2
Fig. 2

NSR versus position (x, y) on the output plane for the n = 8 hologram, with N = 16.

Fig. 3
Fig. 3

Log(SNR) versus hologram code number for N = 64 holograms.

Fig. 4
Fig. 4

Plot of Pim sinc[ji + (y2λ/2Ft)(i2j2) + (λ3/8t3) (i2j2)2] as a function of m and i′ = iM for n = 6 and j = 0.

Fig. 5
Fig. 5

SNR versus hologram code number without code 2.

Fig. 6
Fig. 6

SNR versus the total number of holograms for ϕ (with and without code 2) multiplexing and θ multiplexing.

Equations (9)

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R m = i = - N / 2 N / 2 - 1 P i m exp ( i k i · r ) .
Δ m = - M M - 1 R m * S m + c . c .
S m ( x , y , z ) exp [ i ( 2 π / λ ) z ] d x o d y o f m ( x o , y o ) × exp [ - i ( 2 π / λ F ) ( x x o + y y o ) ] × exp [ - i ( π z / λ F 2 ) ( x o 2 + y o 2 ) ] .
E ( k d ) j = - M M - 1 d r P j n exp [ - i K · r Δ ( r ) ] ,
k d = [ 2 π x 2 λ F , 2 π y 2 λ F , 2 π λ ( 1 - x 2 2 2 F 2 - y 2 2 2 F 2 ) ] ,
E ( x 2 , y 2 ) m = - M M - 1 j = - M M - 1 i = - M M - 1 P j n P i * m f m × ( - x 2 - F λ 2 π Δ K ijx , - y 2 - F λ 2 π Δ K ijy ) × sinc { t 2 π [ Δ K ijy + 1 F ( Δ K ijx x 2 + Δ K ijy y 2 ) + λ 4 π ( Δ K ijx 2 + Δ K ijy 2 ) ] } ,
Δ K ijx = 0 , Δ K ijy = 2 π λ F cos θ ( y j - y i ) + π λ F 2 sin θ ( y i 2 - y j 2 ) , Δ K ijy = 2 π λ F sin θ ( y j - y i ) + π λ F 2 cos θ ( y j 2 - y i 2 ) ,
NSR = 1 N 2 m | j i j P j n P i m × sinc [ t 2 π ( Δ K ijy + Δ K ijy y 2 F + λ Δ K ijy 2 4 π ) ] | 2 .
NSR = 1 N 2 m | j i j P j n P i m × sinc [ j - i + y 2 λ 2 F t ( i 2 - j 2 ) + λ 3 8 t 3 ( i 2 - j 2 ) 2 ] | 2 .

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