Abstract

We describe the rotational alignment sensitivity of three-dimensional holographic disks. It is shown that the reconstructed image always rotates by the angle by which the disk rotates; however, the center and the radius of rotation change as the recording geometry changes. A comparison among image plane, Fourier plane, and Fresnel holograms is given, and an optimum configuration (in terms of alignment sensitivity) in which the radius of rotation is zero is derived. We present experimental results and also discuss how the rotation alignment sensitivity affects the storage density and the readout–recording speed of the three-dimensional disk. A brief summary of other sources of misalignment is given.

© 1995 Optical Society of America

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References

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  1. F. H. Mok, D. Psaltis, G. W. Burr, “Spatial and angle-multiplexing holographic random access memory” 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, 1–12 (1992).
  2. F. H. Mok, “Angle-multiplexed storage of 5,000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  3. L. d’Auria, J. P. Huignard, C. Slezak, E. Spitz, “Experimental holographic read–write memory using 3-D storage,” Appl. Opt. 13, 808–818 (1974).
    [CrossRef]
  4. D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).
  5. S. Tao, D. R. Selviah, J. E. Midwinter, “Spatioangular multiplexed storage of 750 holograms in an Fe:LiNbO3crystal,” Opt. Lett. 18, 912–914 (1993).
    [CrossRef] [PubMed]
  6. F. H. Mok, G. W. Burr, D. Psaltis, “Angle and space multiplexed holographic random access memory (HRAM),” Opt. Mem. Neural Networks 3, 119–127 (1994).
  7. H.-Y. S. Li, D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
    [CrossRef] [PubMed]
  8. J. J. Amodei, D. L. Staebler, “Holographic recording in lithium niobate,” RCA Rev. 33, 71–93 (1972).
  9. F. T. S. Yu, S. D. Wu, A. W. Mayers, S. M. Rajan, “Wavelength multiplexed reflection matched spatial filters using LiNbO3,” Opt. Commun.81, 343–347 (1991).
  10. 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]
  11. J. E. Ford, Y. Fainman, S. H. Lee, “Array interconnection by phase-coded optical correlation,” Opt. Lett. 15, 1088–1090 (1990).
    [CrossRef] [PubMed]
  12. C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
    [CrossRef]
  13. K. Curtis, D. Psaltis, “Cross talk in phase-coded holographic memories,” J. Opt. Soc. Am. A 10, 2547–2550 (1993).
    [CrossRef]
  14. D. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–819 (1990).
    [CrossRef] [PubMed]
  15. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  16. H.-Y. S. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1994).
  17. A. VanderLugt, “Packing density in holographic systems,” Appl. Opt. 14, 1081–1087 (1975).
    [CrossRef]

1994 (2)

F. H. Mok, G. W. Burr, D. Psaltis, “Angle and space multiplexed holographic random access memory (HRAM),” Opt. Mem. Neural Networks 3, 119–127 (1994).

H.-Y. S. Li, D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (2)

1991 (2)

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

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

1990 (2)

1975 (1)

1974 (1)

1972 (1)

J. J. Amodei, D. L. Staebler, “Holographic recording in lithium niobate,” RCA Rev. 33, 71–93 (1972).

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Amodei, J. J.

J. J. Amodei, D. L. Staebler, “Holographic recording in lithium niobate,” RCA Rev. 33, 71–93 (1972).

Brady, D.

Burr, G. W.

F. H. Mok, G. W. Burr, D. Psaltis, “Angle and space multiplexed holographic random access memory (HRAM),” Opt. Mem. Neural Networks 3, 119–127 (1994).

F. H. Mok, D. Psaltis, G. W. Burr, “Spatial and angle-multiplexing holographic random access memory” 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, 1–12 (1992).

Curtis, K.

d’Auria, L.

Denz, C.

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

Fainman, Y.

Ford, J. E.

Hsu, K.

Huignard, J. P.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lee, S. H.

Leyva, V.

Li, H.-Y. S.

H.-Y. S. Li, D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
[CrossRef] [PubMed]

H.-Y. S. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1994).

Mayers, A. W.

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

Midwinter, J. E.

Mok, F. H.

F. H. Mok, G. W. Burr, D. Psaltis, “Angle and space multiplexed holographic random access memory (HRAM),” Opt. Mem. Neural Networks 3, 119–127 (1994).

