Abstract

Spontaneous pattern formation in an optoelectronic system with an optical diffractive feedback loop exhibits a contrast enhancement effect, a spatial filtering effect, and filling-up of vacant space while maintaining surrounding structures. These effects allow image processing with defect tolerance. Aberrations and slight misalignments that inevitably exist in optical systems distort the spatial structures of the formed patterns. Distortion also increases due to a small aspect ratio difference between a display device and an image sensor. We experimentally demonstrate that the spatial distortion of the optoelectronic feedback system is reduced by electronic distortion correction and the initial structure of a seed optical pattern is preserved for a long time. We also demonstrate image processing of a fingerprint pattern based on seeded spontaneous optical pattern formation with electronic distortion correction.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. M. Kreuzer, W. Balzer, and T. Tschudi, �??Formation of spatial structures in bistable optical elements containing nematic liquid crystals,�?? Appl. Opt. 29, 579-582 (1990).
    [CrossRef] [PubMed]
  2. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, �??Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,�?? Phys. Rev. Lett. 65, 2531-2534 (1990).
    [CrossRef] [PubMed]
  3. G. D'Alessandro and W. J. Firth, �??Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,�?? Phys. Rev. Lett. 66, 2597-2600 (1991).
    [CrossRef] [PubMed]
  4. S. A. Akhmanov, M. A. Vorontsov, V. Yu. Ivanov, A. V. Larichev, and N. I. Zheleznykh, �??Controlling transverse-wave interactions in nonlinear optics: generation and interaction of spatiotemporal structures,�?? J. Opt. Soc. Am. B 9, 78-90 (1992).
    [CrossRef]
  5. R. Macdonald and H. J. Eichler, �??Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror,�?? Opt. Commun. 89, 289-295 (1992).
    [CrossRef]
  6. B. Thüring, R. Neubecker, and T. Tschudi, �??Transverse pattern formation in liquid crystal light valve feedback system,�?? Opt. Commun. 102, 111-115 (1993).
    [CrossRef]
  7. E. Ciaramella and M. Tamburrini, and E. Santamoto, �??Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,�?? Appl. Phys. Lett. 63, 1604-1606 (1993).
    [CrossRef]
  8. T. Honda, �??Hexagonal pattern formation due to counterpropagation in KNbO3,�?? Opt. Lett. 18, 598-600 (1993).
    [CrossRef] [PubMed]
  9. P. P. Banerjee, H. L. Yu, D. A. Gregory, N. Kukhtarev, and H. J. Caufield, �??Self-organization of scattering in photorefractive KNbO3 into reconfigurable hexagonal spot array,�?? Opt. Lett. 20, 10-12 (1995).
    [CrossRef] [PubMed]
  10. R. Neubecker, G.-L. Oppo, B. Thuering, and T. Tschudi, �??Pattern formation in a liquid-crystal light valve with feedback including polarization, saturation, and internal threshold effect,�?? Phys. Rev. A 52, 791-808 (1995).
    [CrossRef] [PubMed]
  11. M. A. Vorontsov and W. B. Miller (Eds.), �??Self-organization in Optical systems and applications in information technology,�?? Chapter 2 (Berlin, Springer-Verlag, 1995).
  12. E. V. Degtiarev and M. A. Vorontsov, �??Spatial filtering in nonlinear two-dimensional feedback systems: phase-distortion suppression,�?? J. Opt. Soc. Am. B 12, 1238-1248 (1995).
    [CrossRef]
  13. Y. Hayasaki, H. Yamamoto, and N. Nishida, �??Optical dependence of spatial frequency of formed patterns on focusing condition in a nonlinear optical ring resonator,�?? 151, 263-267 (1998).
    [CrossRef]
  14. V. Mamaev and M. Saffman, �??Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,�?? Phys. Rev. Lett. 80, 3499-3502 (1998).
    [CrossRef]
  15. S. J. Jensen, M. Schwab, and C. Denz, �??Manipulation, stabilization, and control of pattern formation using Fourier space filtering,�?? Phys, Rev. Lett. 81, 1614-1617 (1998).
    [CrossRef]
  16. G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, �??Elimination of spatiotemporal disorder by Fourier space techniques,�?? Phys. Rev. A 58, 2577-2585 (1998).
    [CrossRef]
  17. Y. Hayasaki, H. Yamamoto, and N. Nishida, �??Selection of optical patterns using direct modulation method of spatial frequency in a nonlinear optical feedback system,�?? Opt. Commun. 187, 49-55 (2001).
    [CrossRef]
  18. R. Neubecker , E. Benkler, R. Martin, and G. -L. Oppo, "Manipulation and removal of defects in spontaneous optical patterns," Phys. Rev. Lett. 91, 113903 (2003).
    [CrossRef] [PubMed]
  19. R. Neubecker and A. Zimmermann, �??Spatial forcing of spontaneous optical patterns,�?? Phys. Rev. E 65, 035205(R) (2002).
    [CrossRef]
  20. R. Neubecker, A. Zimmermann, and O. Jakoby, �??Utilizing nonlinear optical pattern formation for a simple image-processing task,�?? Appl. Phys. B 76, 383-392 (2003).
    [CrossRef]
  21. M. A. Vorontsov, G. W. Carhart, and R. Dou, �??Spontaneous optical pattern formation in a large array of optoelectronic feedback circuits,�?? J. Opt. Soc. Am. B 17, 266-274 (2000).
    [CrossRef]
  22. Y. Hayasaki, Y. Tamura, H. Yamamoto, and N. Nishida, �??Spatial property of formed patterns depending on focus condition in a two-dimensional optoelectronic feedback system,�?? Jpn. J. Appl. Phys. 40, 165-169 (2001).
    [CrossRef]
  23. Y. Hayasaki, E. Hikosaka, H. Yamamoto, and N. Nishida, �??Image processing based on seeded spontaneous optical pattern formation using optoelectronic feedback,�?? Appl. Opt. 44, 236-240 (2005).
    [CrossRef] [PubMed]
  24. J. A. Nelder and R. Mead, �??Simplex method for function minimization,�?? Computer J. 7, 308-313 (1965).

