Abstract

We implement experimentally a simple method for accurate measurements of phase distributions of scalar light fields. The method is based on the polarimetric technique for recording the polarization maps of vector fields, where coaxial superposition of orthogonally polarized reference and signal beams allows the signal phase to be reconstructed from the polarization map of the total field. We demonstrate this method by resolving topologically neutral pairs of closely positioned vortices in a speckle field and recovering the positions of vortices within a Laguerre–Gaussian beam with the topological charge three.

© 2008 Optical Society of America

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References

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  1. J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, 1999).
  2. I. V. Basisty, B. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
    [CrossRef]
  3. I. Freund, Opt. Lett. 26, 1996 (2001).
    [CrossRef]
  4. V. G. Denisenko, V. V. Slyusar, M. S. Soskin, and I. Freund, Asian J. Phys. 15, 199 (2006).
  5. M. S. Soskin, M. V. Vasnetsov, and I. V. Basisty, Proc. SPIE 2647, 57 (1995).
    [CrossRef]
  6. Z. S. Sacks, D. Rozas, and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 15, 2226 (1998).
    [CrossRef]
  7. M. Born and E. W. Wolf, Principles of Optics (Pergamon, 1968).
  8. V. G. Denisenko, G. A. Galich, V. V. Slyusar, and M. S. Soskin, Ukr. J. Phys. 48, 594 (2003).
  9. M. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
    [CrossRef] [PubMed]
  10. M. Soskin, V. Denisenko, and R. Egorov, J. Opt. A, Pure Appl. Opt. 6, S281 (2004).
    [CrossRef]
  11. V. G. Denisenko, R. Egorov, and M. S. Soskin, Proc. SPIE 5477, 41 (2004).
    [CrossRef]
  12. G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
    [CrossRef]
  13. M.Vasnetsov and K.Stliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999).
  14. V. G. Denisenko, M. V. Vasnetsov, and M. S. Soskin, Proc. SPIE 4403, 82 (2001).
    [CrossRef]
  15. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
    [CrossRef]
  16. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
    [CrossRef]
  17. M. V. Berry, in Physics of Defects, Les Houches Session XXXV, R.Balian, M.Klman, and J.-P.Poirier, eds. (North-Holland, 1980), pp. 453-543.
  18. K. Creath, in Holographic Interferometry, P.K.Rastogi, ed., Vol. 68 of Springer Series in Optical Science (Springer-Verlag, 1994), p. 109.

2006 (1)

V. G. Denisenko, V. V. Slyusar, M. S. Soskin, and I. Freund, Asian J. Phys. 15, 199 (2006).

2004 (2)

M. Soskin, V. Denisenko, and R. Egorov, J. Opt. A, Pure Appl. Opt. 6, S281 (2004).
[CrossRef]

V. G. Denisenko, R. Egorov, and M. S. Soskin, Proc. SPIE 5477, 41 (2004).
[CrossRef]

2003 (2)

V. G. Denisenko, G. A. Galich, V. V. Slyusar, and M. S. Soskin, Ukr. J. Phys. 48, 594 (2003).

M. Soskin, V. Denisenko, and I. Freund, Opt. Lett. 28, 1475 (2003).
[CrossRef] [PubMed]

2001 (2)

I. Freund, Opt. Lett. 26, 1996 (2001).
[CrossRef]

V. G. Denisenko, M. V. Vasnetsov, and M. S. Soskin, Proc. SPIE 4403, 82 (2001).
[CrossRef]

1998 (1)

1995 (1)

M. S. Soskin, M. V. Vasnetsov, and I. V. Basisty, Proc. SPIE 2647, 57 (1995).
[CrossRef]

1993 (2)

I. V. Basisty, B. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

1992 (1)

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

Asian J. Phys. (1)

V. G. Denisenko, V. V. Slyusar, M. S. Soskin, and I. Freund, Asian J. Phys. 15, 199 (2006).

J. Mod. Opt. (2)

G. Indebetouw, J. Mod. Opt. 40, 73 (1993).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Soskin, V. Denisenko, and R. Egorov, J. Opt. A, Pure Appl. Opt. 6, S281 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

I. V. Basisty, B. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (3)

M. S. Soskin, M. V. Vasnetsov, and I. V. Basisty, Proc. SPIE 2647, 57 (1995).
[CrossRef]

V. G. Denisenko, R. Egorov, and M. S. Soskin, Proc. SPIE 5477, 41 (2004).
[CrossRef]

V. G. Denisenko, M. V. Vasnetsov, and M. S. Soskin, Proc. SPIE 4403, 82 (2001).
[CrossRef]

Ukr. J. Phys. (1)

V. G. Denisenko, G. A. Galich, V. V. Slyusar, and M. S. Soskin, Ukr. J. Phys. 48, 594 (2003).

Other (6)

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics, 1999).

M. Born and E. W. Wolf, Principles of Optics (Pergamon, 1968).

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
[CrossRef]

M. V. Berry, in Physics of Defects, Les Houches Session XXXV, R.Balian, M.Klman, and J.-P.Poirier, eds. (North-Holland, 1980), pp. 453-543.

K. Creath, in Holographic Interferometry, P.K.Rastogi, ed., Vol. 68 of Springer Series in Optical Science (Springer-Verlag, 1994), p. 109.

M.Vasnetsov and K.Stliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup: 1, beam splitters; 2, mirrors; 3, collimator with the diaphragm; 4, polarizers; 5, sample; 6, collimating lens; 7, CCD camera.

Fig. 2
Fig. 2

(a) Intensity, (b) interference pattern, and (c), (d) phase of a speckle field. Circles indicate the positions of vortices, and lines in (d) illustrate deformations of phase contours around the dislocations. The phase surface in (c) and (d) is gray coded from π (black) to π (white).

Fig. 3
Fig. 3

(a) Interference pattern and (b) phase of a vortex beam with topological charge three; circles mark the positions of three single-charge vortices.

Equations (6)

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

E x = A x cos ( Φ 1 + ω t ) ,
E y = A y cos ( Φ 2 + ω t ) .
S 0 = A x 2 + A y 2 , S 1 = A x 2 A y 2 ,
S 2 = 2 A x A y cos δ , S 3 = 2 A x A y sin δ ,
S 2 = I ( 45 , 45 ) I ( 135 , 135 ) ,
S 3 = I ( 45 , 0 ) I ( 135 , 0 ) ,

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