Abstract

It was shown in previous studies that, when a diffuser is illuminated by coherent light with an average spatial intensity distribution obeying a negative power function, the scattered field in the Fraunhofer diffraction region exhibits random fractal properties. The method employed so far for producing such fields has a disadvantage in that generated speckle intensities are low due to small transmittance of fractal apertures used in the illumination optics. To overcome this disadvantage, a generation of fractal speckles by means of a spatial light modulator is proposed. The principle is explained and experimental results are also shown.

© 2007 Optical Society of America

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  1. H. Takayasu, Fractals in Physical Science (Manchester University, Manchester, 1990).
  2. J. Feder, Fractals (Plenum, New York, 1996).
  3. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).
  4. J. Uozumi and T. Asakura, "Optical fractals," in Optical Storage and Retrieval—Memory, Neural Networks, and Fractals, F. T. S. Yu and S. Jutamulia, eds. (Marcel Dekker, New York, 1996), pp. 283-320.
  5. J. Uozumi, H. Kimura, and T. Asakura, "Fraunhofer diffraction by Koch fractals: the dimensionality," J. Mod. Opt. 38, 1335-1347 (1991).
  6. K. Uno, J. Uozumi, and T. Asakura, "Correlation properties of speckles produced by diffractal-illuminated diffusers," Opt. Commun. 124, 16-22 (1996).
    [CrossRef]
  7. J. Uozumi, M. Ibrahim, and T. Asakura, "Fractal speckles," Opt. Commun. 156, 350-358 (1998).
    [CrossRef]
  8. J. Uozumi, "Generation of random fractal fields by a double scattering process," in Fourth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE 3904, 13-24 (1999).
  9. J. Uozumi, "Fractality of the optical fields scattered by power-law-illuminated diffusers," in Selected Papers from Fifth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE 4607, 257-267, (2002).
  10. T. Okamoto, H. Gotou, Y. Kawabata, and M. Takeuchi, "Statistical properties of the three-dimensional intensity distribution formed with orthogonally crossed speckle beams," in Technical Digest of the Sixth Japan-Finland Joint Symposium on Optics in Engineering, J. Uozumi, T. Yatagai and K.-E. Peiponen, eds., (2005), pp. 45-46.
  11. J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed., (Springer, Berlin, 1984), pp. 9-75.
  12. N. Konforti, E. Maron, and S.-T. Wu, "Phase-only modulation with twisted nematic liquid-crystal spatial light modulators," Opt. Lett. 13, 251-253 (1988).
  13. G. Wernicke, S. Kruger, J. Kamps, H. Gruber, N. Demoli, M. Durr, and S. Teiwes, "Application of a liquid crystal display spatial light modulator system as dynamic diffractive element and in optical image processing," J. Opt. Commun. 25, 141-148 (2004).
  14. H. Kim and Y. H. Lee, "Unique measurement of the parameters of a twisted-nematic liquid-crystal display," Appl. Opt. 44, 1642-1649 (2005).
    [CrossRef]
  15. R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).

2005 (1)

2004 (1)

G. Wernicke, S. Kruger, J. Kamps, H. Gruber, N. Demoli, M. Durr, and S. Teiwes, "Application of a liquid crystal display spatial light modulator system as dynamic diffractive element and in optical image processing," J. Opt. Commun. 25, 141-148 (2004).

1998 (1)

J. Uozumi, M. Ibrahim, and T. Asakura, "Fractal speckles," Opt. Commun. 156, 350-358 (1998).
[CrossRef]

1996 (1)

K. Uno, J. Uozumi, and T. Asakura, "Correlation properties of speckles produced by diffractal-illuminated diffusers," Opt. Commun. 124, 16-22 (1996).
[CrossRef]

1991 (1)

J. Uozumi, H. Kimura, and T. Asakura, "Fraunhofer diffraction by Koch fractals: the dimensionality," J. Mod. Opt. 38, 1335-1347 (1991).

1988 (1)

1974 (1)

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).

Asakura, T.

