Abstract

The evaluation accuracy of real optical properties of photonic crystal fibers (PCFs) is determined by the accurate extraction of air hole edges from microscope images of cross sections of practical PCFs. A novel estimation method of point spread function (PSF) based on Kalman filter is presented to rebuild the micrograph image of the PCF cross-section and thus evaluate real optical properties for practical PCFs. Through tests on both artificially degraded images and microscope images of cross sections of practical PCFs, we prove that the proposed method can achieve more accurate PSF estimation and lower PSF variance than the traditional Bayesian estimation method, and thus also reduce the defocus effect. With this method, we rebuild the microscope images of two kinds of commercial PCFs produced by Crystal Fiber and analyze the real optical properties of these PCFs. Numerical results are in accord with the product parameters.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef]
  2. T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
    [CrossRef]
  3. S. S. Mishra and V. K. Singh, “Study of non-linear properties of hollow core photonic crystal fiber,” Optik 122, 687–690 (2011).
    [CrossRef]
  4. L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
    [CrossRef]
  5. N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
    [CrossRef]
  6. Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
    [CrossRef]
  7. F. Tian, Z. H. He, and H. Du, “Numerical and experimental investigation of long-period gratings in photonic crystal fiber for refractive index sensing of gas media,” Opt. Lett. 37, 380–382 (2012).
    [CrossRef]
  8. L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
    [CrossRef]
  9. Y. Shen, L. W. Wang, and S. Q. Lou, “Improved method for fast evaluating optical properties of actual photonic crystal fibers,” Infrared Laser Eng. 41, 1041–1046 (2012).
  10. A. C. Likas and N. P. Galatsanos, “A variational approach for Bayesian blind image deconvolution,” IEEE Trans. Signal Process. 52, 2222–2233 (2004).
    [CrossRef]
  11. D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s t-priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
    [CrossRef]
  12. D. L. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Trans. Neural Netw. 18, 931–935 (2007).
    [CrossRef]
  13. F. Šroubek and P. Milanfar, “Robust multichannel blind deconvolution via fast alternating minimization,” IEEE Trans. Image Process. 21, 1687–1700 (2012).
    [CrossRef]
  14. S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
    [CrossRef]
  15. R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.
  16. R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004), pp. 130–134 .
  17. Crystal Fiber A/S http://www.crystal-fibre.com/datasheets/LMA-PM-5.pdf , 2008.
  18. Crystal Fiber A/S http://www.crystal-fibre.com/datasheets/PM-1550-01.pdf , 2008.
  19. F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fiber—Properties and Applications (Springer, 2007), pp. 219–223.

2012 (5)

N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
[CrossRef]

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

F. Tian, Z. H. He, and H. Du, “Numerical and experimental investigation of long-period gratings in photonic crystal fiber for refractive index sensing of gas media,” Opt. Lett. 37, 380–382 (2012).
[CrossRef]

Y. Shen, L. W. Wang, and S. Q. Lou, “Improved method for fast evaluating optical properties of actual photonic crystal fibers,” Infrared Laser Eng. 41, 1041–1046 (2012).

F. Šroubek and P. Milanfar, “Robust multichannel blind deconvolution via fast alternating minimization,” IEEE Trans. Image Process. 21, 1687–1700 (2012).
[CrossRef]

2011 (2)

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

S. S. Mishra and V. K. Singh, “Study of non-linear properties of hollow core photonic crystal fiber,” Optik 122, 687–690 (2011).
[CrossRef]

2010 (3)

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
[CrossRef]

S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
[CrossRef]

2009 (1)

D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s t-priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef]

2007 (1)

D. L. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Trans. Neural Netw. 18, 931–935 (2007).
[CrossRef]

2004 (1)

A. C. Likas and N. P. Galatsanos, “A variational approach for Bayesian blind image deconvolution,” IEEE Trans. Signal Process. 52, 2222–2233 (2004).
[CrossRef]

1996 (1)

Ahmad, H.

