Abstract

We report on a new method of inspecting deep microstructures manufactured in transparent media. Although their lateral dimension (tens of microns) do not exceed the diffraction limit for optical microscopy resolution, their deepness makes the nondestructive measurements practically impossible with presently available methods. We show that the optical vortex interferometer with a vortex generator can be used to differentiate between the samples of good and poor quality. The measurement system is simple and the interpretation of the results is straightforward.

© 2008 Optical Society of America

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  1. M. S. Soskin and M. V. Vasnetsov, Singular Optics, Prog. Opt. (Elsevier Science, 2001). Vol. 42, pp. 219-276 (2001).
  2. M. Vasnetsov and K. Staliunas, eds., Optical Vortices, (Nova Science, New York, 1999).
  3. J. Masajada, "The interferometry based on the regular lattice of optical vortices," Opt. Appl. 37,167-185 (2007).
  4. J. Masajada, A Popio?ek-Masajada, and D Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207,85-93 (2002).
    [CrossRef]
  5. O. V. Angelsky, R. N. Besha, and I. I. Mokhun, "Appearance of wave front dislocations under interference among beams with simple wave fronts," Opt. Appl. 37,273-278 (1997).
  6. P. Kurzynowski, W. A. Wo?niak, and E. Fr?czek, "Optical vortices generation using Wollastone prism," Appl. Opt. 45, 7898-7903 (2006).
    [CrossRef]
  7. P. Kurzynowski and M. Borwi?ska, "Generation of vortex-type markers in a one-way setup," Appl. Opt. 46,676-679 (2007).
    [CrossRef]
  8. J. Masajada, A. Popio?ek-Masajada, and M. Leniec, "Creation of vortex lattice by a wavefront division," Opt. Express 15, 5196-5207 (2007), http://www.opticsexpress.org/abstract.cfm? URI=oe-15-8-5196
  9. S. Velghe and J. Primot, "Nondiffracting array generation using an N-wave interferometer," J. Opt. Soc. Am. A 16, 293-298 (1999).
    [CrossRef]
  10. S. Vyas and P. Senthilkumaran, "Interferometric optical vortex array generator," Appl. Opt. 46,2893-2898 (2007).
    [CrossRef]
  11. N. R. Heckenberg, R. G. Mcduff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17, 221-223 (1992).
  12. V. A Soifer and M. Golub, Laser beam mode selection by computer generated holograms, (CRC Press, London, 1999).
  13. D. Ganic, X. Gan, and M. Gu, "Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%," Opt. Lett. 27,1351-1353 (2002).
    [CrossRef]
  14. W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
    [CrossRef]
  15. W. Wang, T. Yokozeki, R. Ishjima, A Wada, Y. Miyamoto, M. Takeda, and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express, 14, 120-127 (2006), http://www.opticsexpress.org/abstract.cfm? URI=oe-14-1-120
  16. W. Wang, T. Yokozeki, R. Ishijima, S. G. Hanson, and M. Takeda, "Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern," Opt. Express 14, 10195-10206 (2006), http://www.opticsexpress.org/abstract.cfm? URI=oe-14-22-10195
  17. V. P. Tychinsky and C. H. F. Velzel, Super-resolution in Microscopy, in: Current trends in optics, (Academic Press, 1994), Chap. 18.
  18. M. Totzeck and H. J. Tiziani, "Phase-singularities in 2D diffraction fields and interference microscopy," Opt. Commun. 138,365-382 (1997).
    [CrossRef]
  19. B. Sektor, A. Normatov, and J. Shamir, "Experimetnal validation of 20nm sensitivity of Singular Beam Microscopy," Proc. SPIE 6616,661622 (2007).
  20. B. Sektor, A. Normatov, and J. Shamir, "Singular Beam Microscopy," Appl. Opt. 47, 78-87 (2008).
    [CrossRef]
  21. J. Masajada, Optical vortices and their application to interferometry, (Oficyna Wydawnicza Politechniki Wroc?awskiej, Wroc?aw 2004), monographs of Wroclaw University of Technology.
  22. W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Vol. 2, Physical Image Formation, (Wiley, New York 2005) Chap. 23
  23. J. T. Sheridan and C. J. R. Sheppard, "An examination of the theories for the calculation of diffraction by square wave gratings: 1. Thickness and period variations for normal incidence," Optik 85, 25-32 (1990).
  24. D. P. Biss, K. S. Youngworth, and T. G. Brown, "Dark-field imaging with cylindrical-vector beams," Appl. Opt. 45,470-479 (2006).
    [CrossRef]
  25. I. Freund andV. Freilikher, "Parametrization of anisotropic vortices," J. Opt. Soc. Am. A 14, 1902-1910 (1997).
    [CrossRef]
  26. W. Wang, M. R. Dennis, R. Ishijima, T. Yokozeki, A. Matsuda, S. G. Hanson, and M. Takeda, "Poincaré sphere representation for the anisotropy of phase singularities and its applications to optical vortex metrology for fluid mechanical analysis," Opt. Express 15, 11008-11019 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-17-11008
  27. A. Erdèlyi, ed., Tables of integral transforms, (McGraw-Hill, New York, 1953).

