Abstract

A model describing the angular selectivity of noise gratings in volume holographic recording materials is presented. The noise grating is treated as an ensemble of superimposed, statistically distributed planar gratings. Rigorous coupled-wave analysis is used to treat reconstruction with various polarization states. The model accounts for material properties such as thickness change, absorption, and the angular distribution of scattered light within the recording medium. Results show good agreement with noise gratings that are experimentally formed in a thick cationic ring-opening photopolymer material.

© 2004 Optical Society of America

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  1. A. P. Yakimovich, “Dynamic self-amplification of scattering noise in volume-hologram recording,” Opt. Spectrosc. 49, 191–193 (1980).
  2. K. Biedermann, “The scattered flux spectrum of photographic materials for holography,” Optik (Stuttgart) 31, 367–389 (1970).
  3. S. I. Ragnarsson, “Scattering phenomena in volume holograms with strong coupling,” Appl. Opt. 17, 116–127 (1978).
    [CrossRef] [PubMed]
  4. J. M. Moran, I. P. Kaminow, “Properties of holographic gratings photoinduced in polymethyl methacrylate,” Appl. Opt. 12, 1964–1970 (1973).
    [CrossRef] [PubMed]
  5. M. R. B. Forshaw, “Explanation of the ‘Venetian blind’ effect in holography, using the Ewald sphere concept,” Opt. Commun. 8, 201–206 (1973).
    [CrossRef]
  6. M. R. B. Forshaw, “Explanation of the two-ring diffraction phenomenon observed by Moran and Kaminow,” Appl. Opt. 13, 2 (1974).
    [CrossRef] [PubMed]
  7. M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
    [CrossRef]
  8. R. Magnusson, T. K. Gaylord, “Laser scattering induced holograms in lithium niobate,” Appl. Opt. 13, 1545–1548 (1974).
    [CrossRef]
  9. M. A. Ellabban, R. A. Rupp, M. Fally, “Reconstruction of parasitic holograms to characterize photorefractive materials,” Appl. Phys. B 72, 635–640 (2001).
    [CrossRef]
  10. M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
    [CrossRef]
  11. J. A. Frantz, R. K. Kostuk, D. A. Waldman, “Coherent scattering properties of a cationic ring-opening volume holographic recording material,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, T. J. Trout, eds., Proc. SPIE4296, 267–273 (2001).
    [CrossRef]
  12. A. Beléndez, A. Fimia, L. Carretero, F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording materials,” Appl. Phys. Lett. 67, 3856–3858 (1995).
    [CrossRef]
  13. R. R. A. Syms, L. Solymar, “Noise gratings in photographic emulsion,” Opt. Commun. 43, 107–110 (1982).
    [CrossRef]
  14. R. R. A. Syms, L. Solymar, “Noise gratings in silver halide volume holograms,” Appl. Phys. B 30, 177–182 (1983).
    [CrossRef]
  15. L. Wang, R. K. Kostuk, “Direct formation of planar holograms and noise gratings at 820 nm in bleached silver-halide emulsions,” Opt. Lett. 14, 919–921 (1989).
    [CrossRef] [PubMed]
  16. L. Solymar, G. D. G. Riddy, “Noise gratings for single- and double-beam exposures in silver halide emulsions,” J. Opt. Soc. Am. A 7, 2107–2108 (1990).
    [CrossRef]
  17. A. Beléndez, I. Pascual, A. Fimia, “Noise gratings recorded with single-beam exposures in silver halide emulsions: the influence of the bleach bath,” Opt. Quantum Electron. 25, 139–145 (1993).
    [CrossRef]
  18. A. Fimia, R. Fuentes, A. Beléndez, “Noise gratings in bleached silver halide diffuse-object holograms,” Opt. Lett. 19, 1243–1245 (1994).
    [CrossRef] [PubMed]
  19. L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analysing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
    [CrossRef]
  20. A. Beléndez, L. Carretero, I. Pascual, “Polarization influences on the efficiency of noise gratings recorded in silver halide holograms,” Appl. Opt. 32, 7155–7163 (1993).
    [CrossRef] [PubMed]
  21. L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
    [CrossRef]
  22. L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
    [CrossRef]
  23. G. D. G. Riddy, L. Solymar, “Theoretical model of reconstructed scatter in volume holograms,” Electron. Lett. 22, 872–873 (1986).
    [CrossRef]
  24. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  25. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  26. J. J. DePalma, J. Gasper, “Determining the optical properties of photographic emulsions by the Monte Carlo method,” Photograph. Sci. Eng. 16, 181–191 (1972).
  27. B. R. Frieden, Probability, Statistical Optics, and Data Testing, 2nd ed. (Springer-Verlag, New York, 1991).
  28. A. A. Kokhanovsky, Optics of Light Scattering Media, 2nd ed. (Springer, Chichester, UK, 2001).
  29. R. Xu, Particle Characterization: Light Scattering Methods (Kluwer Academic, Boston, 2000).
  30. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
    [CrossRef]
  31. D. A. Waldman, H.-Y. S. Li, E. A. Cetin, “Holographic recording properties in thick films of ULSH-500 photopolymer,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 89–103 (1998).
    [CrossRef]
  32. D. A. Waldman, H.-Y. S. Li, M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening holographic recording material,” J. Imaging Sci. Technol. 41, 497–514 (1997).
  33. D. A. Waldman, H.-Y. S. Li, “Determination of low transverse shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S. H. Lee, eds., Proc. SPIE3010, 354–372 (1997).
    [CrossRef]
  34. L. Solymar, J. C. W. Newell, “Silver halide noise gratings recorded in dichromated gelatin,” Opt. Commun. 73, 273–276 (1989).
    [CrossRef]
  35. A. A. Ward, J. M. Heaton, L. Solymar, “Efficient noise gratings in silver halide emulsions,” Opt. Quantum Electron. 16, 365–367 (1984).
    [CrossRef]