N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
[CrossRef]

Atkin, D. M.

Babacan, S. D.

S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
[CrossRef]

Birks, T. A.

Chau, Y. F.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Chen, W. G.

L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
[CrossRef]

Cucinotta, A.

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fiber—Properties and Applications (Springer, 2007), pp. 219–223.

Du, H.

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004), pp. 130–134 .

Fu, B.

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

Furukawa, T.

R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.

Galatsanos, N. P.

D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s t-priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef]

A. C. Likas and N. P. Galatsanos, “A variational approach for Bayesian blind image deconvolution,” IEEE Trans. Signal Process. 52, 2222–2233 (2004).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004), pp. 130–134 .

Harun, S. W.

N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
[CrossRef]

He, Z. H.

Hosoda, N.

R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.

Huang, Y. Q.

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

Huang, Y. W.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Jiang, Z. H.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Jing, Q.

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

Katsaggelos, A. K.

S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
[CrossRef]

Knight, J. C.

Li, D. L.

D. L. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Trans. Neural Netw. 18, 931–935 (2007).
[CrossRef]

Li, H. L.

L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
[CrossRef]

Li, S. G.

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

Likas, A. C.

D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s t-priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef]

A. C. Likas and N. P. Galatsanos, “A variational approach for Bayesian blind image deconvolution,” IEEE Trans. Signal Process. 52, 2222–2233 (2004).
[CrossRef]

Lou, S. Q.

Y. Shen, L. W. Wang, and S. Q. Lou, “Improved method for fast evaluating optical properties of actual photonic crystal fibers,” Infrared Laser Eng. 41, 1041–1046 (2012).

L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
[CrossRef]

Ma, H. F.

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

Matsue, H.

R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.

Mersereau, R. M.

D. L. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Trans. Neural Netw. 18, 931–935 (2007).
[CrossRef]

Milanfar, P.

F. Šroubek and P. Milanfar, “Robust multichannel blind deconvolution via fast alternating minimization,” IEEE Trans. Image Process. 21, 1687–1700 (2012).
[CrossRef]

Mishra, S. S.

S. S. Mishra and V. K. Singh, “Study of non-linear properties of hollow core photonic crystal fiber,” Optik 122, 687–690 (2011).
[CrossRef]

Molina, R.

S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
[CrossRef]

Nagayasu, R.

R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.

Poli, F.

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fiber—Properties and Applications (Springer, 2007), pp. 219–223.

Ren, X. M.

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

Russell, P. S. J.

Selleri, S.

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fiber—Properties and Applications (Springer, 2007), pp. 219–223.

Shahabuddin, N. S.

N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
[CrossRef]

Shen, Y.

Y. Shen, L. W. Wang, and S. Q. Lou, “Improved method for fast evaluating optical properties of actual photonic crystal fibers,” Infrared Laser Eng. 41, 1041–1046 (2012).

Simske, S.

D. L. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Trans. Neural Netw. 18, 931–935 (2007).
[CrossRef]

Singh, V. K.

S. S. Mishra and V. K. Singh, “Study of non-linear properties of hollow core photonic crystal fiber,” Optik 122, 687–690 (2011).
[CrossRef]

Šroubek, F.

F. Šroubek and P. Milanfar, “Robust multichannel blind deconvolution via fast alternating minimization,” IEEE Trans. Image Process. 21, 1687–1700 (2012).
[CrossRef]

Tanabe, N.

R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.

Tian, F.

Tsai, D. P.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Tzikas, D. G.

D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s t-priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef]

Wang, J. N.

S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
[CrossRef]

Wang, L.

L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
[CrossRef]

Wang, L. W.

Y. Shen, L. W. Wang, and S. Q. Lou, “Improved method for fast evaluating optical properties of actual photonic crystal fibers,” Infrared Laser Eng. 41, 1041–1046 (2012).

