Abstract

Nonlinear recording effects on holographic reflection gratings recorded on BB640 emulsions have been studied. Using an analyticalapproach to the characteristic curve of these emulsions, we obtained the recorded density profiles corresponding to the original light pattern generated by the holographic setup. The final spatial profiles of the refraction index resulting from different exposure levels and different bleaching processes were evaluated studying the experimental diffraction efficiency and comparing it with Kogelnik’s theory. The quality of the fittings of this model with the experimental spectral responses of the final gratings was used as a measure of concordance between the original sinusoidal, periodical light distribution and the resulting modulation profile of the processed hologram. The range of applicability of the theoretical model to the experimental results was evaluated using different bleaching processes.

© 2003 Optical Society of America

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References

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  1. F. Hurter and V. C. Driffield, “Photo-chemical investigations and a new method of determination of the sensitiveness of photographic plates,” J. Soc. Chem. Ind. 9, 455–469 (1890).
    [CrossRef]
  2. C. E. K. Mees and T. H. James, The Theory of the Photographic Process, The Macmillan Company (New York1966).
  3. R. Magnusson and T. K. Gaylord, “Analysis of multiwave diffraction of thick gratings,” J. Opt. Soc. Am. 67, 1165–1170 (1977).
    [CrossRef]
  4. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 37–45 (1981).
    [CrossRef]
  5. L. Solymar and D. J. Cooke, Volume holography and volume gratings, Academic Press (London1981).
  6. D. Liu and J. Zhou, “Non linear analysis for a reflection hologram,” Opt. Commun. 107, 471–479 (1994).
    [CrossRef]
  7. A. Bac and P. J. Twardowski, “Analysis of broadband lippmann-bragg holographic filters with substrate defects,” Opt. Laser Technol. 33, 37–41 (2001).
    [CrossRef]
  8. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” The Bell Syst. Tech. J. 48, 2909–2945 (1969).
  9. L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Belendez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. 26, 786–788 (2001).
    [CrossRef]
  10. R. R. A. Syms, Practical Volume Holography, Oxford University Press (Oxford1990).
  11. 2001. Personal Communication on pre-sensitizing methods for BB640 holographic emulsions with M. Medora of Colourholographics Ltd. (2002)
  12. Y. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, vol. MS 171 of Milestone Series, 22–24. SPIE (2001).
  13. M. Ulibarrena, M. J. Méndez, L. Carretero, R. Madrigal, and A. Fimia, “Comparison of direct, rehalogenating and solvent bleaching processes with BB640 plates,” Appl. Opt. 41, 4120–4123 (2002).
    [CrossRef] [PubMed]
  14. E. K. Company. Black-and-White Processing Using KODAK Chemicals (1985).
  15. S. Wolfram, The Mathematica book, Wolfram media, fourth edition (1999).
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  17. M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, “D-log E curve of BB640 plates with D8 developer: a modified response,” in Practical Holography XVI and Holographic Materials VIII, 388–398, SPIE (2002).
    [CrossRef]
  18. W. T. Cathey, “Three-dimensional Wavefront Reconstruction Using a Phase Hologram,” J. Opt. Soc. Am. 55, 457 (1965).
    [CrossRef]
  19. H. I. Bjelkhagen, Silver-Halide Recording Materials, Springer-Verlag (New York1993).
  20. N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).
  21. R. L. Lamberts and C. N. Kurtz, “Reversal Bleaching for Low Flare Light in Holograms,” Appl. Opt. 10, 1342–1347 (1971).
    [CrossRef] [PubMed]
  22. P. Hariharan, C. S. Ramanathan, and G. S. Kaushik, “Simplified processing technique for photographic phase holograms,” Opt. Commun. 3, 246–247 (1971).
    [CrossRef]
  23. K. S. Pennington and J. S. Harper, “Techniques for Producing Low-Noise, Improved Efficiency Holograms,” Appl. Opt. 9, 1643–1650 (1970).
    [CrossRef] [PubMed]
  24. J. Crespo, A. Fimia, and J. A. Quintana, “Fixation-free Methods in Bleached Reflection Holography,” Appl. Opt. 25, 1642–1645 (1986).
    [CrossRef] [PubMed]

2002 (1)

2001 (2)

A. Bac and P. J. Twardowski, “Analysis of broadband lippmann-bragg holographic filters with substrate defects,” Opt. Laser Technol. 33, 37–41 (2001).
[CrossRef]

L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Belendez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. 26, 786–788 (2001).
[CrossRef]

1994 (1)

D. Liu and J. Zhou, “Non linear analysis for a reflection hologram,” Opt. Commun. 107, 471–479 (1994).
[CrossRef]

1987 (1)

1986 (1)

1981 (1)

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 37–45 (1981).
[CrossRef]

1980 (1)

N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).

