Abstract

The efficiency of noise gratings recorded with single-beam exposures in bleached silver halide emulsions is analyzed as a function of the polarization state of the readout wave. Experimental results are presented and discussed on the basis of a theoretical model that considers both a linear and a nonlinear relation between the refractive-index modulation and the exposure. The dependence of the noise gratings’ efficiency on the relative polarization between the construction and reconstruction beams is analyzed, and we find that this is represented by a quadratic curve of cos2 δ, where δ is the polarization angle. The quantitative analysis is carried out with this model based on the coupled-wave theory, and the calculated results obtained by use of the theoretical model agree well with the experimental ones.

© 1993 Optical Society of America

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References

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  1. K. Biedermann, “The scattered flux spectrum of photographic materials for holography,” Optik 31, 367–389 (1970).
  2. R. R. A. Syms, L. Solymar, “Noise gratings in photographic emulsions,” Opt. Commun. 43, 107–110 (1982).
    [CrossRef]
  3. R. R. A. Syms, L. Solymar, “Noise gratings in silver halide volume holograms,” Appl. Phys. B 30, 177–182 (1983).
    [CrossRef]
  4. A. A. Ward, J. M. Heaton, L. Solymar, “Efficient noise gratings in silver halide emulsions,” Opt. Quantum Electron. 16, 365–367 (1984).
    [CrossRef]
  5. 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]
  6. 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]
  7. G. D. G. Riddy, “The effect of light scattering on the recording and replay of holographic optical elements,” Ph.D. dissertation (Oxford University, Oxford, 1988).
  8. L. Solymar, J. C. W. Newell, “Silver halide noise gratings recorded in dichromated gelatin,” Opt. Commun. 73, 273–276 (1989).
    [CrossRef]
  9. L. T. Blair, L. Solymar, “Angular selectivity of silver halide transmission noise gratings copied into dichromated gelatin,” Appl. Opt. 29, 2985–2986 (1990).
    [CrossRef] [PubMed]
  10. L. T. Blair, L. Solymar, “Silver halide reflection noise gratings recorded in dichromated gelatin,” Opt. Commun. 77, 126–128 (1990).
    [CrossRef]
  11. R. K. Kostuk, G. T. Sincerbox, “Polarization sensitivity of noise gratings recorded in silver halide volume holograms,” Appl. Opt. 27, 2993–2998 (1988).
    [CrossRef] [PubMed]
  12. 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]
  13. L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analyzing and optimizing photochemical processings in bleached silver halide emulsions,” J. Mod. Opt. 40, 687–697 (1993).
    [CrossRef]
  14. G. D. G. Riddy, L. Solymar, “Theoretical model of reconstructed scatter in volume holograms,” Electron. Lett. 22, 872–873 (1986).
    [CrossRef]
  15. L. Carretero, A. Fimia, A. Beléndez, “Statistical model for noise gratings recorded in volume holograms,” J. Mod. Opt. 40, 1299–1308 (1993).
    [CrossRef]
  16. J. Crespo, A. Fimia, J. A. Quintana, “Fixation-free methods in bleached reflection holography,” Appl. Opt. 25, 1642–1645 (1986).
    [CrossRef] [PubMed]
  17. R. K. Kostuk, “Factorial optimization of bleach constituents for silver halide holograms,” Appl. Opt. 30, 1611–1616 (1991).
    [CrossRef] [PubMed]
  18. C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear recording in silver halide planar volume holograms,” Appl. Phys. B 36, 217–224 (1985).
    [CrossRef]

1993 (3)

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 analyzing 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]

1991 (1)

1990 (3)

1989 (2)

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]

1988 (1)

1986 (2)

J. Crespo, A. Fimia, J. A. Quintana, “Fixation-free methods in bleached reflection holography,” Appl. Opt. 25, 1642–1645 (1986).
[CrossRef] [PubMed]

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

1985 (1)

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear recording in silver halide planar volume holograms,” Appl. Phys. B 36, 217–224 (1985).
[CrossRef]

1984 (1)

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

1983 (1)

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

1982 (1)

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

1970 (1)

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

Beléndez, A.

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 analyzing 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 31, 367–389 (1970).

Blair, L. T.

L. T. Blair, L. Solymar, “Angular selectivity of silver halide transmission noise gratings copied into dichromated gelatin,” Appl. Opt. 29, 2985–2986 (1990).
[CrossRef] [PubMed]

L. T. Blair, L. Solymar, “Silver halide reflection noise gratings recorded in dichromated gelatin,” Opt. Commun. 77, 126–128 (1990).
[CrossRef]

Carretero, L.

L. Carretero, A. Beléndez, A. Fimia, “Holographic noise gratings for analyzing 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]

Crespo, J.

Fimia, A.

