Abstract

A single frame fork fringe pattern automatic processing method for detecting optical vortices in coherent light fields using two-dimensional continuous wavelet transformation is proposed. When a vortex sign is of no importance, it is sufficient to calculate the fork interferogram modulation distribution and its normalized gradient map to establish vortex locations without resorting to complicated phase calculations. Normalization of modulation gradient maps enables unambiguous vortex discrimination from local modulation minima without phase singularity. The issue of vortex detection resolution versus carrier fringe frequency and orientation is discussed. Corroboration of simulation and experimental studies of integer and noninteger singular light beams as well as speckle fields reported in the literature and analyzed using different approaches is presented.

© 2011 Optical Society of America

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  1. J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
    [CrossRef]
  2. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol.  42, pp. 219–276.
    [CrossRef]
  3. J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interferfence,” Opt. Commun. 198, 21–27 (2001).
    [CrossRef]
  4. P. Kurzynowski, W. A. Woźniak, and E. Fraczek, “Optical vortices generation using the Wollaston prism,” Appl. Opt. 45, 7898–7903 (2006).
    [CrossRef] [PubMed]
  5. S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
    [CrossRef] [PubMed]
  6. S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46, 7862–7867 (2007).
    [CrossRef] [PubMed]
  7. V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scalar light fields,” Opt. Lett. 33, 89–91(2008).
    [CrossRef]
  8. A. Federico and G. H. Kaufmann, “Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier,” Appl. Opt. 47, 5201–5207(2008).
    [CrossRef] [PubMed]
  9. F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett. 32, 2291–2293 (2007).
    [CrossRef] [PubMed]
  10. K. Murphy, D. Burke, N. Devaney, and C. Dainty, “Experimental detection of optical vortices with a Shack-Hartmann wavefront sensor,” Opt. Express 18, 15448–15460 (2010).
    [CrossRef] [PubMed]
  11. O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
    [CrossRef]
  12. I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
    [CrossRef]
  13. I. Freund, “Vortex derivatives,” Opt. Commun. 137, 118–126(1997).
    [CrossRef]
  14. M. Vasnetsov, Optical Vortices (Nova Science, 1999).
  15. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
    [CrossRef] [PubMed]
  16. K. Pokorski and K. Patorski, “Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform,” Appl. Opt. 49, 3640–3651 (2010).
    [CrossRef] [PubMed]
  17. Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
    [CrossRef]
  18. J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).
  19. D. L. Fried and J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef] [PubMed]
  20. M. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A Pure Appl. Opt. 6, 259–268 (2004).
    [CrossRef]
  21. 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]
  22. I. V. Basistiy, V. A. Pasko, 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]
  23. S. Baumann and E. Galvez, “Non-integral vortex structures in diffracted light beams,” Proc. SPIE 6483, 64830T(2007).
    [CrossRef]
  24. W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
    [CrossRef] [PubMed]
  25. M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
    [CrossRef]
  26. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
    [CrossRef]
  27. K. O’Holleran, M. Dennis, and M. Padget, “Illustrations of optical vortices in three dimensions,” J. Europ. Opt. Soc. Rap. Public. 1, 06008 (2006).
    [CrossRef]
  28. Laboratoire de Télédection et Télédétection, “YAWTb: yet another wavelet toolbox,” http://rhea.tele.ucl.ac.be/yawtb/.
  29. E. Galvez and S. Baumann, “Composite vortex patterns formed by component light beams with non-integral topological charge,” Proc. SPIE 6905, 69050D (2008).
    [CrossRef]
  30. E. Galvez, N. Smiley, and N. Fernandes, “Composite optical vortices formed by collinear Laguerre-Gauss beams,” Proc. SPIE 6131, 613105 (2006).
    [CrossRef]

2010 (2)

2009 (1)

O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
[CrossRef]

2008 (4)

E. Galvez and S. Baumann, “Composite vortex patterns formed by component light beams with non-integral topological charge,” Proc. SPIE 6905, 69050D (2008).
[CrossRef]

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scalar light fields,” Opt. Lett. 33, 89–91(2008).
[CrossRef]

A. Federico and G. H. Kaufmann, “Phase retrieval of singular scalar light fields using a two-dimensional directional wavelet transform and a spatial carrier,” Appl. Opt. 47, 5201–5207(2008).
[CrossRef] [PubMed]

2007 (4)

2006 (6)

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

K. O’Holleran, M. Dennis, and M. Padget, “Illustrations of optical vortices in three dimensions,” J. Europ. Opt. Soc. Rap. Public. 1, 06008 (2006).
[CrossRef]

E. Galvez, N. Smiley, and N. Fernandes, “Composite optical vortices formed by collinear Laguerre-Gauss beams,” Proc. SPIE 6131, 613105 (2006).
[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

P. Kurzynowski, W. A. Woźniak, and E. Fraczek, “Optical vortices generation using the Wollaston prism,” Appl. Opt. 45, 7898–7903 (2006).
[CrossRef] [PubMed]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[CrossRef] [PubMed]

2005 (1)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

2004 (3)

M. 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]

I. V. Basistiy, V. A. Pasko, 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]

2001 (3)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol.  42, pp. 219–276.
[CrossRef]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interferfence,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[CrossRef]

1999 (1)

M. Vasnetsov, Optical Vortices (Nova Science, 1999).

1997 (1)

I. Freund, “Vortex derivatives,” Opt. Commun. 137, 118–126(1997).
[CrossRef]

1994 (1)

1992 (1)

1974 (1)

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

Aksenov, V. P.