1977 (1)

1971 (2)

R. L. Lamberts and C. N. Kurtz, “Reversal Bleaching for Low Flare Light in Holograms,” Appl. Opt. 10, 1342–1347 (1971).
[CrossRef] [PubMed]

P. Hariharan, C. S. Ramanathan, and G. S. Kaushik, “Simplified processing technique for photographic phase holograms,” Opt. Commun. 3, 246–247 (1971).
[CrossRef]

1970 (1)

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” The Bell Syst. Tech. J. 48, 2909–2945 (1969).

1965 (1)

1890 (1)

F. Hurter and V. C. Driffield, “Photo-chemical investigations and a new method of determination of the sensitiveness of photographic plates,” J. Soc. Chem. Ind. 9, 455–469 (1890).
[CrossRef]

Bac, A.

A. Bac and P. J. Twardowski, “Analysis of broadband lippmann-bragg holographic filters with substrate defects,” Opt. Laser Technol. 33, 37–41 (2001).
[CrossRef]

Belendez, A.

Bjelkhagen, H. I.

H. I. Bjelkhagen, Silver-Halide Recording Materials, Springer-Verlag (New York1993).

Blaya, S.

L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Belendez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. 26, 786–788 (2001).
[CrossRef]

M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, “D-log E curve of BB640 plates with D8 developer: a modified response,” in Practical Holography XVI and Holographic Materials VIII, 388–398, SPIE (2002).
[CrossRef]

Carretero, L.

Cathey, W. T.

Cooke, D. J.

L. Solymar and D. J. Cooke, Volume holography and volume gratings, Academic Press (London1981).

Crespo, J.

Cullen, R.

N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).

Denisyuk, Y. N.

Y. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, vol. MS 171 of Milestone Series, 22–24. SPIE (2001).

Driffield, V. C.

F. Hurter and V. C. Driffield, “Photo-chemical investigations and a new method of determination of the sensitiveness of photographic plates,” J. Soc. Chem. Ind. 9, 455–469 (1890).
[CrossRef]

Fimia, A.

Gaylord, T. K.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 37–45 (1981).
[CrossRef]

R. Magnusson and T. K. Gaylord, “Analysis of multiwave diffraction of thick gratings,” J. Opt. Soc. Am. 67, 1165–1170 (1977).
[CrossRef]

Hariharan, P.

P. Hariharan, C. S. Ramanathan, and G. S. Kaushik, “Simplified processing technique for photographic phase holograms,” Opt. Commun. 3, 246–247 (1971).
[CrossRef]

Harper, J. S.

Hurter, F.

F. Hurter and V. C. Driffield, “Photo-chemical investigations and a new method of determination of the sensitiveness of photographic plates,” J. Soc. Chem. Ind. 9, 455–469 (1890).
[CrossRef]

James, T. H.

C. E. K. Mees and T. H. James, The Theory of the Photographic Process, The Macmillan Company (New York1966).

Kasprzak, H.

Kaushik, G. S.

P. Hariharan, C. S. Ramanathan, and G. S. Kaushik, “Simplified processing technique for photographic phase holograms,” Opt. Commun. 3, 246–247 (1971).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” The Bell Syst. Tech. J. 48, 2909–2945 (1969).

Kurtz, C. N.

Lamberts, R. L.

Liu, D.

D. Liu and J. Zhou, “Non linear analysis for a reflection hologram,” Opt. Commun. 107, 471–479 (1994).
[CrossRef]

Madrigal, R.

Madrigal, R. F.