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

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

J. Crespo, A. Fimia, J. A. Quintana, “Fixation-free methods in bleached reflection holography,” Appl. Opt. 25, 1642–1645 (1986).
[CrossRef] [PubMed]

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]

Kostuk, R. K.

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, 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]

Quintana, J. A.

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]

G. D. G. Riddy, “The effect of light scattering on the recording and replay of holographic optical elements,” Ph.D. dissertation (Oxford University, Oxford, 1988).

Sincerbox, G. T.

Slinger, C. W.

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear recording in silver halide planar volume holograms,” Appl. Phys. B 36, 217–224 (1985).
[CrossRef]

Solymar, L.

L. T. Blair, L. Solymar, “Silver halide reflection noise gratings recorded in dichromated gelatin,” Opt. Commun. 77, 126–128 (1990).
[CrossRef]

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. T. Blair, L. Solymar, “Angular selectivity of silver halide transmission noise gratings copied into dichromated gelatin,” Appl. Opt. 29, 2985–2986 (1990).
[CrossRef] [PubMed]

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]

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear recording in silver halide planar volume holograms,” Appl. Phys. B 36, 217–224 (1985).
[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 emulsions,” Opt. Commun. 43, 107–110 (1982).
[CrossRef]

Syms, R. R. A.

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear recording in silver halide planar volume holograms,” Appl. Phys. B 36, 217–224 (1985).
[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 emulsions,” Opt. Commun. 43, 107–110 (1982).
[CrossRef]

Wang, L.

Ward, A. A.

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

Appl. Opt. (4)

Appl. Phys. B (2)

C. W. Slinger, R. R. A. Syms, L. Solymar, “Nonlinear recording in silver halide planar volume holograms,” Appl. Phys. B 36, 217–224 (1985).
[CrossRef]

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

Electron. Lett. (1)

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

J. Mod. Opt. (2)

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

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

Opt. Commun. (3)

L. T. Blair, L. Solymar, “Silver halide reflection noise gratings recorded in dichromated gelatin,” Opt. Commun. 77, 126–128 (1990).
[CrossRef]

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

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

Opt. Lett. (1)

Opt. Quantum Electron. (2)

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

Optik (1)

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

Other (1)

G. D. G. Riddy, “The effect of light scattering on the recording and replay of holographic optical elements,” Ph.D. dissertation (Oxford University, Oxford, 1988).

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Figures (11)

Fig. 1
Fig. 1

Typical plot of transmittance as a function of the reconstruction angle for noise gratings recorded with a single beam of light.

Fig. 2
Fig. 2

Noise-grating efficiency as a function of the incident exposures for polarization angles δ equal to 0°, 30°, 45°, 60°, and 90°.

Fig. 3
Fig. 3

Measured diffraction efficiency of the noise gratings as a function of cos2 δ for holograms exposed with different total energies E. Solid curves show the adjustments of the experimental data by a quadratic curve.

Fig. 4
Fig. 4

Geometry for analysis of dipole scattering, p is the dipolar moment induced in each silver halide grain.

Fig. 5
Fig. 5

Intensity profile (from Ref. 9) in a plane (a) perpendicular and (b) parallel to the dipole vector p.

Fig. 6
Fig. 6

Geometry for analysis of the reconstruction of the noise gratings. δ is the angle between the er and ec vectors.

Fig. 7
Fig. 7

Normalized diffraction efficiency ΔIn(δ)/ΔIn of the noise gratings as a function of cos2 δ for various values of the incident exposure E when the effect of nonlinearities is taken into account.

Fig. 8
Fig. 8

Experimental data (■) and theoretical curves for the normalized efficiency of noise gratings ΔIn(δ)/ΔIn as a function of cos2 δ for low exposures. In each graph the solid curve corresponds to the theoretical curve calculated assuming a linear relation between Δn and exposure, and each dashed curve is calculated with the effect of nonlinearities taken into account.

Fig. 9
Fig. 9

Same as Fig. 8 but for high exposures.

Fig. 10
Fig. 10

Experimental and theoretical data for parameter ΔIn90°In as a function of the incident exposure. The solid line corresponds to the values obtained when Δn is proportional to exposure, and the dashed curve was obtained assuming a nonlinear relation between Δn and exposure.

Fig. 11
Fig. 11

Scheme for analyzing the influence of the direction of observation in a plane parallel to the hologram plane on noise-grafting efficiency ΔIn: (a) direction parallel and (b) perpendicular to the polarization of the reconstruction beam.