Appl. Opt. (2)

Appl. Phys. B (1)

R. Neubecker, A. Zimmermann, and O. Jakoby, �??Utilizing nonlinear optical pattern formation for a simple image-processing task,�?? Appl. Phys. B 76, 383-392 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

E. Ciaramella and M. Tamburrini, and E. Santamoto, �??Talbot assisted hexagonal beam patterning in a thin liquid crystal film with a single feedback mirror at negative distance,�?? Appl. Phys. Lett. 63, 1604-1606 (1993).
[CrossRef]

Computer J. (1)

J. A. Nelder and R. Mead, �??Simplex method for function minimization,�?? Computer J. 7, 308-313 (1965).

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

Y. Hayasaki, Y. Tamura, H. Yamamoto, and N. Nishida, �??Spatial property of formed patterns depending on focus condition in a two-dimensional optoelectronic feedback system,�?? Jpn. J. Appl. Phys. 40, 165-169 (2001).
[CrossRef]

Opt. Commun. (4)

Y. Hayasaki, H. Yamamoto, and N. Nishida, �??Selection of optical patterns using direct modulation method of spatial frequency in a nonlinear optical feedback system,�?? Opt. Commun. 187, 49-55 (2001).
[CrossRef]

R. Macdonald and H. J. Eichler, �??Spontaneous optical pattern formation in a nematic liquid crystal with feedback mirror,�?? Opt. Commun. 89, 289-295 (1992).
[CrossRef]

B. Thüring, R. Neubecker, and T. Tschudi, �??Transverse pattern formation in liquid crystal light valve feedback system,�?? Opt. Commun. 102, 111-115 (1993).
[CrossRef]

Y. Hayasaki, H. Yamamoto, and N. Nishida, �??Optical dependence of spatial frequency of formed patterns on focusing condition in a nonlinear optical ring resonator,�?? 151, 263-267 (1998).
[CrossRef]

Opt. Lett. (2)

Phys, Rev. Lett. (1)

S. J. Jensen, M. Schwab, and C. Denz, �??Manipulation, stabilization, and control of pattern formation using Fourier space filtering,�?? Phys, Rev. Lett. 81, 1614-1617 (1998).
[CrossRef]

Phys. Rev. A (2)

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, and W. J. Firth, �??Elimination of spatiotemporal disorder by Fourier space techniques,�?? Phys. Rev. A 58, 2577-2585 (1998).
[CrossRef]

R. Neubecker, G.-L. Oppo, B. Thuering, and T. Tschudi, �??Pattern formation in a liquid-crystal light valve with feedback including polarization, saturation, and internal threshold effect,�?? Phys. Rev. A 52, 791-808 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