2001

M. A. Ellabban, R. A. Rupp, M. Fally, “Reconstruction of parasitic holograms to characterize photorefractive materials,” Appl. Phys. B 72, 635–640 (2001).
[CrossRef]

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

1999

M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
[CrossRef]

1998

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
[CrossRef]

1997

D. A. Waldman, H.-Y. S. Li, M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening holographic recording material,” J. Imaging Sci. Technol. 41, 497–514 (1997).

1995

A. Beléndez, A. Fimia, L. Carretero, F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording materials,” Appl. Phys. Lett. 67, 3856–3858 (1995).
[CrossRef]

1994

1993

L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analysing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
[CrossRef]

A. Beléndez, L. Carretero, I. Pascual, “Polarization influences on the efficiency of noise gratings recorded in silver halide holograms,” Appl. Opt. 32, 7155–7163 (1993).
[CrossRef] [PubMed]

L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
[CrossRef]

A. Beléndez, I. Pascual, A. Fimia, “Noise gratings recorded with single-beam exposures in silver halide emulsions: the influence of the bleach bath,” Opt. Quantum Electron. 25, 139–145 (1993).
[CrossRef]

1990

1989

L. Wang, R. K. Kostuk, “Direct formation of planar holograms and noise gratings at 820 nm in bleached silver-halide emulsions,” Opt. Lett. 14, 919–921 (1989).
[CrossRef] [PubMed]

L. Solymar, J. C. W. Newell, “Silver halide noise gratings recorded in dichromated gelatin,” Opt. Commun. 73, 273–276 (1989).
[CrossRef]

1986

G. D. G. Riddy, L. Solymar, “Theoretical model of reconstructed scatter in volume holograms,” Electron. Lett. 22, 872–873 (1986).
[CrossRef]

1984

A. A. Ward, J. M. Heaton, L. Solymar, “Efficient noise gratings in silver halide emulsions,” Opt. Quantum Electron. 16, 365–367 (1984).
[CrossRef]

1983

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[CrossRef]

R. R. A. Syms, L. Solymar, “Noise gratings in silver halide volume holograms,” Appl. Phys. B 30, 177–182 (1983).
[CrossRef]

1982

R. R. A. Syms, L. Solymar, “Noise gratings in photographic emulsion,” Opt. Commun. 43, 107–110 (1982).
[CrossRef]

1980

A. P. Yakimovich, “Dynamic self-amplification of scattering noise in volume-hologram recording,” Opt. Spectrosc. 49, 191–193 (1980).