L. Carretero, R. F. Madrigal, A. Fimia, S. Blaya, and A. Belendez, “Study of angular responses of mixed amplitude-phase holographic gratings: shifted Borrmann effect,” Opt. Lett. 26, 786–788 (2001).
[CrossRef]

M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, “D-log E curve of BB640 plates with D8 developer: a modified response,” in Practical Holography XVI and Holographic Materials VIII, 388–398, SPIE (2002).
[CrossRef]

Magnusson, R.

Mees, C. E. K.

C. E. K. Mees and T. H. James, The Theory of the Photographic Process, The Macmillan Company (New York1966).

Méndez, M. J.

M. Ulibarrena, M. J. Méndez, L. Carretero, R. Madrigal, and A. Fimia, “Comparison of direct, rehalogenating and solvent bleaching processes with BB640 plates,” Appl. Opt. 41, 4120–4123 (2002).
[CrossRef] [PubMed]

M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, “D-log E curve of BB640 plates with D8 developer: a modified response,” in Practical Holography XVI and Holographic Materials VIII, 388–398, SPIE (2002).
[CrossRef]

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 37–45 (1981).
[CrossRef]

Pennington, K. S.

Phillips, N. J.

N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).

Podbielska, H.

Porter, D.

N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).

Quintana, J. A.

Ramanathan, C. S.

P. Hariharan, C. S. Ramanathan, and G. S. Kaushik, “Simplified processing technique for photographic phase holograms,” Opt. Commun. 3, 246–247 (1971).
[CrossRef]

Solymar, L.

L. Solymar and D. J. Cooke, Volume holography and volume gratings, Academic Press (London1981).

Sultanova, N.

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography, Oxford University Press (Oxford1990).

Twardowski, P. J.

A. Bac and P. J. Twardowski, “Analysis of broadband lippmann-bragg holographic filters with substrate defects,” Opt. Laser Technol. 33, 37–41 (2001).
[CrossRef]

Ulibarrena, M.

M. Ulibarrena, M. J. Méndez, L. Carretero, R. Madrigal, and A. Fimia, “Comparison of direct, rehalogenating and solvent bleaching processes with BB640 plates,” Appl. Opt. 41, 4120–4123 (2002).
[CrossRef] [PubMed]

M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, “D-log E curve of BB640 plates with D8 developer: a modified response,” in Practical Holography XVI and Holographic Materials VIII, 388–398, SPIE (2002).
[CrossRef]

Ward, A. A.

N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).

Wolfram, S.

S. Wolfram, The Mathematica book, Wolfram media, fourth edition (1999).

Zhou, J.

D. Liu and J. Zhou, “Non linear analysis for a reflection hologram,” Opt. Commun. 107, 471–479 (1994).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. (3)

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

J. Soc. Chem. Ind. (1)

F. Hurter and V. C. Driffield, “Photo-chemical investigations and a new method of determination of the sensitiveness of photographic plates,” J. Soc. Chem. Ind. 9, 455–469 (1890).
[CrossRef]

Opt. Commun. (2)

D. Liu and J. Zhou, “Non linear analysis for a reflection hologram,” Opt. Commun. 107, 471–479 (1994).
[CrossRef]

P. Hariharan, C. S. Ramanathan, and G. S. Kaushik, “Simplified processing technique for photographic phase holograms,” Opt. Commun. 3, 246–247 (1971).
[CrossRef]

Opt. Laser Technol. (1)

A. Bac and P. J. Twardowski, “Analysis of broadband lippmann-bragg holographic filters with substrate defects,” Opt. Laser Technol. 33, 37–41 (2001).
[CrossRef]

Opt. Lett. (1)

Photograph. Sci. Eng. (1)

N. J. Phillips, A. A. Ward, R. Cullen, and D. Porter, “Advances in Holographic Bleaches,” Photograph. Sci. Eng. 24, 120–124 (1980).

The Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” The Bell Syst. Tech. J. 48, 2909–2945 (1969).

Other (9)

E. K. Company. Black-and-White Processing Using KODAK Chemicals (1985).

S. Wolfram, The Mathematica book, Wolfram media, fourth edition (1999).

M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, “D-log E curve of BB640 plates with D8 developer: a modified response,” in Practical Holography XVI and Holographic Materials VIII, 388–398, SPIE (2002).
[CrossRef]

H. I. Bjelkhagen, Silver-Halide Recording Materials, Springer-Verlag (New York1993).

R. R. A. Syms, Practical Volume Holography, Oxford University Press (Oxford1990).

2001. Personal Communication on pre-sensitizing methods for BB640 holographic emulsions with M. Medora of Colourholographics Ltd. (2002)

Y. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, vol. MS 171 of Milestone Series, 22–24. SPIE (2001).