F. H. Mok, “Angle-multiplexed storage of 5,000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
[CrossRef] [PubMed]

F. H. Mok, D. Psaltis, G. W. Burr, “Spatial and angle-multiplexing holographic random access memory” 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, 1–12 (1992).

Pauliat, G.

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

Psaltis, D.

H.-Y. S. Li, D. Psaltis, “Three-dimensional holographic disks,” Appl. Opt. 33, 3764–3774 (1994).
[CrossRef] [PubMed]

F. H. Mok, G. W. Burr, D. Psaltis, “Angle and space multiplexed holographic random access memory (HRAM),” Opt. Mem. Neural Networks 3, 119–127 (1994).

K. Curtis, D. Psaltis, “Cross talk in phase-coded holographic memories,” J. Opt. Soc. Am. A 10, 2547–2550 (1993).
[CrossRef]

D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).

D. Brady, K. Hsu, D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–819 (1990).
[CrossRef] [PubMed]

F. H. Mok, D. Psaltis, G. W. Burr, “Spatial and angle-multiplexing holographic random access memory” 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, 1–12 (1992).

Rajan, S. M.

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

Rakuljic, G. A.

Roosen, G.

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

Selviah, D. R.

Slezak, C.

Spitz, E.

Staebler, D. L.

J. J. Amodei, D. L. Staebler, “Holographic recording in lithium niobate,” RCA Rev. 33, 71–93 (1972).

Tao, S.

Tschudi, T.

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

VanderLugt, A.

Wu, S. D.

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

Yariv, A.

Yu, F. T. S.

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

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Byte (1)

D. Psaltis, “Parallel optical memories,” Byte 17, 179–182 (1992).

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

Opt. Commun. (2)

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

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

Opt. Lett. (5)

Opt. Mem. Neural Networks (1)

F. H. Mok, G. W. Burr, D. Psaltis, “Angle and space multiplexed holographic random access memory (HRAM),” Opt. Mem. Neural Networks 3, 119–127 (1994).

RCA Rev. (1)

J. J. Amodei, D. L. Staebler, “Holographic recording in lithium niobate,” RCA Rev. 33, 71–93 (1972).

Other (2)

F. H. Mok, D. Psaltis, G. W. Burr, “Spatial and angle-multiplexing holographic random access memory” 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, 1–12 (1992).

H.-Y. S. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1994).

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Figures (10)

Fig. 1
Fig. 1

3D holographic disk.

Fig. 2
Fig. 2

FT-type holograms have plane-wave impulse responses.

Fig. 3
Fig. 3

Fresnel holograms have spherical-wave impulse responses. Image-plane holograms are a special case of Fresnel holograms.

Fig. 4
Fig. 4

Experimental data. Reconstructions of (a) an image-plane hologram by means of the configuration shown in Fig. 5(a)ϕ = 0.4°), (b) a Fourier-plane hologram by means of the configuration shown in Fig. 5(b)ϕ = 0.4°).

Fig. 5
Fig. 5

Recording geometries for the experimental results shown in Fig. 4: (a) for image-plane holograms [RH = 1.7 cm and θ = 27° (outside the crystal)], (b) for Fourier-plane holograms [RH = 1.7 cm and θ = 27° (outside the crystal)]. The hologram is 4 cm before the FT plane.

Fig. 6
Fig. 6

Bragg-matching representation in k space.

Fig. 7
Fig. 7

Reconstructed images from rotated holograms: top row, rotation of an image-plane hologram; middle row, rotation of a Fourier-plane hologram; bottom row, rotation of a hologram recorded in the optimum configuration for minimizing alignment sensitivity.

Fig. 8
Fig. 8

Optimum recording configuration system with minimum rotational alignment sensitivity.

Fig. 9
Fig. 9

VanderLugt imaging system.

Fig. 10
Fig. 10

Conventional 4-F imaging system.

