Abstract

A spiral phase plate with an azimuthal structure exp[iϕ] (0ϕ<2π) has been used as a filter in a 4f system to achieve edge enhancement. Generally such edge-enhanced effect is isotropic, i.e., each edge of an input pattern is enhanced to the same degree regardless of its orientation. We found that one can achieve anisotropic edge enhancement by breaking down the symmetry of the filtering process. This can be done in two ways: first, by use of a fractional spiral phase filter (SPF) with a fractional topological charge and a controllable orientation of the edge discontinuity, and second, by the lateral shifting of the SPF. We interpret this process as a vortex formation due to the diffraction of the Fourier spectrum of the input pattern by a SPF with an integer and fractional topological charge. Optical experiments using a spatial light modulator were carried out to verify our proposal.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
    [CrossRef]
  2. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffraction of a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849-861 (2005).
    [CrossRef]
  3. V. V. Kotlyar, S. N. Khonina, A. A. Kovalev, V. A. Soifer, H. Elfstrom, and J. Turunen, “Diffraction of a plane, finite-radius wave by a spiral phase plate,” Opt. Lett. 31, 1597-1599 (2006).
    [CrossRef] [PubMed]
  4. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955-1964 (2007).
    [CrossRef]
  5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
    [CrossRef] [PubMed]
  6. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
    [CrossRef] [PubMed]
  7. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313-315 (2001).
    [CrossRef]
  8. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147-1154 (1992).
    [CrossRef]
  9. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25, 99-101 (2000).
    [CrossRef]
  10. J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Analysis of the fractional Hilbert transform,” Appl. Opt. 37, 6911-6913 (1998).
    [CrossRef]
  11. C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
    [CrossRef]
  12. K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862-1870 (2001).
    [CrossRef]
  13. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Sprial phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
    [CrossRef] [PubMed]
  14. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
    [CrossRef] [PubMed]
  15. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
    [CrossRef]
  16. A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635-2637 (2007).
    [CrossRef] [PubMed]
  17. Q. Xie and D. Zhao, “Generation of dark hollow beams by using a fractional radial Hilbert transform system,” Opt. Commun. 275, 394-398 (2007).
    [CrossRef]
  18. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).
  19. J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
    [CrossRef]
  20. D. Cao, P. P. Banerjee, and T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37, 3007-3014 (1998).
    [CrossRef]
  21. A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28, 1510-1512 (2003).
    [CrossRef] [PubMed]
  22. S. Greenberg and D. Kogan, “Structure-adaptive anisotropic filter applied to fingerprints,” Opt. Eng. (Bellingham) 44, 127004 (2005).
    [CrossRef]
  23. X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
    [CrossRef]
  24. J. A. Davis, D. A. Smith, D. E. McNamara, D. M. Cottrell, and J. Campos, “Fractional derivatives--analysis and experimental implementation,” Appl. Opt. 40, 5943-5948 (2001).
    [CrossRef]
  25. J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 23, 4835-4839 (2002).
    [CrossRef]
  26. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional Hilbert transform,” Opt. Lett. 21, 281-283 (1996).
    [CrossRef] [PubMed]
  27. A. W. Lohmann, E. Tepichin, and J. G. Ramirez, “Optical implementation of the fractional Hilbert transform,” Appl. Opt. 36, 6620-6626 (1997).
    [CrossRef]
  28. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6, 259-268 (2004).
    [CrossRef]
  29. J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
    [CrossRef]
  30. W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129-135 (2004).
    [CrossRef]
  31. J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723-1738 (2007).
    [CrossRef]
  32. J. B. Götte, K. O'Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993-1006 (2008).
    [CrossRef] [PubMed]
  33. S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
    [CrossRef] [PubMed]
  34. I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
    [CrossRef]
  35. G. B. Arfken and H. J. Weber, Mathematical Methods For Physicists, 5th ed. (Academic, 2001).
  36. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1970).
  37. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960-967 (2006).
    [CrossRef] [PubMed]

2008 (1)

2007 (5)

