Abstract

We discuss two types of optical processing using vortex-producing angular phase plates. In the most common spatial-filtering operation, an input object is Fourier transformed (either by Fraunhofer diffraction or with a lens system). The Fourier transform is then multiplied by an angular phase pattern, and the product is again Fourier transformed. The output is a space-invariant, edge-enhanced version of the input object. Alternatively we can directly image the object using a lens multiplied by the angular phase. The space-variant image is severely distorted along the optical axis of the system. We encode the phase plates onto a liquid-crystal display and present experimental results on both systems.

© 2004 Optical Society of America

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    [CrossRef]
  2. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
    [CrossRef]
  3. P. Coullet, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
    [CrossRef]
  4. M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
    [CrossRef]
  5. V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).
  6. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef] [PubMed]
  7. Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
    [CrossRef]
  8. J. A. Davis, E. Carcole, D. M. Cottrell, “Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator,” Appl. Opt. 35, 593–598 (1996).
    [CrossRef] [PubMed]
  9. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankivic, T. Tschudi, “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]
  10. A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
    [CrossRef]
  11. G. Biener, A. Niv, V. Kleiner, E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27, 1875–1877 (2002).
    [CrossRef]
  12. M. Reicherter, T. Haist, E. U. Wageman, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
    [CrossRef]
  13. H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
    [CrossRef]
  14. K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  15. J. A. Davis, L. L. Haavig, D. M. Cottrell, “Bessel function output from an optical correlator,” Appl. Opt. 36, 2376–2379 (1997).
    [CrossRef] [PubMed]
  16. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Bessel function output from an optical correlator with a phase-only encoded inverse filter,” Appl. Opt. 38, 6709–6713 (1999).
    [CrossRef]
  17. J. A. Davis, D. E. McNamara, D. M. Cottrell, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25, 99–101 (2000).
    [CrossRef]
  18. G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
    [CrossRef]
  19. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
    [CrossRef]
  20. J. A. Davis, J. Adachi, D. M. Cottrell, “Diffraction efficiency of nonsynchronously sampled diffraction gratings,” Opt. Eng. 41, 2983–2986 (2002).
    [CrossRef]
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5.
  22. T. R. Walsh, J. E. Cravatt, B. A. Kast, M. K. Giles, “A time-sequenced rotation and scale-invariant optical correlator for multiple target recognition,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 203–219 (1990).
  23. W. T. Rhodes, “Simple procedure for the analysis of coherent imaging systems,” Opt. Lett. 19, 1559–1561 (1994).
    [CrossRef] [PubMed]
  24. D. Palacios, D. Rozas, G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).
    [CrossRef] [PubMed]
  25. J. A. Davis, E. Carcole, D. M. Cottrell, “Nondiffracting interference patterns generated with programmable spatial light modulators,” Appl. Opt. 35, 599–602 (1996).
    [CrossRef] [PubMed]

2002

2001

2000

1999

M. Reicherter, T. Haist, E. U. Wageman, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

M. Mansuripur, E. M. Wright, “Linear optical vortices,” Opt. Photon News 9, 40–43 (1999).
[CrossRef]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Bessel function output from an optical correlator with a phase-only encoded inverse filter,” Appl. Opt. 38, 6709–6713 (1999).
[CrossRef]

1997

1996

1995

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

1994

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

W. T. Rhodes, “Simple procedure for the analysis of coherent imaging systems,” Opt. Lett. 19, 1559–1561 (1994).
[CrossRef] [PubMed]

1993

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

1992

1990

V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).

1989

P. Coullet, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

1974

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

Adachi, J.

J. A. Davis, J. Adachi, D. M. Cottrell, “Diffraction efficiency of nonsynchronously sampled diffraction gratings,” Opt. Eng. 41, 2983–2986 (2002).
[CrossRef]

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Bazhenov,

V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).

Berry, M. V.

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

Biener, G.

Campos, J.

Carcole, E.

Cottrell, D. M.

Coullet, P.

P. Coullet, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Cravatt, J. E.

T. R. Walsh, J. E. Cravatt, B. A. Kast, M. K. Giles, “A time-sequenced rotation and scale-invariant optical correlator for multiple target recognition,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 203–219 (1990).

Davis, J. A.

Gahagan, K. T.

Gan, X.

Ganic, D.

Gil, L.