2008 (1)

B. Sektor, A. Normatov, and J. Shamir, "Singular Beam Microscopy," Appl. Opt. 47, 78-87 (2008).
[CrossRef]

2007 (4)

J. Masajada, "The interferometry based on the regular lattice of optical vortices," Opt. Appl. 37,167-185 (2007).

B. Sektor, A. Normatov, and J. Shamir, "Experimetnal validation of 20nm sensitivity of Singular Beam Microscopy," Proc. SPIE 6616,661622 (2007).

P. Kurzynowski and M. Borwi?ska, "Generation of vortex-type markers in a one-way setup," Appl. Opt. 46,676-679 (2007).
[CrossRef]

S. Vyas and P. Senthilkumaran, "Interferometric optical vortex array generator," Appl. Opt. 46,2893-2898 (2007).
[CrossRef]

2006 (2)

2005 (1)

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

2002 (2)

J. Masajada, A Popio?ek-Masajada, and D Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207,85-93 (2002).
[CrossRef]

D. Ganic, X. Gan, and M. Gu, "Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%," Opt. Lett. 27,1351-1353 (2002).
[CrossRef]

1999 (1)

1997 (3)

I. Freund andV. Freilikher, "Parametrization of anisotropic vortices," J. Opt. Soc. Am. A 14, 1902-1910 (1997).
[CrossRef]

O. V. Angelsky, R. N. Besha, and I. I. Mokhun, "Appearance of wave front dislocations under interference among beams with simple wave fronts," Opt. Appl. 37,273-278 (1997).

M. Totzeck and H. J. Tiziani, "Phase-singularities in 2D diffraction fields and interference microscopy," Opt. Commun. 138,365-382 (1997).
[CrossRef]

1992 (1)

1990 (1)

J. T. Sheridan and C. J. R. Sheppard, "An examination of the theories for the calculation of diffraction by square wave gratings: 1. Thickness and period variations for normal incidence," Optik 85, 25-32 (1990).

Angelsky, O. V.

O. V. Angelsky, R. N. Besha, and I. I. Mokhun, "Appearance of wave front dislocations under interference among beams with simple wave fronts," Opt. Appl. 37,273-278 (1997).

Besha, R. N.

O. V. Angelsky, R. N. Besha, and I. I. Mokhun, "Appearance of wave front dislocations under interference among beams with simple wave fronts," Opt. Appl. 37,273-278 (1997).

Biss, D. P.

Borwinska, M.

Brown, T. G.

Fraczek, E.

Freilikher, V.

Freund, I.

Gan, X.

Ganic, D.

Gu, M.

Hanson, S.

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

Heckenberg, N. R.

Ishii, N

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

Kurzynowski, P.

Masajada, J.

J. Masajada, "The interferometry based on the regular lattice of optical vortices," Opt. Appl. 37,167-185 (2007).

J. Masajada, A Popio?ek-Masajada, and D Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207,85-93 (2002).
[CrossRef]

Mcduff, R. G.

Miyamoto, Y

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

Mokhun, I. I.

O. V. Angelsky, R. N. Besha, and I. I. Mokhun, "Appearance of wave front dislocations under interference among beams with simple wave fronts," Opt. Appl. 37,273-278 (1997).

Normatov, A.

B. Sektor, A. Normatov, and J. Shamir, "Singular Beam Microscopy," Appl. Opt. 47, 78-87 (2008).
[CrossRef]

B. Sektor, A. Normatov, and J. Shamir, "Experimetnal validation of 20nm sensitivity of Singular Beam Microscopy," Proc. SPIE 6616,661622 (2007).

Popiolek-Masajada, A

J. Masajada, A Popio?ek-Masajada, and D Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207,85-93 (2002).
[CrossRef]

Primot, J.

Sektor, B.

B. Sektor, A. Normatov, and J. Shamir, "Singular Beam Microscopy," Appl. Opt. 47, 78-87 (2008).
[CrossRef]

B. Sektor, A. Normatov, and J. Shamir, "Experimetnal validation of 20nm sensitivity of Singular Beam Microscopy," Proc. SPIE 6616,661622 (2007).

Senthilkumaran, P.

Shamir, J.

B. Sektor, A. Normatov, and J. Shamir, "Singular Beam Microscopy," Appl. Opt. 47, 78-87 (2008).
[CrossRef]

B. Sektor, A. Normatov, and J. Shamir, "Experimetnal validation of 20nm sensitivity of Singular Beam Microscopy," Proc. SPIE 6616,661622 (2007).

Sheppard, C. J. R.