Equations (34)

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Δ I n ( δ ) = a 1 + a 2 cos 2 δ + a 3 cos 4 δ
E s = E s ( θ ) exp ( j ψ s ) e s .
I r s = | E r + E s | 2 = | E r exp ( j ψ r ) e r + E s ( θ ) exp ( j ψ s ) e s | 2 = | E r | 2 + | E s ( θ ) | 2 + 2 E r E s cos ψ r s sin θ ( e r · e s ) ,
Δ n E r E s sin θ ( e r · e s ) sin θ ( e r · e s ) .
κ Δ n ( e c · e d ) .
η ( θ , ϕ , δ ) κ 2 Δ n 2 ( e c · e d ) 2 ,
η ( θ , ϕ , δ ) ( e r · e s ) 2 ( e c · e d ) 2 sin 2 θ ,
η ( θ , ϕ , δ ) ( e c · e d ) 2 sin 4 θ .
u θ = cos ϕ cos θ u x + sin ϕ cos θ u y sin θ u z ,
u ϕ = sin ϕ u x + cos ϕ u y ,
e c = sin δ u x + cos δ u z ,
e d = cos δ u θ sin d u ϕ ,
e c · e d = sin θ cos 2 δ + sin ϕ sin 2 δ cos θ cos ϕ sin δ cos δ .
η ( θ , ϕ , δ ) sin 6 θ cos 4 δ + sin 4 θ sin 2 ϕ sin 4 δ + 2 sin 5 θ sin ϕ sin 2 δ cos 2 δ + sin 4 θ cos 2 θ cos 2 ϕ sin 2 δ cos 2 δ 2 sin 4 θ cos θ cos ϕ sin ϕ sin 3 δ cos δ 2 sin 5 θ cos θ cos ϕ sin δ cos 3 δ .
η ( δ ) 2 0 π d ϕ 0 π d θ sin θη ( θ , ϕ , δ ) .
Δ I n ( δ ) 0 π d ϕ 0 π d θ sin θη ( θ , ϕ , δ ) .
Δ I n ( δ ) Δ I n 0 ° = 0 π d ϕ 0 π d θ sin θη ( θ , ϕ , δ ) 0 π d ϕ 0 π d θ sin θη ( θ , ϕ , 0 ° ) .
Δ I n ( δ ) Δ I n 0 ° = 1 384 ( 224 + 109 cos 2 δ + 51 cos 4 δ ) 0 . 583 + 0 . 284 cos 2 δ + 0 . 133 cos 4 δ .
Δ I n 90 ° Δ I n 0 ° = 7 12 0 . 583 .
Δ n = Δ n 0 [ 1 exp ( E sin 2 θ / E 0 ) ] ,
Δ n Δ n 0 [ ( E / E 0 ) sin 2 θ ( 1 / 2 ) ( E / E 0 ) 2 sin 4 θ ] .
Δ n 2 Δ n 0 2 ( E / E 0 ) 2 [ sin 4 θ ( E / E 0 ) sin 6 θ + ( 1 / 4 ) ( E / E 0 ) 2 sin 8 θ ] .
Δ I n ( δ ) Δ I n 0 ° = 1 B ( A 1 + A 2 cos 2 δ + A 3 cos 4 δ ) ,
A 1 = 3 . 351 2 . 872 ( E / E 0 ) + 0 . 638 ( E / E 0 ) 2 ,
A 2 = 1 . 631 1 . 447 ( E / E 0 ) + 0 . 328 ( E / E 0 ) 2 ,
A 3 = 0 . 763 0 . 787 ( E / E 0 ) + 1 . 161 ( E / E 0 ) 2 ,
B = 5 . 745 5 . 106 ( E / E 0 ) + 2 . 127 ( E / E 0 ) 2 .
Δ I n 90 ° Δ I n 0 ° = 3 . 351 2 . 872 ( E / E 0 ) + 0 . 638 ( E / E 0 ) 2 5 . 745 5 . 106 ( E / E 0 ) + 2 . 127 ( E / E 0 ) 2 .
η ( θ , ϕ , δ = 0 ° ) sin 6 θ .
Δ I n ( ϕ = 90 ° , δ = 0 ° ) 0 π η ( θ , ϕ = 90 ° , δ = 0 ° ) sin θ d θ = 0 π sin 7 θ d θ = 32 35 .
Δ I n ( ϕ = 90 ° , δ = 0 ° ) 0 π η ( θ = 90 ° , ϕ , δ = 0 ° ) d ϕ = 0 π d ϕ = π .
Δ I n ( θ = 90 ° , δ = 0 ° ) Δ I n ( ϕ = 90 ° , δ = 0 ° ) = π 32 / 35 3 . 44
Δ I n ( θ = 90 ° , δ = 0 ° ) > Δ I n ( ϕ = 90 ° , δ = 0 ° ) .
Δ I n ( θ = 90 ° , δ = 90 ° ) > Δ I n ( ϕ = 90 ° , δ = 90 ° ) .

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