J. Uozumi, M. Ibrahim, and T. Asakura, "Fractal speckles," Opt. Commun. 156, 350-358 (1998).
[CrossRef]

K. Uno, J. Uozumi, and T. Asakura, "Correlation properties of speckles produced by diffractal-illuminated diffusers," Opt. Commun. 124, 16-22 (1996).
[CrossRef]

J. Uozumi, H. Kimura, and T. Asakura, "Fraunhofer diffraction by Koch fractals: the dimensionality," J. Mod. Opt. 38, 1335-1347 (1991).

Gerchberg, R.W.

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).

Ibrahim, M.

J. Uozumi, M. Ibrahim, and T. Asakura, "Fractal speckles," Opt. Commun. 156, 350-358 (1998).
[CrossRef]

Kim, H.

Kimura, H.

J. Uozumi, H. Kimura, and T. Asakura, "Fraunhofer diffraction by Koch fractals: the dimensionality," J. Mod. Opt. 38, 1335-1347 (1991).

Konforti, N.

Lee, Y. H.

Maron, E.

Uno, K.

K. Uno, J. Uozumi, and T. Asakura, "Correlation properties of speckles produced by diffractal-illuminated diffusers," Opt. Commun. 124, 16-22 (1996).
[CrossRef]

Uozumi, J.

J. Uozumi, M. Ibrahim, and T. Asakura, "Fractal speckles," Opt. Commun. 156, 350-358 (1998).
[CrossRef]

K. Uno, J. Uozumi, and T. Asakura, "Correlation properties of speckles produced by diffractal-illuminated diffusers," Opt. Commun. 124, 16-22 (1996).
[CrossRef]

J. Uozumi, H. Kimura, and T. Asakura, "Fraunhofer diffraction by Koch fractals: the dimensionality," J. Mod. Opt. 38, 1335-1347 (1991).

Wernicke, G.

G. Wernicke, S. Kruger, J. Kamps, H. Gruber, N. Demoli, M. Durr, and S. Teiwes, "Application of a liquid crystal display spatial light modulator system as dynamic diffractive element and in optical image processing," J. Opt. Commun. 25, 141-148 (2004).

Wu, S.-T.

Appl. Opt. (1)

J. Mod. Opt. (1)

J. Uozumi, H. Kimura, and T. Asakura, "Fraunhofer diffraction by Koch fractals: the dimensionality," J. Mod. Opt. 38, 1335-1347 (1991).

J. Opt. Commun. (1)

G. Wernicke, S. Kruger, J. Kamps, H. Gruber, N. Demoli, M. Durr, and S. Teiwes, "Application of a liquid crystal display spatial light modulator system as dynamic diffractive element and in optical image processing," J. Opt. Commun. 25, 141-148 (2004).

Opt. Acta (1)

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).

Opt. Commun. (2)

K. Uno, J. Uozumi, and T. Asakura, "Correlation properties of speckles produced by diffractal-illuminated diffusers," Opt. Commun. 124, 16-22 (1996).
[CrossRef]

J. Uozumi, M. Ibrahim, and T. Asakura, "Fractal speckles," Opt. Commun. 156, 350-358 (1998).
[CrossRef]

Opt. Lett. (1)

Other (8)

J. Uozumi, "Generation of random fractal fields by a double scattering process," in Fourth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE 3904, 13-24 (1999).

J. Uozumi, "Fractality of the optical fields scattered by power-law-illuminated diffusers," in Selected Papers from Fifth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE 4607, 257-267, (2002).

T. Okamoto, H. Gotou, Y. Kawabata, and M. Takeuchi, "Statistical properties of the three-dimensional intensity distribution formed with orthogonally crossed speckle beams," in Technical Digest of the Sixth Japan-Finland Joint Symposium on Optics in Engineering, J. Uozumi, T. Yatagai and K.-E. Peiponen, eds., (2005), pp. 45-46.

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed., (Springer, Berlin, 1984), pp. 9-75.

H. Takayasu, Fractals in Physical Science (Manchester University, Manchester, 1990).

J. Feder, Fractals (Plenum, New York, 1996).

T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992).

J. Uozumi and T. Asakura, "Optical fractals," in Optical Storage and Retrieval—Memory, Neural Networks, and Fractals, F. T. S. Yu and S. Jutamulia, eds. (Marcel Dekker, New York, 1996), pp. 283-320.

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