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

1978

1974

1973

J. M. Moran, I. P. Kaminow, “Properties of holographic gratings photoinduced in polymethyl methacrylate,” Appl. Opt. 12, 1964–1970 (1973).
[CrossRef] [PubMed]

M. R. B. Forshaw, “Explanation of the ‘Venetian blind’ effect in holography, using the Ewald sphere concept,” Opt. Commun. 8, 201–206 (1973).
[CrossRef]

1972

J. J. DePalma, J. Gasper, “Determining the optical properties of photographic emulsions by the Monte Carlo method,” Photograph. Sci. Eng. 16, 181–191 (1972).

1970

K. Biedermann, “The scattered flux spectrum of photographic materials for holography,” Optik (Stuttgart) 31, 367–389 (1970).

1969

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

Beléndez, A.

A. Beléndez, A. Fimia, L. Carretero, F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording materials,” Appl. Phys. Lett. 67, 3856–3858 (1995).
[CrossRef]

A. Fimia, R. Fuentes, A. Beléndez, “Noise gratings in bleached silver halide diffuse-object holograms,” Opt. Lett. 19, 1243–1245 (1994).
[CrossRef] [PubMed]

A. Beléndez, L. Carretero, I. Pascual, “Polarization influences on the efficiency of noise gratings recorded in silver halide holograms,” Appl. Opt. 32, 7155–7163 (1993).
[CrossRef] [PubMed]

A. Beléndez, I. Pascual, A. Fimia, “Noise gratings recorded with single-beam exposures in silver halide emulsions: the influence of the bleach bath,” Opt. Quantum Electron. 25, 139–145 (1993).
[CrossRef]

L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analysing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
[CrossRef]

L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
[CrossRef]

Biedermann, K.

K. Biedermann, “The scattered flux spectrum of photographic materials for holography,” Optik (Stuttgart) 31, 367–389 (1970).

Blaya, S.

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
[CrossRef]

Carretero, L.

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
[CrossRef]

A. Beléndez, A. Fimia, L. Carretero, F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording materials,” Appl. Phys. Lett. 67, 3856–3858 (1995).
[CrossRef]

L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analysing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
[CrossRef]

L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
[CrossRef]

A. Beléndez, L. Carretero, I. Pascual, “Polarization influences on the efficiency of noise gratings recorded in silver halide holograms,” Appl. Opt. 32, 7155–7163 (1993).
[CrossRef] [PubMed]

Cetin, E. A.

D. A. Waldman, H.-Y. S. Li, E. A. Cetin, “Holographic recording properties in thick films of ULSH-500 photopolymer,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 89–103 (1998).
[CrossRef]

DePalma, J. J.

J. J. DePalma, J. Gasper, “Determining the optical properties of photographic emulsions by the Monte Carlo method,” Photograph. Sci. Eng. 16, 181–191 (1972).

Ellabban, M. A.

M. A. Ellabban, R. A. Rupp, M. Fally, “Reconstruction of parasitic holograms to characterize photorefractive materials,” Appl. Phys. B 72, 635–640 (2001).
[CrossRef]

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

Fally, M.

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

M. A. Ellabban, R. A. Rupp, M. Fally, “Reconstruction of parasitic holograms to characterize photorefractive materials,” Appl. Phys. B 72, 635–640 (2001).
[CrossRef]

Fimia, A.

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
[CrossRef]

A. Beléndez, A. Fimia, L. Carretero, F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording materials,” Appl. Phys. Lett. 67, 3856–3858 (1995).
[CrossRef]

A. Fimia, R. Fuentes, A. Beléndez, “Noise gratings in bleached silver halide diffuse-object holograms,” Opt. Lett. 19, 1243–1245 (1994).
[CrossRef] [PubMed]

A. Beléndez, I. Pascual, A. Fimia, “Noise gratings recorded with single-beam exposures in silver halide emulsions: the influence of the bleach bath,” Opt. Quantum Electron. 25, 139–145 (1993).
[CrossRef]

L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analysing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
[CrossRef]

L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
[CrossRef]

Fink, M.

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

Forshaw, M. R. B.

M. R. B. Forshaw, “Explanation of the two-ring diffraction phenomenon observed by Moran and Kaminow,” Appl. Opt. 13, 2 (1974).
[CrossRef] [PubMed]

M. R. B. Forshaw, “Explanation of the ‘Venetian blind’ effect in holography, using the Ewald sphere concept,” Opt. Commun. 8, 201–206 (1973).
[CrossRef]

Frantz, J. A.