V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, O. Y. Moiseev, and V. A. Soifer, “Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate,” J. Opt. Soc. Am. A 24, 1955-1964 (2007).
[CrossRef]

A. Sakdinawat and Y. Liu, “Soft-x-ray microscopy using spiral zone plates,” Opt. Lett. 32, 2635-2637 (2007).
[CrossRef] [PubMed]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

Q. Xie and D. Zhao, “Generation of dark hollow beams by using a fractional radial Hilbert transform system,” Opt. Commun. 275, 394-398 (2007).
[CrossRef]

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723-1738 (2007).
[CrossRef]

2006 (3)

2005 (5)

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Sprial phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
[CrossRef] [PubMed]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffraction of a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22, 849-861 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

S. Greenberg and D. Kogan, “Structure-adaptive anisotropic filter applied to fingerprints,” Opt. Eng. (Bellingham) 44, 127004 (2005).
[CrossRef]

X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
[CrossRef]

2004 (5)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6, 259-268 (2004).
[CrossRef]

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129-135 (2004).
[CrossRef]

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

2003 (1)

2002 (1)

J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 23, 4835-4839 (2002).
[CrossRef]

2001 (3)

2000 (1)

1998 (2)

1997 (1)

1996 (2)

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
[CrossRef]

A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional Hilbert transform,” Opt. Lett. 21, 281-283 (1996).
[CrossRef] [PubMed]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
[CrossRef]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
[CrossRef] [PubMed]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1970).

Aiello, A.

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
[CrossRef] [PubMed]

Almazov, A. A.

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods For Physicists, 5th ed. (Academic, 2001).

Banerjee, P. P.

D. Cao, P. P. Banerjee, and T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37, 3007-3014 (1998).
[CrossRef]

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
[CrossRef]

Barnett, S. M.

Basistiy, I. V.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
[CrossRef] [PubMed]

Beléndez, A.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Sprial phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6, 259-268 (2004).
[CrossRef]

Bone, D. J.

Campos, J.

Cao, D.

Chen, X.

X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
[CrossRef]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Dholakia, K.

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129-135 (2004).
[CrossRef]

Ding, J.-P.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
[CrossRef]

Dunn, D. B.

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
[CrossRef]

Elfstrom, H.

Eliel, E. R.

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

Flossmann, F.

Franke-Arnold, S.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Sprial phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

Gallego, S.

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Götte, J. B.

Greenberg, S.

S. Greenberg and D. Kogan, “Structure-adaptive anisotropic filter applied to fingerprints,” Opt. Eng. (Bellingham) 44, 127004 (2005).
[CrossRef]

Guo, C.-S.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
[CrossRef]

Han, Y.-J.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Sprial phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

Khonina, S. N.

Kogan, D.

S. Greenberg and D. Kogan, “Structure-adaptive anisotropic filter applied to fingerprints,” Opt. Eng. (Bellingham) 44, 127004 (2005).
[CrossRef]

Kohler, C.

Kotlyar, V. V.

Kovalev, A. A.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Larkin, K. G.

Leach, J.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

Lee, W. M.

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129-135 (2004).
[CrossRef]

Liu, Y.

Lohmann, A. W.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313-315 (2001).
[CrossRef]

Márquez, A.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

McNamara, D. E.

Mendlovic, D.

Moiseev, O. Y.

Neipp, C.

Nienhuis, G.

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

Nowak, M. D.

J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 23, 4835-4839 (2002).
[CrossRef]

Oemrawsingh, S. S. R.

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

O'Holleran, K.

Oldfield, M. A.

Ortuño, M.

Osten, W.

Padgett, M. J.

Pascual, I.

Pas'ko, V. A.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

Poon, T.-C.

D. Cao, P. P. Banerjee, and T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37, 3007-3014 (1998).
[CrossRef]

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
[CrossRef]

Preece, D.

Ramirez, J. G.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Sprial phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Sakdinawat, A.

Schwab, X.

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Skidanov, R. V.

Slyusar, V. V.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

Smith, D. A.