P. Coullet, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Giles, M. K.

T. R. Walsh, J. E. Cravatt, B. A. Kast, M. K. Giles, “A time-sequenced rotation and scale-invariant optical correlator for multiple target recognition,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 203–219 (1990).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5.

Gu, M.

Haavig, L. L.

Hain, M.

Haist, T.

Harris, M.

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Harvey, E.

Hasman, E.

Hayes, J. P.

He, H.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

Hill, C. A.

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Jaroszewicz, Z.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Kast, B. A.

T. R. Walsh, J. E. Cravatt, B. A. Kast, M. K. Giles, “A time-sequenced rotation and scale-invariant optical correlator for multiple target recognition,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 203–219 (1990).

Kleiner, V.

Kolodziejczyk, A.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

Lai, B.

Mancuso, A. P.

Mansuripur, M.

M. Mansuripur, E. M. Wright, “Linear optical vortices,” Opt. Photon News 9, 40–43 (1999).
[CrossRef]

McDuff, R.

McMahon, P. J.

McNamara, D. E.

McNulty, I.

Moreno, I.

Niv, A.

Nugent, K. A.

Nye, J. F.

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

Palacios, D.

D. Palacios, D. Rozas, G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef] [PubMed]

Paterson, D.

Peele, A. G.

Reicherter, M.

Rhodes, W. T.

Rocca, F.

P. Coullet, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

Rozas, D.

D. Palacios, D. Rozas, G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

Smith, C. P.

Somalingam, S.

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Soskin, M. S.

V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).

Stankivic, S.

Swartzlander, G. A.

Tiziani, H. J.

Tran, C. Q.

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

Tschudi, T.

Vaughan, J. M.

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Wageman, E. U.

Walsh, T. R.

T. R. Walsh, J. E. Cravatt, B. A. Kast, M. K. Giles, “A time-sequenced rotation and scale-invariant optical correlator for multiple target recognition,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 203–219 (1990).

White, A. G.

Wright, E. M.

M. Mansuripur, E. M. Wright, “Linear optical vortices,” Opt. Photon News 9, 40–43 (1999).
[CrossRef]

Yasnetsov, M. V.

V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).

Yu, V.

V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).

Yzuel, M. J.

Appl. Opt.

J. Mod. Opt.

H. He, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[CrossRef]

JETP Lett.

V. Yu, Bazhenov, M. V. Yasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 428–429 (1990).

Opt. Commun.

Z. Jaroszewicz, A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391–396 (1993).
[CrossRef]

P. Coullet, L. Gil, F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
[CrossRef]

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Opt. Eng.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38, 1051–1057 (1999).
[CrossRef]

J. A. Davis, J. Adachi, D. M. Cottrell, “Diffraction efficiency of nonsynchronously sampled diffraction gratings,” Opt. Eng. 41, 2983–2986 (2002).
[CrossRef]

Opt. Lett.

K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
[CrossRef] [PubMed]

J. A. Davis, D. E. McNamara, D. M. Cottrell, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25, 99–101 (2000).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

W. T. Rhodes, “Simple procedure for the analysis of coherent imaging systems,” Opt. Lett. 19, 1559–1561 (1994).
[CrossRef] [PubMed]

M. Reicherter, T. Haist, E. U. Wageman, H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24, 608–610 (1999).
[CrossRef]

G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
[CrossRef]

D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankivic, T. Tschudi, “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]

A. G. Peele, P. J. McMahon, D. Paterson, C. Q. Tran, A. P. Mancuso, K. A. Nugent, J. P. Hayes, E. Harvey, B. Lai, I. McNulty, “Observation of an x-ray vortex,” Opt. Lett. 27, 1752–1754 (2002).
[CrossRef]

G. Biener, A. Niv, V. Kleiner, E. Hasman, “Formation of helical beams by use of Pancharatnam-Berry phase optical elements,” Opt. Lett. 27, 1875–1877 (2002).
[CrossRef]

Opt. Photon News

M. Mansuripur, E. M. Wright, “Linear optical vortices,” Opt. Photon News 9, 40–43 (1999).
[CrossRef]

Phys. Rev. Lett.

D. Palacios, D. Rozas, G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A

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

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 5.

T. R. Walsh, J. E. Cravatt, B. A. Kast, M. K. Giles, “A time-sequenced rotation and scale-invariant optical correlator for multiple target recognition,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 203–219 (1990).

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