J. A. Frantz, R. K. Kostuk, D. A. Waldman, “Coherent scattering properties of a cationic ring-opening volume holographic recording material,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, T. J. Trout, eds., Proc. SPIE4296, 267–273 (2001).
[CrossRef]

Frieden, B. R.

B. R. Frieden, Probability, Statistical Optics, and Data Testing, 2nd ed. (Springer-Verlag, New York, 1991).

Fuentes, R.

Gasper, J.

J. J. DePalma, J. Gasper, “Determining the optical properties of photographic emulsions by the Monte Carlo method,” Photograph. Sci. Eng. 16, 181–191 (1972).

Gaylord, T. K.

Heaton, J. M.

A. A. Ward, J. M. Heaton, L. Solymar, “Efficient noise gratings in silver halide emulsions,” Opt. Quantum Electron. 16, 365–367 (1984).
[CrossRef]

Horner, M. G.

D. A. Waldman, H.-Y. S. Li, M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening holographic recording material,” J. Imaging Sci. Technol. 41, 497–514 (1997).

Imlau, M.

M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
[CrossRef]

Kaminow, I. P.

Kogelnik, H.

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

Kokhanovsky, A. A.

A. A. Kokhanovsky, Optics of Light Scattering Media, 2nd ed. (Springer, Chichester, UK, 2001).

Kostuk, R. K.

L. Wang, R. K. Kostuk, “Direct formation of planar holograms and noise gratings at 820 nm in bleached silver-halide emulsions,” Opt. Lett. 14, 919–921 (1989).
[CrossRef] [PubMed]

J. A. Frantz, R. K. Kostuk, D. A. Waldman, “Coherent scattering properties of a cationic ring-opening volume holographic recording material,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, T. J. Trout, eds., Proc. SPIE4296, 267–273 (2001).
[CrossRef]

Li, H.-Y. S.

D. A. Waldman, H.-Y. S. Li, M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening holographic recording material,” J. Imaging Sci. Technol. 41, 497–514 (1997).

D. A. Waldman, H.-Y. S. Li, E. A. Cetin, “Holographic recording properties in thick films of ULSH-500 photopolymer,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 89–103 (1998).
[CrossRef]

D. A. Waldman, H.-Y. S. Li, “Determination of low transverse shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S. H. Lee, eds., Proc. SPIE3010, 354–372 (1997).
[CrossRef]

Madrigal, R. F.

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
[CrossRef]

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

R. Magnusson, T. K. Gaylord, “Laser scattering induced holograms in lithium niobate,” Appl. Opt. 13, 1545–1548 (1974).
[CrossRef]

Mallavia, R.

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
[CrossRef]

Mateos, F.

A. Beléndez, A. Fimia, L. Carretero, F. Mateos, “Self-induced phase gratings due to the inhomogeneous structure of acrylamide photopolymer systems used as holographic recording materials,” Appl. Phys. Lett. 67, 3856–3858 (1995).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

Moran, J. M.

Newell, J. C. W.

L. Solymar, J. C. W. Newell, “Silver halide noise gratings recorded in dichromated gelatin,” Opt. Commun. 73, 273–276 (1989).
[CrossRef]

Pascual, I.

A. Beléndez, L. Carretero, I. Pascual, “Polarization influences on the efficiency of noise gratings recorded in silver halide holograms,” Appl. Opt. 32, 7155–7163 (1993).
[CrossRef] [PubMed]

A. Beléndez, I. Pascual, A. Fimia, “Noise gratings recorded with single-beam exposures in silver halide emulsions: the influence of the bleach bath,” Opt. Quantum Electron. 25, 139–145 (1993).
[CrossRef]

Ragnarsson, S. I.

Riddy, G. D. G.

L. Solymar, G. D. G. Riddy, “Noise gratings for single- and double-beam exposures in silver halide emulsions,” J. Opt. Soc. Am. A 7, 2107–2108 (1990).
[CrossRef]

G. D. G. Riddy, L. Solymar, “Theoretical model of reconstructed scatter in volume holograms,” Electron. Lett. 22, 872–873 (1986).
[CrossRef]

Rupp, R. A.

M. A. Ellabban, R. A. Rupp, M. Fally, “Reconstruction of parasitic holograms to characterize photorefractive materials,” Appl. Phys. B 72, 635–640 (2001).
[CrossRef]

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
[CrossRef]

Schieder, R.