Equations (61)

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R = A exp [ j k ( u x x + u y y + u z z ) ] ,
S = B exp [ j k ( v x x + v y y + v z z ) ] ,
v x = x 0 / F ,
v y = y 0 / F ,
v z = ( 1 - v x 2 - v y 2 ) 1 / 2 ,
T = T 0 exp [ j ( K x x + K y y ) ] ,
K x = k ( v x - u x ) ,
K y = k ( v y - u y ) .
T T 0 exp { j [ K x - K y Δ ϕ ) x + ( K y - K x Δ ϕ ) y ] } ,
R T C exp [ j k ( v x x + v y y + v z z ) ] ,
v x = v x - ( v y - u y ) Δ ϕ ,
v y = v y + ( v x - u x ) Δ ϕ ,
v z = ( 1 - v x 2 - v y 2 ) 1 / 2 .
x 0 = x 0 - ( y 0 - F u y ) Δ ϕ ,
y 0 = y 0 + ( x 0 - F u x ) Δ ϕ .
x c = F u x ,
y c = F u y .
R I = F ( u x 2 + u y 2 ) 1 / 2 .
R = A exp [ j k ( u x x + u y y + u z z ) ] ,
S = B z + l exp [ j k ( z + l ) × exp { j k 2 ( z + l ) [ ( x - x 0 ) 2 + ( y - y 0 ) 2 } .
T = T 0 exp { j k 2 l [ ( x - a ) 2 + ( y - b ) 2 ] } ,
a = x 0 + u x l ,
b = y 0 + u y l .
x = x - ( y - y c ) Δ ϕ ,
y = y + ( x - x c ) Δ ϕ .
T = T 0 exp { j k 2 l [ ( x - a ) 2 + ( y - b ) 2 ] } ,
a = a - ( b - y c ) Δ ϕ ,
b = b + ( a - x c ) Δ ϕ .
R T = A T 0 exp { j k 2 l [ ( x - a ) 2 + ( y - b ) 2 + 2 l u x x + 2 l u y y ] } = C exp { j k 2 l [ ( x - a + l u x ) 2 + ( y - b + l u y ) 2 ] } ,
x 0 = x 0 - ( y 0 - y c ) Δ ϕ ,
y 0 = y 0 + ( x 0 - x c ) Δ ϕ ,
x c = x c - u x l ,
y c = y c - u y l .
R I = [ R H 2 + ( u x 2 + u y 2 ) l 2 - 2 l ( x c u x + y c u y ) ] 1 / 2 .
k S k ( v x , v y , v z ) = k [ x 0 F , y 0 F , ( 1 - x 0 2 + y 0 2 F 2 ) 1 / 2 ] ,
k R = k ( u x , u y , u z ) = k ( 0 , - sin θ R , cos θ R ) ,
K = k R - k S = k [ - x 0 F , - sin θ R - y 0 F , cos θ R - ( 1 - x 0 2 + y 0 2 F 2 ) 1 / 2 ] .
K = k [ - x 0 F + ( sin θ R + y 0 F ) Δ ϕ , - sin θ R - y 0 F - x 0 F Δ ϕ , cos θ R - ( 1 - x 0 2 + y 0 2 F 2 ) 1 / 2 ] .
k S = k R - K = k [ x 0 F - ( sin θ R + y 0 F ) Δ ϕ , y 0 F + x 0 F Δ ϕ , ( 1 - x 0 2 + y 0 2 F 2 ) 1 / 2 ] .
Δ k z k x 0 F sin θ R Δ ϕ ,
sinc ( L 2 π Δ k z ) = sinc ( k L x 0 2 π F sin θ R Δ ϕ ) ,
sinc ( L w x sin θ R Δ ϕ ) .
Δ x 0 = 2 λ F L sin θ R Δ ϕ ,
Δ x w = F sin θ R Δ ϕ .
Δ ϕ = λ L 1 sin θ R .
x c = u x l ,
y c = u y l .
1 F 1 + 1 l 2 = 1 F 2 ,
a = 2 λ F 1 δ = 2 λ N p ( F 1 N p δ ) = λ N p ( F / # ) ,
Δ x = R Δ ϕ ( 1 / 2 ) δ .
τ = T 2 π Δ ϕ T 2 π δ 2 R = T 2 π N p ( N p δ 2 R ) .
Δ ϕ 1 N p ,
τ = T 2 π N p .
Δ y = F Δ ϕ = F sin θ Δ ϕ ,
N p δ = 2 λ F / δ .
δ = 2 λ F N p δ .
Δ ϕ λ N p δ sin θ .
τ = T 2 π N p ( λ δ sin θ ) ,
η P inc N p 2 τ = M h c λ ,
τ = M h c N p 2 η P inc λ ,
N p 2 τ = η P inc λ M h c .

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