Abstract

In this paper, our simplified model for grating formation in photopolymers is extended to describe the effects of uniform post-exposure on an existing hologram, and further to present a new model of holographic multiplexing for calculating the exposure schedule for multiplexed gratings with uniform diffraction efficiency. It is experimentally verified that the refractive-index modulation of the existing gratings continues to increase when a current grating is being recorded. Twenty gratings were multiplexed using the exposure schedule calculated with the uniform post-exposure model, and comparison with the result from traditional method confirmed the validity of this model.

©2009 Optical Society of America

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References

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  1. G. H. Zhao and P. Mouroulis, “Diffusion-Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
    [Crossref]
  2. S. Piazzolla and B. K. Jenkins, “First-harmonic diffusion model for holographic grating formation in photopolymers,” J. Opt. Soc. Am. B 17(7), 1147–1157 (2000).
    [Crossref]
  3. A. Pu, K. Curtis, and D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35(10), 2824–2829 (1996).
    [Crossref]
  4. E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
    [Crossref] [PubMed]
  5. M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
    [Crossref]
  6. S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
    [Crossref]
  7. J. T. Sheridan, F. T. O'Neill, and J. V. Kelly, “Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model”, ” J. Opt. Soc. Am. 21(8), 1443–1451 (2004).
    [Crossref]
  8. J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
    [Crossref]
  9. P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
    [Crossref]
  10. T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
    [Crossref]
  11. Z. Tao, T. Shiquan, Z. Qianli, and S. Wei, “The Effects of Recording Modes to the Formation of Holographic Grating in Photopolymer,” Acta Photonica Sin.in press. (in Chinese).
  12. X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).
  13. S. Tao, D. R. Selviah, and J. E. Midwinter, “Spatioangular Multiplexed Storage of 750 Holograms in an Fe-Linbo3 Crystal,” Opt. Lett. 18(11), 912–914 (1993).
    [Crossref] [PubMed]
  14. D. Psaltis, M. Levene, A. Pu, G. Barbastathis, and K. Curtis, “Holographic Storage Using Shift Multiplexing,” Opt. Lett. 20, 782–784 (1995).
    [Crossref] [PubMed]

2008 (2)

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

2007 (4)

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

2006 (1)

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
[Crossref]

2004 (1)

J. T. Sheridan, F. T. O'Neill, and J. V. Kelly, “Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model”, ” J. Opt. Soc. Am. 21(8), 1443–1451 (2004).
[Crossref]

2000 (1)

1996 (1)

A. Pu, K. Curtis, and D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35(10), 2824–2829 (1996).
[Crossref]

1995 (1)

1994 (1)

G. H. Zhao and P. Mouroulis, “Diffusion-Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

1993 (1)

Barbastathis, G.

Belendez, A.

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

Beléndez, A.

Close, C. E.

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
[Crossref]

Curtis, K.

A. Pu, K. Curtis, and D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35(10), 2824–2829 (1996).
[Crossref]

D. Psaltis, M. Levene, A. Pu, G. Barbastathis, and K. Curtis, “Holographic Storage Using Shift Multiplexing,” Opt. Lett. 20, 782–784 (1995).
[Crossref] [PubMed]

Fernandez, E.

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

Fernández, E.

Gallego, S.

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

García, C.

Gleeson, M. R.

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
[Crossref]

Jenkins, B. K.

Kelly, J. V.

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
[Crossref]

J. T. Sheridan, F. T. O'Neill, and J. V. Kelly, “Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model”, ” J. Opt. Soc. Am. 21(8), 1443–1451 (2004).
[Crossref]

Levene, M.

Liu, P.

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

Liu, P. F.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Liu, Y.

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

Marquez, A.

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

Midwinter, J. E.

Mouroulis, P.

G. H. Zhao and P. Mouroulis, “Diffusion-Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

Neipp, C.

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

O'Neill, F. T.

J. T. Sheridan, F. T. O'Neill, and J. V. Kelly, “Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model”, ” J. Opt. Soc. Am. 21(8), 1443–1451 (2004).
[Crossref]

Ortuno, M.

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

Ortuño, M.