C. E. K. Mees and T. H. James, The Theory of the Photographic Process, The Macmillan Company (New York1966).

L. Solymar and D. J. Cooke, Volume holography and volume gratings, Academic Press (London1981).

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Figures (9)

Fig. 1.
Fig. 1.

Spectral response curve of a reflection hologram. The envelope curve shows the spectral dependence of the optical absorption of the holographic emulsion. The measured characteristics of the hologram, diffraction efficiency (η), replay wavelength (λ 0) and bandwidth (Δλ) are shown.

Fig. 2.
Fig. 2.

(a) Sinusoidal light energy pattern generated by a holographic setup with a spatial frequency of 4997 lp/mm, average exposure E 0 of 1200 µJ/cm2 and fringe visibility of 0.98. (b) Drawing showing the sinusoidal profile generated in a recording material with thickness d.

Fig. 3.
Fig. 3.

D-Log E curve of BB640 plates for a reflection setup processed with developer AAC and fixed with non hardening fixer F-24. Experimental data and analytical fitting are presented.

Fig. 4.
Fig. 4.

Simulations of the spatial density profiles of reflection gratings recorded with exposure energies of (a) 300 µJ/cm2, (b) 600 µJ/cm2, (c) 900 µJ/cm2 and (d) 1200 µJ/cm2, compared with the corresponding recording profile.

Fig. 5.
Fig. 5.

Spatial distributions of the concentration of silver halide crystals ([AgHal]) after reversal bleach for an exposure energy of (a) 300 µJ/cm2 and (b) 900 µJ/cm2, compared to a reference sinusoidal profile.

Fig. 6.
Fig. 6.

Spatial distribution of the concentration of silver halide crystals ([AgHal]) and diffusion processes of rehalogenated crystals after fixation free rehalogenating bleach for a exposure energy of 900 µJ/cm2. A sinusoidal profile has been included for reference.

Fig. 7.
Fig. 7.

Transmission curves of holographic mirrors recorded in BB640 emulsions with a exposure energy of (a) 300 µJ/cm2 and (b) 900 µJ/cm2 bleached with fixation free rehalogenating bleach R-10. Similar curves obtained for reflection gratings recorded with (c) 300 µJ/cm2 and (d) 900 µJ/cm2 bleached with reversal bleach R-9. All curves compared with the resulting transmittance curve calculated with the model.

Fig. 8.
Fig. 8.

Residuals Qmin of the analytical fittings of holographic reflection gratings recorded with different exposure levels bleached with fixation free rehalogenating bleach R-10 and reversal bleach R-9.

Fig. 9.
Fig. 9.

Diffraction efficiencies of holographic reflection gratings recorded with different exposure levels bleached with fixation free rehalogenating bleach R-10 and reversal bleach R-9.

Equations (11)

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T ( λ ) = 100 γ 2 γ 1 ( α + j ϑ γ 1 ) exp ( γ 1 d ) ( α + j ϑ γ 2 ) exp ( γ 2 d ) 2
γ 1 = j ϑ + ( 2 α + j ϑ ) 2 + 4 κ 2 2
γ 2 = j ϑ ( 2 α + j ϑ ) 2 + 4 κ 2 2 ,
ϑ = 2 π Λ ( 1 λ 4 πn ) ,
κ = π n 1 λ j α 1 2 ,
T e = A + B ( 1 e C ( λ 450 ) ) + D ( sin 2 [ π 4 + π 250 ( λ 450 ) ] )
α = log [ 0.01 T e ] 2 d
α 1 = S α ,
Q ( n 1 , α 1 ) = 1 N i = 1 N ( T ( λ i ) T i ) 2 ,
E ( x ) = E 0 ( 1 V cos ( 2 πx 0.2 ) )
D = 0.14 + 8 1 + exp ( 8.06 3.02 log E ) + exp ( 5.58 + 1.58 log E )

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