Ali, S. T.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).

Angelsky, O.

O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
[CrossRef]

Antoine, J.-P.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).

Atuchin, V. V.

Basistiy, I. V.

I. V. Basistiy, V. A. Pasko, 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]

Baumann, S.

E. Galvez and S. Baumann, “Composite vortex patterns formed by component light beams with non-integral topological charge,” Proc. SPIE 6905, 69050D (2008).
[CrossRef]

S. Baumann and E. Galvez, “Non-integral vortex structures in diffracted light beams,” Proc. SPIE 6483, 64830T(2007).
[CrossRef]

Berry, M.

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

Berry, M. V.

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

Burke, D.

Burton, D. R.

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Dainty, C.

Denisenko, V. G.

Dennis, M.

K. O’Holleran, M. Dennis, and M. Padget, “Illustrations of optical vortices in three dimensions,” J. Europ. Opt. Soc. Rap. Public. 1, 06008 (2006).
[CrossRef]

Dennis, M. R.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[CrossRef]

Desyatnikov, A. S.

Devaney, N.

Duan, Z.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Dubik, B.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interferfence,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Federico, A.

Fernandes, N.

E. Galvez, N. Smiley, and N. Fernandes, “Composite optical vortices formed by collinear Laguerre-Gauss beams,” Proc. SPIE 6131, 613105 (2006).
[CrossRef]

Fraczek, E.

Freund, I.

Fried, D. L.

Galvez, E.

E. Galvez and S. Baumann, “Composite vortex patterns formed by component light beams with non-integral topological charge,” Proc. SPIE 6905, 69050D (2008).
[CrossRef]

S. Baumann and E. Galvez, “Non-integral vortex structures in diffracted light beams,” Proc. SPIE 6483, 64830T(2007).
[CrossRef]

E. Galvez, N. Smiley, and N. Fernandes, “Composite optical vortices formed by collinear Laguerre-Gauss beams,” Proc. SPIE 6131, 613105 (2006).
[CrossRef]

Gdeisat, M. A.

Hanson, S.

O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
[CrossRef]

Hanson, S. G.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Izmailov, I. V.

Kanev, F. Y.

Kaufmann, G. H.

Kivshar, Y. S.

Kochemasov, G. G.

Krolikowski, W.

Kulikov, S. M.

Kurzynowski, P.

Lalor, M. J.

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[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]

Ma, H.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Maksimyak, A.

O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
[CrossRef]

Maksimyak, P.

O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
[CrossRef]

Manachinsky, A. N.

Masajada, J.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interferfence,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Maslov, N. V.

Minovich, A.

Miyamoto, Y.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Murenzi, R.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).

Murphy, K.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

O’Holleran, K.

K. O’Holleran, M. Dennis, and M. Padget, “Illustrations of optical vortices in three dimensions,” J. Europ. Opt. Soc. Rap. Public. 1, 06008 (2006).
[CrossRef]

Ogorodnikov, A. V.

Padget, M.

K. O’Holleran, M. Dennis, and M. Padget, “Illustrations of optical vortices in three dimensions,” J. Europ. Opt. Soc. Rap. Public. 1, 06008 (2006).
[CrossRef]

Padgett, M. J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[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]

Pasko, V. A.

I. V. Basistiy, V. A. Pasko, 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]

Patorski, K.

Pokorski, K.

Senthilkumaran, P.

Slyusar, V. V.

I. V. Basistiy, V. A. Pasko, 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]

Smiley, N.

E. Galvez, N. Smiley, and N. Fernandes, “Composite optical vortices formed by collinear Laguerre-Gauss beams,” Proc. SPIE 6131, 613105 (2006).
[CrossRef]

Soldatenkov, I. S.

Soskin, M. S.

V. G. Denisenko, A. Minovich, A. S. Desyatnikov, W. Krolikowski, M. S. Soskin, and Y. S. Kivshar, “Mapping phases of singular scalar light fields,” Opt. Lett. 33, 89–91(2008).
[CrossRef]

I. V. Basistiy, V. A. Pasko, 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]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol.  42, pp. 219–276.
[CrossRef]

Starikov, F. A.

Sukharev, S. A.