Soifer, V. A.

Soskin, M. S.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
[CrossRef] [PubMed]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1970).

Tepichin, E.

Tian, J.

X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
[CrossRef]

Turunen, J.

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313-315 (2001).
[CrossRef]

Wang, H.-T.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
[CrossRef]

Weber, H. J.

G. B. Arfken and H. J. Weber, Mathematical Methods For Physicists, 5th ed. (Academic, 2001).

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313-315 (2001).
[CrossRef]

Woerdman, J. P.

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
[CrossRef] [PubMed]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Xia, J.

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
[CrossRef]

Xie, Q.

Q. Xie and D. Zhao, “Generation of dark hollow beams by using a fractional radial Hilbert transform system,” Opt. Commun. 275, 394-398 (2007).
[CrossRef]

Yang, X.

X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
[CrossRef]

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

Yuan, X. C.

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129-135 (2004).
[CrossRef]

Zalevsky, Z.

Zambrini, R.

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723-1738 (2007).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313-315 (2001).
[CrossRef]

Zhang, Y.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
[CrossRef]

X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
[CrossRef]

Zhao, D.

Q. Xie and D. Zhao, “Generation of dark hollow beams by using a fractional radial Hilbert transform system,” Opt. Commun. 275, 394-398 (2007).
[CrossRef]

Appl. Opt. (6)

J. Microsc. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Upgrading a microscope with a spiral phase plate,” J. Microsc. 230, 134-142 (2007).
[CrossRef]

J. Mod. Opt. (2)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

J. B. Götte, S. Franke-Arnold, R. Zambrini, and S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54, 1723-1738 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (2)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A, Pure Appl. Opt. 6, 259-268 (2004).
[CrossRef]

I. V. Basistiy, V. A. Pas'ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6, S166-S169 (2004).
[CrossRef]

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

Lect. Notes Comput. Sci. (1)

X. Chen, J. Tian, Y. Zhang, and X. Yang, “Enhancement of low quality fingerprints based on anisotropic filtering,” Lect. Notes Comput. Sci. 3832, 302-308 (2005).
[CrossRef]

Nature (London) (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313-315 (2001).
[CrossRef]

New J. Phys. (1)

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

Opt. Commun. (5)

W. M. Lee, X. C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129-135 (2004).
[CrossRef]

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259, 449-454 (2006).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Q. Xie and D. Zhao, “Generation of dark hollow beams by using a fractional radial Hilbert transform system,” Opt. Commun. 275, 394-398 (2007).
[CrossRef]

J. Xia, D. B. Dunn, T.-C. Poon, and P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1-7 (1996).
[CrossRef]

Opt. Eng. (Bellingham) (1)

S. Greenberg and D. Kogan, “Structure-adaptive anisotropic filter applied to fingerprints,” Opt. Eng. (Bellingham) 44, 127004 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185-8190 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef] [PubMed]

S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. 92, 217901 (2004).
[CrossRef] [PubMed]

Other (3)

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

G. B. Arfken and H. J. Weber, Mathematical Methods For Physicists, 5th ed. (Academic, 2001).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1970).

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

Density plot of u 1 ( r , φ , ϑ ) .

Fig. 2
Fig. 2

Density plots of u p ( ρ , ϕ , ϑ = 0 , z = 200 λ ) with p = 0.8 in the vicinity of the origin.

Fig. 3
Fig. 3

Value of c m versus m: p = (a) 0.2, (b) 0.5, (c) 0.85.

Fig. 4
Fig. 4

Density plots of u p ( r , φ , ϑ = 0 ) with p = ( a ) 0.2, (b) 0.5, (c) 0.8. On the upper-left side of these figures we plot the status of the SPF.

Fig. 5
Fig. 5

Density plot of u p ( r , φ , ϑ = π 2 ) with p = 0.5 .