R. Neubecker and A. Zimmermann, �??Spatial forcing of spontaneous optical patterns,�?? Phys. Rev. E 65, 035205(R) (2002).
[CrossRef]

Phys. Rev. Lett. (4)

V. Mamaev and M. Saffman, �??Selection of unstable patterns and control of optical turbulence by Fourier plane filtering,�?? Phys. Rev. Lett. 80, 3499-3502 (1998).
[CrossRef]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, �??Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics,�?? Phys. Rev. Lett. 65, 2531-2534 (1990).
[CrossRef] [PubMed]

G. D'Alessandro and W. J. Firth, �??Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror,�?? Phys. Rev. Lett. 66, 2597-2600 (1991).
[CrossRef] [PubMed]

R. Neubecker , E. Benkler, R. Martin, and G. -L. Oppo, "Manipulation and removal of defects in spontaneous optical patterns," Phys. Rev. Lett. 91, 113903 (2003).
[CrossRef] [PubMed]

Other (1)

M. A. Vorontsov and W. B. Miller (Eds.), �??Self-organization in Optical systems and applications in information technology,�?? Chapter 2 (Berlin, Springer-Verlag, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Schematic representation of a model of an OEFS. CCD: charge-coupled device image sensor, LCD: liquid crystal display.

Fig. 2.
Fig. 2.

Experimental setup. See text the description.

Fig. 3.
Fig. 3.

Temporal evolution of (a) patterns whose operating center coincides with the optical axis of the system (on-axis region), and (b) patterns whose operating center is shifted from the optical axis (off-axis region) by 100 pixels in the x-axis and 100 pixels in the y-axis on the LCD. These patterns are observed at 1/30 s, 5/30 s, 10/30 s, 15/30 s, and 20/30 s from the left, respectively.

Fig. 4.
Fig. 4.

Temporal evolutions of patterns (a) in the on-axis region, and (b) in the off-axis region in the OEFS with electronic distortion correction.

Fig. 5.
Fig. 5.

Temporal changes of the SSDs between each temporally evolving pattern and the pattern at the 1st frame (a) in the on-axis region and (b) in the off-axis region in the OEFS with electronic distortion correction. The dotted and the solid lines indicate the SSDs of the pattern evolutions in the OEFS (a) without and (b) with the electronic distortion correction, respectively.

Fig. 6.
Fig. 6.

(a) An original fingerprint pattern A and (b) the same pattern A′ with an artificial defect.

Fig. 7.
Fig. 7.

Temporal evolutions at 1/30 s, 10/30 s, and 22/30 s when the fingerprint patterns without and with the artificial defect are initially supplied to the OEFS with the electronic distortion correction.

Fig. 8.
Fig. 8.

The bold dashed curve and the bold solid curve indicate the temporal changes of the SSDs between the temporal evolutions of the original fingerprint pattern and those of the fingerprint pattern with the artificial defect, when the OEFS was used without and with the electronic distortion correction, respectively. The thin dashed curve and the thin solid curve indicate the temporal changes of the SSDs between two trials starting from same initial pattern in the OEFS without and with the electronic distortion correction, respectively.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

τ u ( x , y , t ) t = u ( x , y , t ) + l 2 2 u ( x , y , t ) + p ( x , y , t ) ,
I ( x , y , t ) = A ( x , y , t ) 2 = F [ u ( x , y , t ) ] .
p ( x , y , t ) = G [ I d ( x , y , Z , t ) ] ,
2 A d ( x , y , Z , t ) 2 ik A d z = 0 ,
x 1 = A 0 + A 1 x
y 1 = B 0 + B 1 y .
x 2 = x 1 cos Θ + y 1 sin Θ ,
y 2 = x 1 sin Θ + y 1 cos Θ .
r = r 2 ( 1 + Cr 2 2 ) ,
u = r 2 cos θ 2 ,
v = r 2 sin θ 2 ,
I ( u , v ) = ( 1 q ) { ( 1 p ) I ( i , j ) + pI ( i + 1 , j ) } + q { ( 1 p ) I ( i , j + 1 ) + pI ( i + 1 , j + 1 ) } ,
D ( t ) = i j { [ I 1 ( i , j , t ) μ 1 ( t ) ] σ 1 ( t ) [ I 2 ( i , j , t ) μ 2 ( t ) ] σ 2 ( t ) } 2 N ,

Metrics