Pascual, I.

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

Piazzolla, S.

Psaltis, D.

A. Pu, K. Curtis, and D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35(10), 2824–2829 (1996).
[Crossref]

D. Psaltis, M. Levene, A. Pu, G. Barbastathis, and K. Curtis, “Holographic Storage Using Shift Multiplexing,” Opt. Lett. 20, 782–784 (1995).
[Crossref] [PubMed]

Pu, A.

A. Pu, K. Curtis, and D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35(10), 2824–2829 (1996).
[Crossref]

D. Psaltis, M. Levene, A. Pu, G. Barbastathis, and K. Curtis, “Holographic Storage Using Shift Multiplexing,” Opt. Lett. 20, 782–784 (1995).
[Crossref] [PubMed]

Qianli, Z.

Z. Tao, T. Shiquan, Z. Qianli, and S. Wei, “The Effects of Recording Modes to the Formation of Holographic Grating in Photopolymer,” Acta Photonica Sin.in press. (in Chinese).

Selviah, D. R.

Sheridan, J. T.

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
[Crossref]

J. T. Sheridan, F. T. O'Neill, and J. V. Kelly, “Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model”, ” J. Opt. Soc. Am. 21(8), 1443–1451 (2004).
[Crossref]

Shi, M.

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

Shiquan, T.

Z. Tao, T. Shiquan, Z. Qianli, and S. Wei, “The Effects of Recording Modes to the Formation of Holographic Grating in Photopolymer,” Acta Photonica Sin.in press. (in Chinese).

Tao, S.

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

S. Tao, D. R. Selviah, and J. E. Midwinter, “Spatioangular Multiplexed Storage of 750 Holograms in an Fe-Linbo3 Crystal,” Opt. Lett. 18(11), 912–914 (1993).
[Crossref] [PubMed]

Tao, S. Q.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Tao, Z.

Z. Tao, T. Shiquan, Z. Qianli, and S. Wei, “The Effects of Recording Modes to the Formation of Holographic Grating in Photopolymer,” Acta Photonica Sin.in press. (in Chinese).

Wan, X.

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

Wan, X. J.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Wan, Y.

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

Wang, H. Y.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Wei, S.

Z. Tao, T. Shiquan, Z. Qianli, and S. Wei, “The Effects of Recording Modes to the Formation of Holographic Grating in Photopolymer,” Acta Photonica Sin.in press. (in Chinese).

Wu, F.

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

Wu, F. P.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Xue, J. Q.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Zhai, Q.

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

Zhang, T.

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

Zhao, G. H.

G. H. Zhao and P. Mouroulis, “Diffusion-Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

Zhao, Y.

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

Zhao, Y. X.

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

Acta Photonica Sin. (1)

Z. Tao, T. Shiquan, Z. Qianli, and S. Wei, “The Effects of Recording Modes to the Formation of Holographic Grating in Photopolymer,” Acta Photonica Sin.in press. (in Chinese).

Appl. Opt. (1)

Imag. Sci. Photoch (1)

X. J. Wan, J. Q. Xue, H. Y. Wang, P. F. Liu, Y. X. Zhao, F. P. Wu, and S. Q. Tao, “Study on Novel Photopolymers for Holographic Storage,” Imag. Sci. Photoch 26, 343–348 (2008) (in Chinese).

J. Mod. Opt. (1)

G. H. Zhao and P. Mouroulis, “Diffusion-Model of Hologram Formation in Dry Photopolymer Materials,” J. Mod. Opt. 41(10), 1929–1939 (1994).
[Crossref]

J. Opt. Soc. Am. (1)

J. T. Sheridan, F. T. O'Neill, and J. V. Kelly, “Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model”, ” J. Opt. Soc. Am. 21(8), 1443–1451 (2004).
[Crossref]

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

Opt. Commun. (2)

M. Ortuno, A. Marquez, E. Fernandez, S. Gallego, A. Belendez, and I. Pascual, “Hologram multiplexing in acrylamide hydrophilic photopolymers,” Opt. Commun. 281(6), 1354–1357 (2008).
[Crossref]