M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
[CrossRef]

Solymar, L.

L. Solymar, G. D. G. Riddy, “Noise gratings for single- and double-beam exposures in silver halide emulsions,” J. Opt. Soc. Am. A 7, 2107–2108 (1990).
[CrossRef]

L. Solymar, J. C. W. Newell, “Silver halide noise gratings recorded in dichromated gelatin,” Opt. Commun. 73, 273–276 (1989).
[CrossRef]

G. D. G. Riddy, L. Solymar, “Theoretical model of reconstructed scatter in volume holograms,” Electron. Lett. 22, 872–873 (1986).
[CrossRef]

A. A. Ward, J. M. Heaton, L. Solymar, “Efficient noise gratings in silver halide emulsions,” Opt. Quantum Electron. 16, 365–367 (1984).
[CrossRef]

R. R. A. Syms, L. Solymar, “Noise gratings in silver halide volume holograms,” Appl. Phys. B 30, 177–182 (1983).
[CrossRef]

R. R. A. Syms, L. Solymar, “Noise gratings in photographic emulsion,” Opt. Commun. 43, 107–110 (1982).
[CrossRef]

Syms, R. R. A.

R. R. A. Syms, L. Solymar, “Noise gratings in silver halide volume holograms,” Appl. Phys. B 30, 177–182 (1983).
[CrossRef]

R. R. A. Syms, L. Solymar, “Noise gratings in photographic emulsion,” Opt. Commun. 43, 107–110 (1982).
[CrossRef]

Tillmanns, E.

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

Waldman, D. A.

D. A. Waldman, H.-Y. S. Li, M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening holographic recording material,” J. Imaging Sci. Technol. 41, 497–514 (1997).

D. A. Waldman, H.-Y. S. Li, E. A. Cetin, “Holographic recording properties in thick films of ULSH-500 photopolymer,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 89–103 (1998).
[CrossRef]

J. A. Frantz, R. K. Kostuk, D. A. Waldman, “Coherent scattering properties of a cationic ring-opening volume holographic recording material,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, T. J. Trout, eds., Proc. SPIE4296, 267–273 (2001).
[CrossRef]

D. A. Waldman, H.-Y. S. Li, “Determination of low transverse shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S. H. Lee, eds., Proc. SPIE3010, 354–372 (1997).
[CrossRef]

Wang, L.

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[CrossRef]

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M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
[CrossRef]

Wolfsberger, J.

M. Fally, M. A. Ellabban, R. A. Rupp, M. Fink, J. Wolfsberger, E. Tillmanns, “Characterization of parasitic gratings in LiNbO3,” Phys. Rev. B 61, 15778–15784 (2001).
[CrossRef]

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Appl. Opt.

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D. A. Waldman, H.-Y. S. Li, M. G. Horner, “Volume shrinkage in slant fringe gratings of a cationic ring-opening holographic recording material,” J. Imaging Sci. Technol. 41, 497–514 (1997).

J. Mod. Opt.

L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analysing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
[CrossRef]

L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
[CrossRef]

L. Carretero, S. Blaya, R. Mallavia, R. F. Madrigal, A. Fimia, “A theoretical model for noise gratings recorded in acrylamide photopolymer materials used in real-time holography,” J. Mod. Opt. 45, 2345–2354 (1998).
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[CrossRef]

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[CrossRef]

Phys. Rev. Lett.

M. Imlau, T. Woike, R. Schieder, R. A. Rupp, “Holographic scattering in centrosymmetric Na2[Fe(CN)5NO]·2H2O,” Phys. Rev. Lett. 82, 2860–2863 (1999).
[CrossRef]

Other

J. A. Frantz, R. K. Kostuk, D. A. Waldman, “Coherent scattering properties of a cationic ring-opening volume holographic recording material,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, T. J. Trout, eds., Proc. SPIE4296, 267–273 (2001).
[CrossRef]

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R. Xu, Particle Characterization: Light Scattering Methods (Kluwer Academic, Boston, 2000).