J. T. Sheridan and C. J. R. Sheppard, "An examination of the theories for the calculation of diffraction by square wave gratings: 1. Thickness and period variations for normal incidence," Optik 85, 25-32 (1990).

Sheridan, J. T.

J. T. Sheridan and C. J. R. Sheppard, "An examination of the theories for the calculation of diffraction by square wave gratings: 1. Thickness and period variations for normal incidence," Optik 85, 25-32 (1990).

Smith, C. P.

Takeda, M.

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

Tiziani, H. J.

M. Totzeck and H. J. Tiziani, "Phase-singularities in 2D diffraction fields and interference microscopy," Opt. Commun. 138,365-382 (1997).
[CrossRef]

Totzeck, M.

M. Totzeck and H. J. Tiziani, "Phase-singularities in 2D diffraction fields and interference microscopy," Opt. Commun. 138,365-382 (1997).
[CrossRef]

Velghe, S.

Vyas, S.

Wang, W.

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

White, A. G.

Wieliczka, D

J. Masajada, A Popio?ek-Masajada, and D Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207,85-93 (2002).
[CrossRef]

Wozniak, W. A.

Youngworth, K. S.

Appl. Opt. (5)

J. Opt. Soc. Am. A (2)

Opt. Appl. (2)

O. V. Angelsky, R. N. Besha, and I. I. Mokhun, "Appearance of wave front dislocations under interference among beams with simple wave fronts," Opt. Appl. 37,273-278 (1997).

J. Masajada, "The interferometry based on the regular lattice of optical vortices," Opt. Appl. 37,167-185 (2007).

Opt. Commun. (3)

J. Masajada, A Popio?ek-Masajada, and D Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207,85-93 (2002).
[CrossRef]

W. Wang, N Ishii, S. Hanson, Y Miyamoto, and M. Takeda, "Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement," Opt. Commun. 248,59-68 (2005).
[CrossRef]

M. Totzeck and H. J. Tiziani, "Phase-singularities in 2D diffraction fields and interference microscopy," Opt. Commun. 138,365-382 (1997).
[CrossRef]

Opt. Lett. (2)

Optik (1)

J. T. Sheridan and C. J. R. Sheppard, "An examination of the theories for the calculation of diffraction by square wave gratings: 1. Thickness and period variations for normal incidence," Optik 85, 25-32 (1990).

Proc. SPIE (1)

B. Sektor, A. Normatov, and J. Shamir, "Experimetnal validation of 20nm sensitivity of Singular Beam Microscopy," Proc. SPIE 6616,661622 (2007).

Other (11)

J. Masajada, A. Popio?ek-Masajada, and M. Leniec, "Creation of vortex lattice by a wavefront division," Opt. Express 15, 5196-5207 (2007), http://www.opticsexpress.org/abstract.cfm? URI=oe-15-8-5196

V. A Soifer and M. Golub, Laser beam mode selection by computer generated holograms, (CRC Press, London, 1999).

W. Wang, M. R. Dennis, R. Ishijima, T. Yokozeki, A. Matsuda, S. G. Hanson, and M. Takeda, "Poincaré sphere representation for the anisotropy of phase singularities and its applications to optical vortex metrology for fluid mechanical analysis," Opt. Express 15, 11008-11019 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-17-11008

A. Erdèlyi, ed., Tables of integral transforms, (McGraw-Hill, New York, 1953).

J. Masajada, Optical vortices and their application to interferometry, (Oficyna Wydawnicza Politechniki Wroc?awskiej, Wroc?aw 2004), monographs of Wroclaw University of Technology.

W. Singer, M. Totzeck, and H. Gross, Handbook of Optical Systems, Vol. 2, Physical Image Formation, (Wiley, New York 2005) Chap. 23

W. Wang, T. Yokozeki, R. Ishjima, A Wada, Y. Miyamoto, M. Takeda, and S. Hanson, "Optical vortex metrology for nanometric speckle displacement measurement," Opt. Express, 14, 120-127 (2006), http://www.opticsexpress.org/abstract.cfm? URI=oe-14-1-120

W. Wang, T. Yokozeki, R. Ishijima, S. G. Hanson, and M. Takeda, "Optical vortex metrology based on the core structures of phase singularities in Laguerre-Gauss transform of a speckle pattern," Opt. Express 14, 10195-10206 (2006), http://www.opticsexpress.org/abstract.cfm? URI=oe-14-22-10195

V. P. Tychinsky and C. H. F. Velzel, Super-resolution in Microscopy, in: Current trends in optics, (Academic Press, 1994), Chap. 18.

M. S. Soskin and M. V. Vasnetsov, Singular Optics, Prog. Opt. (Elsevier Science, 2001). Vol. 42, pp. 219-276 (2001).

M. Vasnetsov and K. Staliunas, eds., Optical Vortices, (Nova Science, New York, 1999).

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