Fig. 6
Fig. 6

Density plot of u 1 s with ( ρ 0 , θ ) equal to (a) ( 0.2 R , π 4 ) , (b) ( 0.55 R , π 4 ) , (c) ( 0.85 R , π 4 ) , (d) ( 0.55 R , 3 π 4 ) . On the upper-left-side of these figures we plot the status of the SPF. The dark ring in the figure is the boundary of the filter. Note that in the calculation the area of the SPF outside the boundary is zero. It is shown here just for a clearer illustration of the state of the SPF.

Fig. 7
Fig. 7

Setup of the optical experiment. A, analyzer; P, polarizer; C, collimator; O, object. The focal lengths of the Fourier lenses L1 and L2 are 160 and 250 mm , respectively.

Fig. 8
Fig. 8

Experimental results of method 1. The ( p , ϑ ) values are (a) ( 0.8 , π ) , (b) ( 0.6 , 5 π 4 ) , (c) ( 0.4 , 7 π 4 ) , (d) ( 0.9 , π 2 ) . It is shown that φ e = 3 π 2 , 7 π 4 , π 4 , and π, i.e., respectively along the arrows in (a)–(d). The stages of the SPP are shown, respectively, in the upper-left corner of these figures. The subfigures in the upper-right corners show the cross sections of the arrows and the output patterns. One can see from (c) that the filtered output appears with an intensity gradient when p < 0.5 . High-contrast edge enhancement takes place when p 0.5 .

Fig. 9
Fig. 9

Experimental results of method 2. The ( ρ 0 , θ ) values are (a) ( 3 δ , π 2 ) , (b) ( 6 δ , 0 ) , (c) ( 11 δ , 3 π 2 ) , (d) ( 10 δ , π ) , where δ = 9.5 μ m is the pixel dimension of the LCD. It is shown in these figures that φ e = π , π 2 , 0, and 3 π 2 , i.e., respectively along the arrows in (a)–(d). The stages of the SPP are shown, respectively, in the upper-left corner of these figures. The subfigures in the upper-right corners show the cross sections of the arrows and the output patterns. The stages of the SPP are shown, respectively, in the upper-left corner of these figures.

Equations (31)