D. A. Waldman, H.-Y. S. Li, E. A. Cetin, “Holographic recording properties in thick films of ULSH-500 photopolymer,” in Diffractive and Holographic Device Technologies and Applications V, I. Cindrich, S. H. Lee, eds., Proc. SPIE3291, 89–103 (1998).
[CrossRef]

D. A. Waldman, H.-Y. S. Li, “Determination of low transverse shrinkage in slant fringe gratings of a cationic ring-opening volume hologram recording material,” in Diffractive and Holographic Device Technologies and Applications IV, I. Cindrich, S. H. Lee, eds., Proc. SPIE3010, 354–372 (1997).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Reconstruction geometry for a single planar grating.

Fig. 2
Fig. 2

Scatter distribution together with a graph of the resulting transmittance as a function of angle for (a) a spherical distribution, (b) a cos2(δ) distribution, and (c) a circular distribution lying in the plane of incidence. (a) and (b) Results by use of RCWA are shown, and (c) results by use of both RCWA and two-beam coupled-wave theory are shown.

Fig. 3
Fig. 3

Transmittance versus angle for simulations with (a) N=100 gratings, (b) N=1000 gratings, (c) N=10,000 gratings, and (d) N=20,000 gratings.

Fig. 4
Fig. 4

Transmittance versus angle for simulations with the thickness change varying from 0.0% to -2.0%.

Fig. 5
Fig. 5

Transmittance versus angle for various values of ψ, the polarization of the replay beam.

Fig. 6
Fig. 6

Transmittance versus angle for (a) a 10-µm-thick noise grating and (b) a 100-µm-thick noise grating. Results including ±1 and ±2 diffracted orders are shown.

Fig. 7
Fig. 7

Scatter characterization setup.

Fig. 8
Fig. 8

Transmittance as a function of exposure for nonpreheated and preheated ULSH-500-7A. The transmittance drops sharply, indicating the formation of a noise grating.

Fig. 9
Fig. 9

Cross section of the far-field scattered light with varying exposure for preheated ULSH-500-7A.

Fig. 10
Fig. 10

Experimental measurement of the transmittance versus angle for a noise grating recorded in preheated ULSH-500-7A. The data obtained with both TM- and TE-polarized replay beams are shown along with results from a Monte Carlo simulation.

Equations (33)

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pT(θr)=pR¯(θr)pA¯(θr)pD¯(θr),
pT(θr)=[1-pR(θr)][1-pA(θr)]i=1N[1-pDi(θr)],
pA(θr)=exp-αdcos(θf),
K=K sin ϕ cos xˆ-K sin ϕ sin yˆ+K cos ϕzˆ,
k1=k1(sin θrxˆ+cos θryˆ),
uˆ=cos ψ cos θrxˆ+sin ψyˆ-cos ψ sin θrzˆ.
E1=Einc+mRmexp(-jk1m·rˆ),
E3=mTmexp[-jk3m·(rˆ-dzˆ)],
klm=[(k1-mK)·xˆ]xˆ-[(k1-mK)·yˆ]yˆ+kzlmzˆ=kxmxˆ+kymyˆ+kzlmzˆ,
kxm=k1 sin α-mK sin ϕ cos δ,
kym=mK sin ϕ sin δ,
kzlm=(kl2-kxm2-kym2)1/2.
E2=m[Sxm(z)xˆ+Sym(z)yˆ+Szm(z)zˆ]exp(-jσm·r),
H2=(0/μ0)1/2m[Uxm(z)xˆ+Uym(z)yˆ+Uzm(z)zˆ]exp(-jσm·r),
σm=kxmxˆ+kymyˆ-mKzzˆ.
×E2=-jωμ0H2,
×H2=jω0(x, y, z)E2,
E2=S0(z)exp(-jk1·rˆ)+S1(z)exp(-jkd·rˆ),
ϑ=ΔθK sin(ϕ-θB),
κ=(π/2λ)(Δ/0),
cR=cos θr,
cS=cos θr-(K/k2)cos(ϕ).
S1=-j(cR/cS)1/2exp(-αd/cR)exp(ξ)sin(ν2-ξ2)(1-ν2/ξ2)1/2,
ν=κd/cRcS,
ξ=d2αcR-αcS-jϑcS.
S1=(cR/cS)1/2sinh(ν cosh a)cosh(a+ν cosh a),
ν=jκd/cRcS,
sinh a=ξ/ν,
ηi=(|cS|/cR)S1S1*.
ηiκ2ni2
pT(θr)i=1N[1-pDi(θr)]i=1N[1-ηi(θr)],
pT(θr)1-i=1Nηi(θr).
ni=nc/N,

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