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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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]

MS 171 of Milestone Series (1)

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).

Opt. Commun. (2)

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

D. Liu and J. Zhou, �??Non linear analysis for a reflection hologram,�?? Opt. Commun. 107, 471�??479 (1994).
[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).

Proc. SPIE (1)

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]

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 (7)

R. R. A. Syms, Practical Volume Holography, Oxford University Press (Oxford 1990).

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

C. E. K. Mees and T. H. James, The Theory of the Photographic Process, The Macmillan Company (New York 1966).

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

S. Wolfram, The Mathematica Book, Wolfram Media, Fourth edition (1999).

H. I. Bjelkhagen, Silver-Halide Recording Materials, Springer-Verlag (New York 1993).

L. Solymar and D. J. Cooke, Volume holography and volume gratings, Academic Press (London 1981).

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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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