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

ψ n ( ρ , ϕ , ϑ ) = exp [ i n ( ϕ + ϑ ) ] ,
G ( ρ , ϕ ) = G ( ξ , η ) = F { g ( x , y ) } ,
ξ = ρ cos ϕ , η = ρ sin ϕ ,
G ( ρ , ϕ ) = G ( ρ , ϕ ) ψ n ( ρ , ϕ , ϑ ) .
g ̃ ( r , φ ) = F { G ( ρ , ϕ ) } = g ( r , φ ) F { ψ n ( ρ , ϕ , ϑ ) } ,
u n ( ρ , ϕ , ϑ , z ) = i k 2 π z exp [ i k 2 z ρ 2 ] × 0 R 0 2 π exp [ i n ( ϕ + ϑ ) ] exp ( i k 2 z ρ 2 ) × exp [ i k z ρ ρ cos ( ϕ ϕ ) ] ρ d ρ d ϕ ,
exp ( i ρ cos ϕ ) = m = i m J m ( ρ ) exp ( i m ϕ ) ,
u n ( ρ , ϕ , ϑ , z ) = ( i ) n + 1 k z exp [ i n ( ϕ + ϑ ) + i k 2 z ρ 2 ] 0 R exp ( i k 2 z ρ 2 ) J n ( k z ρ ρ ) ρ d ρ ,
0 2 π exp [ i ( n m ) ϕ ] d ϕ = 2 π δ n m ,
G ( ρ , ϕ ) = G ( ρ = 0 , ϕ ) + G ( ρ 0 , ϕ ) ,
u n ( r , φ , ϑ ) = ( i ) n + 1 k f exp [ i n ( φ + ϑ ) ] 0 R J n ( k r ρ f ) ρ d ρ ,
u n ( r , φ , ϑ ) = ( i ) n + 1 f exp [ i n ( φ + ϑ ) ] k r 2 × { n [ r 0 R J 0 ( r ρ ) d ρ 2 m = 0 κ 1 J 2 m + 1 ( r R ) ] r R J n 1 ( r R ) , if n = 2 κ + 1 n [ 1 J 0 ( r R ) 2 m = 1 κ J 2 m ( r R ) ] r R J n 1 ( r R ) , if n = 2 κ + 2 } ,
0 R J 0 ( ρ ) d ρ = R π 2 [ J 1 ( R ) H 0 ( R ) J 0 ( R ) H 1 ( R ) ] + R J 0 ( R ) ,
g ̃ ( r , φ ) = g ( r , φ ) u 1 ( r , φ , ϑ ) = g ( r , φ ) k R π 2 f r [ J 1 ( r R ) H 0 ( r R ) J 0 ( r R ) H 1 ( r R ) ] exp [ i ( φ + ϑ ) ] .
ψ p ( ρ , ϕ , ϑ ) = exp ( i p π ) sin ( p π ) π n = ψ n ( ρ , ϕ , ϑ ) p n .
u p ( ρ , ϕ , ϑ , z ) = exp ( i p π ) sin ( p π ) π n = u n ( ρ , ϕ , ϑ , z ) p n ,
u p ( ρ = 0 , ϕ , ϑ , z ) = exp [ i p π ] sin ( p π ) p π u 0 ( ρ , ϕ , ϑ , z ) .
ρ 1.3293 8 z k π ( 1 p )
u p ( r , φ , ϑ ) = k 2 π f m = ( i ) m exp [ i m ( φ + ϑ ) ] exp [ i 2 π ( p m ) ] 1 p m 0 R J m ( r ρ ) ρ d ρ ,
c m = exp [ i 2 π ( p m ) ] 1 p m .
g ̃ ( r , φ ) = g ( r , φ ) u p ( r , φ , ϑ ) .
ψ 1 s ( ρ , ϕ , ρ 0 , θ ) = ρ exp ( i ϕ ) + ρ 0 exp ( i θ ) ρ 2 + ρ 0 2 + 2 ρ ρ 0 cos ( ϕ θ ) ,
u 1 s ( ρ , ϕ , ρ 0 , θ , z ) = A ( ρ , z ) ρ 0 exp ( i θ ) 0 R J 0 ( k z ρ ρ ) B ( ρ , z , ρ 0 , θ ) ρ d ρ i A ( ρ , z ) exp ( i ϕ ) 0 R ρ J 1 ( k z ρ ρ ) B ( ρ , z , ρ 0 , θ ) ρ d ρ ,
A ( ρ , z ) = i k 2 π z exp ( i k 2 z ρ 2 )
B ( ρ , z , ρ 0 , θ ) = 2 ρ + ρ 0 [ F ( θ 2 , 2 ρ ρ 0 ( ρ + ρ 0 ) 2 ) F ( θ 2 π 2 , 2 ρ ρ 0 ( ρ + ρ 0 ) 2 ) ] exp ( i k 2 z ρ 2 ) ,
F ( θ , m ) = 0 θ 1 1 m sin 2 ϕ d ϕ
u 1 s ( r , φ , ρ 0 , θ , z ) = i k 2 π z ρ 0 exp ( i θ ) 0 R J 0 ( k z r ρ ) B ( ρ , z = , ρ 0 , θ ) ρ d ρ k 2 π z exp ( i φ ) 0 R ρ J 1 ( k z r ρ ) B ( ρ , z = , ρ 0 , θ ) ρ d ρ ,
φ e = θ + π 2 ,
d d ρ [ ρ n J n ( ρ ) ] = ρ n J n + 1 ( ρ ) ,
0 R J n ( ρ ) ρ d ρ = n 0 R J n 1 ( ρ ) d ρ R J n 1 ( R ) .
0 R J n 1 ( ρ ) d ρ = { 0 R J 0 ( ρ ) d ρ 2 m = 0 κ 1 J 2 m + 1 ( R ) , if n = 2 κ + 1 1 J 0 ( R ) 2 m = 1 κ J 2 m ( R ) , if n = 2 κ + 2 } ,

Metrics