Woods, R. E.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004), pp. 130–134 .

Yang, K. Y.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Yang, T. J.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Yao, Y. Y.

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

Yeh, H. H.

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Yusoff, Z.

N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
[CrossRef]

Zhang, L.

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

Zhang, M. Y.

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

Zhang, X.

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

Appl. Phys. A (1)

T. J. Yang, Y. F. Chau, H. H. Yeh, Z. H. Jiang, Y. W. Huang, K. Y. Yang, and D. P. Tsai, “Dispersion properties, birefringence and confinement loss of rotational elliptic air-hole photonic crystal fiber,” Appl. Phys. A 104, 857–861 (2011).
[CrossRef]

Chin. Phys. B (1)

L. Wang, S. Q. Lou, W. G. Chen, and H. L. Li, “A novel method for rapidly modeling optical properties of actual photonic crystal fibers,” Chin. Phys. B 19, 084209 (2010).
[CrossRef]

IEEE Photon. J. (1)

N. S. Shahabuddin, H. Ahmad, Z. Yusoff, and S. W. Harun, “Spacing-switchable multiwavelength fiber laser based on nonlinear polarization rotation and Brillouin scattering in photonic crystal fiber,” IEEE Photon. J. 4, 34–38 (2012).
[CrossRef]

IEEE Trans. Image Process. (3)

F. Šroubek and P. Milanfar, “Robust multichannel blind deconvolution via fast alternating minimization,” IEEE Trans. Image Process. 21, 1687–1700 (2012).
[CrossRef]

S. D. Babacan, J. N. Wang, R. Molina, and A. K. Katsaggelos, “Bayesian blind deconvolution from differently exposed image pairs,” IEEE Trans. Image Process. 19, 2874–2888 (2010).
[CrossRef]

D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s t-priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef]

IEEE Trans. Neural Netw. (1)

D. L. Li, R. M. Mersereau, and S. Simske, “Blind image deconvolution through support vector regression,” IEEE Trans. Neural Netw. 18, 931–935 (2007).
[CrossRef]

IEEE Trans. Signal Process. (1)

A. C. Likas and N. P. Galatsanos, “A variational approach for Bayesian blind image deconvolution,” IEEE Trans. Signal Process. 52, 2222–2233 (2004).
[CrossRef]

Infrared Laser Eng. (1)

Y. Shen, L. W. Wang, and S. Q. Lou, “Improved method for fast evaluating optical properties of actual photonic crystal fibers,” Infrared Laser Eng. 41, 1041–1046 (2012).

J. Opt. (2)

Q. Jing, X. Zhang, H. F. Ma, Y. Q. Huang, and X. M. Ren, “Flatly broadened supercontinuum generation in dispersion-flattened photonic crystal fibre using compressed picosecond pulses,” J. Opt. 14, 015203 (2012).
[CrossRef]

L. Zhang, S. G. Li, Y. Y. Yao, B. Fu, and M. Y. Zhang, “Properties of high birefringence chalcogenide glass holey fiber for mid-infrared transparency,” J. Opt. 12, 035207 (2010).
[CrossRef]

Opt. Lett. (2)

Optik (1)

S. S. Mishra and V. K. Singh, “Study of non-linear properties of hollow core photonic crystal fiber,” Optik 122, 687–690 (2011).
[CrossRef]

Other (5)

R. Nagayasu, N. Hosoda, N. Tanabe, H. Matsue, and T. Furukawa, “Restoration method for degraded images using two-dimensional block Kalman filter with colored driving source,” in Proceedings of Digital Signal Procession Workshop and IEEE Signal Processing Education Workshop (IEEE DSP/SPE) (2011), pp. 151–156.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice-Hall, 2004), pp. 130–134 .

Crystal Fiber A/S http://www.crystal-fibre.com/datasheets/LMA-PM-5.pdf , 2008.

