Abstract

Various fundamental cross-talk effects that limit the information storage capacity of the spatial-frequency-multiplexed Fourier-transform volume holograms are identified and analyzed. The methods for eliminating the identified cross-talk effects are presented. The signal-to-noise ratio, which determines the actual storage capacity, is derived.

© 1988 Optical Society of America

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References

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  1. P. Van Heerden, Appl. Opt. 2, 387 (1963).
    [CrossRef]
  2. C. W. Stinger, L. Solymar, Appl. Opt. 25, 3283 (1986).
    [CrossRef]
  3. R. K. Kostuk, J. W. Goodman, L. Hesselink, Appl. Opt. 25, 4362 (1986).
    [CrossRef] [PubMed]
  4. L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).
  5. P. Gunter, Phys. Rep. 93, 199 (1982).
    [CrossRef]
  6. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  7. P. Gunter, Phys. Rep. 93, 259 (1982).
    [CrossRef]

1986 (2)

1982 (2)

P. Gunter, Phys. Rep. 93, 199 (1982).
[CrossRef]

P. Gunter, Phys. Rep. 93, 259 (1982).
[CrossRef]

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

1963 (1)

Cooke, D. J.

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

Goodman, J. W.

Gunter, P.

P. Gunter, Phys. Rep. 93, 199 (1982).
[CrossRef]

P. Gunter, Phys. Rep. 93, 259 (1982).
[CrossRef]

Hesselink, L.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kostuk, R. K.

Solymar, L.

C. W. Stinger, L. Solymar, Appl. Opt. 25, 3283 (1986).
[CrossRef]

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

Stinger, C. W.

Van Heerden, P.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Phys. Rep. (2)

P. Gunter, Phys. Rep. 93, 259 (1982).
[CrossRef]

P. Gunter, Phys. Rep. 93, 199 (1982).
[CrossRef]

Other (1)

L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, London, 1981).

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Figures (3)

Fig. 1
Fig. 1

Illustration of the Fourier-transform volume hologram between an objective point 1 and a reference point 2. One grating is stored by interfering the two beams coming from point sources 1 and 2 after it passes through a Fourier-transforming lens. After storing the grating, light coming from point 2 is diffracted by the grating and yields a reconstructed objective wave.

Fig. 2
Fig. 2

Arrangement of the objective and reference points for maximum storage. The patterns are Fourier transformed and interfered to make Fourier-transform volume holograms as in Fig. 1. The vertical direction corresponds to the ϕ = 0 direction in Fig. 3.

Fig. 3
Fig. 3

Wave-vector diagram for calculating the phase mismatch. The spherical coordinates for the input wave 1 are θ = 0 and ϕ = 0. The coordinates for the output wave 2 are ϕ = 0 and θ = θ2.

Equations (7)

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I p = i η p i I i ,
I 1 = j l I i η j l sinc 2 [ Δ k j l ( i ) L / 2 ] - I i η i p ,
Δ k j l ( i ) = ( 2 π / λ ) n - ( 2 π / λ ) n n i + K j l ,
Δ k ( θ , ϕ ) = ( 2 π n / λ ) ( 1 - { 1 + 2 sin θ 2 sin θ [ cos ϕ + cot ( θ 2 / 2 ) tan ( θ / 2 ) ] } 1 / 2 ) ,
I 2 = q ( 1 / 4 ) I i η i q η q p ,
I 3 = q l ( 1 / 36 ) I i η i q η q l η l p ,
SNR = [ ( 1 / 36 ) N 4 η 2 + ( 1 / 14 , 400 ) ( N 4 η 2 ) 2 + ] - 1 .

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