Takeda, M.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Vandergheynst, P.

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).

Vasnetsov, M.

M. Vasnetsov, Optical Vortices (Nova Science, 1999).

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pasko, 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]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol.  42, pp. 219–276.
[CrossRef]

Vaughn, J. L.

Vyas, S.

Wang, W.

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Wang, Z.

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Wozniak, W. A.

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]

Appl. Opt. (7)

J. Europ. Opt. Soc. Rap. Public. (1)

K. O’Holleran, M. Dennis, and M. Padget, “Illustrations of optical vortices in three dimensions,” J. Europ. Opt. Soc. Rap. Public. 1, 06008 (2006).
[CrossRef]

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

M. 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. Pasko, 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 (1)

New J. Phys. (2)

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]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. 7, 55 (2005).
[CrossRef]

Open Opt. J. (1)

O. Angelsky, A. Maksimyak, P. Maksimyak, and S. Hanson, “Spatial behaviour of singularities in Fractal- and Gaussian speckle fields,” Open Opt. J. 3, 29–43 (2009).
[CrossRef]

Opt. Commun. (2)

I. Freund, “Vortex derivatives,” Opt. Commun. 137, 118–126(1997).
[CrossRef]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interferfence,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Opt. Eng. (1)

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45, 045601 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

W. Wang, Z. Duan, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function,” Phys. Rev. Lett. 96, 073902 (2006).
[CrossRef] [PubMed]

Proc. R. Soc. A (2)

M. V. Berry and M. R. Dennis, “Knotted and linked phase singularities in monochromatic waves,” Proc. R. Soc. A 457, 2251–2263 (2001).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[CrossRef]

Proc. SPIE (3)

S. Baumann and E. Galvez, “Non-integral vortex structures in diffracted light beams,” Proc. SPIE 6483, 64830T(2007).
[CrossRef]

E. Galvez and S. Baumann, “Composite vortex patterns formed by component light beams with non-integral topological charge,” Proc. SPIE 6905, 69050D (2008).
[CrossRef]

E. Galvez, N. Smiley, and N. Fernandes, “Composite optical vortices formed by collinear Laguerre-Gauss beams,” Proc. SPIE 6131, 613105 (2006).
[CrossRef]

Other (4)

Laboratoire de Télédection et Télédétection, “YAWTb: yet another wavelet toolbox,” http://rhea.tele.ucl.ac.be/yawtb/.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (North-Holland, 2001), Vol.  42, pp. 219–276.
[CrossRef]

M. Vasnetsov, Optical Vortices (Nova Science, 1999).

J.-P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and Their Relatives (Cambridge University, 2008).

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Figures (8)

Fig. 1
Fig. 1

Method accuracy check: (a) scale and (b) angle mismatch errors, (c) fringe curvature errors.

Fig. 2
Fig. 2

Modulation drops with (a) Gaussian and (c) rectangular profiles and their (b), (d) processing results.

Fig. 3
Fig. 3

Resolution analysis: (a) vortex detection errors, (b) fringe pattern of two vortices of same sign separated by 0.05 fringe and (c) its processing result, (d) fringe pattern of two vortices of opposite signs separated by 1.75 fringe (critical value for separating two vortices) and (e) its processing result.

Fig. 4
Fig. 4

Simulation of a three wavefront beam interference (a) without carrier fringes and (b) with carrier fringes and additive Gaussian noise. (c) CWT vortex processing result of (b).

Fig. 5
Fig. 5

(a) Experimental fork fringes [4], (b) filtered image and (c) its modulation map, (d) magnitude of the modulation gradient map, (e) normalized modulation gradient map, and (f) enhanced fork pattern.

Fig. 6
Fig. 6

(a) Experimental fringe pattern [7], (b) filtered image, (c) modulation map, (d) magnitude of the modulation gradient map, (e) normalized modulation gradient distribution, and (f) normalized fork fringes.

Fig. 7
Fig. 7

(a) Experimental fork fringe pattern for high-resolution analysis of a half-integer phase structure with topological charge l = 1.5 (courtesy of E. Galvez). (b) Filtered image, (c) modulation map, (d) modulation gradient map, (e) normalized modulation gradient map, and (f) enhanced (normalized) fringes. Note additional vortices on right periphery of the beam as compared to the case presented in [23].

Fig. 8
Fig. 8

Processing results of (a) the normalized fringe pattern in Fig. 7a, and (b) an interpolated version of the normalized interferogram in Fig. 7f (see Section 4 for details).

Equations (3)

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S 2 D ( s , b , θ ) = s η R 2 ψ * ( s 1 r θ ( x b ) ) f ( x ) d 2 x ,
ψ Morlet ( x ) = e i k 0 x e m | x | 2 ,
I ( x , y ) = 0.5 + cos ( 2 π x l + q · arctan ( y y 0 x x 0 ) + φ 0 ) / 2 ,

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