Crystal Fiber A/S http://www.crystal-fibre.com/datasheets/PM-1550-01.pdf , 2008.

F. Poli, A. Cucinotta, and S. Selleri, Photonic Crystal Fiber—Properties and Applications (Springer, 2007), pp. 219–223.

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 (9)

Fig. 1.
Fig. 1.

Photographing and restoring process for the cross-section image of PCF.

Fig. 2.
Fig. 2.

Assumed size and values of PSF.

Fig. 3.
Fig. 3.

Transfer process of the observation matrix B(k).

Fig. 4.
Fig. 4.

Restored images with PSF=3×3 at different SNR. (a)–(d) are the results of the Bayesian method with SNR=45, 40, 35, and 30 dB; (e)–(h) are the results of the proposed method with SNR=45, 40, 35, and 30 dB.

Fig. 5.
Fig. 5.

Restored images with SNR=30dB at different PSF. (a)–(d) are the results of the Bayesian method with PSF=3×3, 4×4, 5×5, and 6×6; (e)–(h) are the results of the proposed method with PSF=3×3, 4×4, 5×5, and 6×6.

Fig. 6.
Fig. 6.

Comparison of variance of the Bayesian and the proposed method with PSF=3×3, SNR=30, 35, 40, and 45 dB (a) and SNR=30dB, PSF=3×3, 4×4, 5×5, and 6×6 (b).

Fig. 7.
Fig. 7.

Microscope images of the cross-section of several practical PCFs. (a) Large mode area PCF, (b) polarization maintaining PCF, and (c) homemade, single-mode PCF.

Fig. 8.
Fig. 8.

(a), (d), and (g) represent the three enlarged PCFs images of Figs. 7(a) , 7(b), and 7(c); (b), (e), and (h) are the corresponding restoration results by the Bayesian method and (c), (f), and (i) are the results by the proposed method.

Fig. 9.
Fig. 9.

Mesh of (a) large mode area PCF and (b) polarization-maintaining PCF.

Tables (3)

Tables Icon

Table 1. Mode Field Diameter of the Fundamental Mode

Tables Icon

Table 2. Comparisons of the Numerical Results with the Product Parameters

Tables Icon

Table 3. Comparisons of the Beat Length with the Product Parameters

Equations (19)

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

gi,j=lmhil,jmfl,m+ni,j,f^i,j=F(gi,j),
p(k)=A(k,k1)p(k1)+ξ(k),
g(k)=G(p(k))+η(k),
ξ(k)N(0,Rξ),η(k)N(0,Rη).
C(k)=[0000c11c210c12c22000c11c21c31c12c22c32000c21c310c22c3200c11c210c12c220c13c23c11c21c31c12c22c32c13c23c33c21c310c22c320c23c3300c12c220c13c23000c12c22c32c13c23c33000c22c320c23c330000].
p^(k|k)=p^(k|k1)+H(k)·W(k),
W(k)=g(k)C(k)p^(k|k1).
H(k)={P(k|k1)C(k)T}·{C(k)P(k|k1)C(k)T+Rη}1,
P(k|k1)=A(k,k1)P(k1|k1)AT(k,k1)+Rξ.
P(k|k)={IH(k)C(k)}P(k|k1).
f(k)=E(k,k1)f(k1)+U(k)+w(k),
g(k)=D·f(k)+v(k),
E(k,k1)=[000100000000010000000001000000000100000000010000000001000000000000000000000000000].
PSF1=[0.039760.039750.039810.039750.039760.039750.039950.039970.039950.039750.039810.039970.040120.039970.039810.039750.039950.039970.039950.039750.039760.039750.039810.039750.03976],
PSF2=[0.10800.10950.10800.10950.13120.10950.10800.10950.1080],
PSF3=[0.10520.10810.10520.10810.13720.10810.10520.10810.1052],
MFA=(s|E|2dxdy)2s|E|4dxdy,
D=λcd2ndλ2,
L=λB,

Metrics