S. Gallego, C. Neipp, M. Ortuno, A. Belendez, E. Fernandez, and I. Pascual, “Analysis of monomer diffusion in depth in photopolymer materials,” Opt. Commun. 274(1), 43–49 (2007).
[Crossref]

Opt. Eng. (1)

A. Pu, K. Curtis, and D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35(10), 2824–2829 (1996).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (3)

J. V. Kelly, M. R. Gleeson, C. E. Close, and J. T. Sheridan, “Optimized scheduling technique for holographic data storage,” Proc. SPIE 6335, 63350J (2006).
[Crossref]

P. Liu, T. Zhang, Y. Liu, Q. Zhai, S. Tao, X. Wan, and F. Wu, “The investigation of the effect of recording conditions on grating formation in a novel holographic photopolymer,” Proc. SPIE 6832, 68320Y (2007).
[Crossref]

T. Zhang, S. Tao, Y. Wan, M. Shi, Y. Zhao, and F. Wu, “Research on the dark diffusion transient for a blue-green sensitized holographic photopolymer material,” Proc. SPIE 6796, 67961M (2007).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 The six-order polynomial fitting curve of cumulative Δn versus cumulative recording time. The data were extracted from experiment of 20 gratings angle-multiplexed with equal exposure time. The fitting curve is extended from the point marked by the red arrow to verify whether the model is accordance with the physical fact.

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Fig. 2
Fig. 2 The schematic of growth process of every grating when multiplexing N gratings in photopolymer

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Fig. 3
Fig. 3 Experimental Setup. f 1, f 2, f 3 are focal lengths of lenses L1, L2, L3, respectively. M: mirror, BE: beam expander, PM: power meter.

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Fig. 4
Fig. 4 Sampled curves of scanned readout of two angle-multiplexed gratings at different time. The starting time of each scanning is marked in the figure.

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Fig. 5
Fig. 5 The dynamics curve of two grating multiplexing. The red arrow indicates the time when the first recording ended and the second started. The angle addressing time for the second grating was less than 0.3s that is too short to display in the figure.

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Fig. 6
Fig. 6 (a) Fitting curve of dark enhancement experiment. The fitted τD is 354. (b) Fitting and experiment curve of a single grating formation. Fitting result is: Δnsat = 6.84 × 10−4, τP = 152.

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Fig. 7
Fig. 7 Exposure Schedule calculated with UPE model

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Fig. 8
Fig. 8 Diffraction efficiency of 20 multiplexed holograms recorded using the schedule in Fig. 7, and measured immediately after the multiplexing recording.

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Fig. 9
Fig. 9 Exposure Schedule calculated with the six-order polynomial model

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Fig. 10
Fig. 10 Diffraction power of 20 multiplexed gratings resulted from exposure schedule calculated by the traditional method.

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Equations (10)

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

I(x)=I0(1+mcosKx)
Δn(t)=ΔnSAT{1+τDτpexp[−(1τp+1τD)t]−(1+τDτp)exp(−tτp)}
u0(te)=Uexp(−te/τP)
u1(te)=mUτD2τPexp[−(1τP+1τD)te]⋅[exp(teτD)−1]
Δn(t)=Δn(te)+Cnu1(te)⋅[1−exp(−t−teτD)]                     (t>te)
Δn(t)=Δn(te)+Cnu1(te)τpτp+τD{1−exp[−(1τp+1τD)⋅(t−te)]}           (t>te)
Δnn(t)=ΔnsatτP+τD{τP[exp(−tn−1τP)−exp(−tnτP)]−τDexp[−(1τP+1τD)t]⋅[exp(tnτD)−exp(tn−1τD)]}
t∈[tn,T],t0=0,n=1, 2, 3…N
ΔnTotal=∑n=1NΔnn(T)=NΔn0=ΔnsatτP+τD{−τP[exp(−TτP)−1]−τDexp[−(1τP+1τD)T]⋅[exp(TτD)−1]}
nΔn0=Δnsat(τD+τP){−τP[exp(−tnτP)−1]−τDexp[−(1τP+1τD)⋅T]⋅[exp(tnτD)−1]}

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