Abstract

We report a new optical vortex phase-shifting method for digital holography, in which an optical vortex mode is taken as the reference beam for holographic recording, and the required phase shifts are directly generated by rotating the vortex mode. In digital reconstruction, the complex amplitude of the object wave can be retrieved by use of the conventional phase shifting algorithm on condition that the digital illumination beam is replaced by an vortex beam with the same topological charge as the reference used. Both the theoretical analysis and experimental results demonstrate the feasibility of this approach.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. U. Schnars and W. Juptner, �??Direct recording of holograms by a CCD target and numerical reconstruction,�?? Appl. Opt. 33, 179-181 (1994)
    [CrossRef] [PubMed]
  2. J. Pomarico, U. Schnars, H.-J. Hartmann and W. Juptner, �??Digital recording and numerical reconstruction of holograms: a new method for displaying light in flight,�?? Appl. Opt. 34, 8095-8099 (1995).
    [CrossRef] [PubMed]
  3. C. Wagner, W. Osten, S. Seebacher, �??Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,�?? Opt. Eng. 39, 79-85 (2000).
    [CrossRef]
  4. M. K. Kim, �??Tomographic three-dimensional imaging of a biological specimen using wavelength scanning digital interference holography,�?? Opt. Express 7, 305-310 (2000). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-9-305">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-9-305</a>
    [CrossRef] [PubMed]
  5. S. Grilli, P. Ferraro, M. Paturzo, D. Alfieri, P. D. Natale, M. D. Angelis, S. D. Nicola, A. Finizio and G. Pierattini, �??In-situ visualization, monitoring and analysis of electric field domain reversal process in ferroelectric crystals by digital holography,�?? Opt. Express 12, 1832-1842 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1832">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1832</a>
    [CrossRef] [PubMed]
  6. I. Yamaguchi and T. Zhang, �??Phase-shifting digital holography,�?? Opt. Lett. 22, 1268-1270 (1997). S. Lai, Brian King and M. A. Neifeld, �??Wave front reconstruction by means of phase-shifting digital in-line holography,�?? Opt. Commun. 173, 155-160 (2000).
    [CrossRef] [PubMed]
  7. T. Zhang and I. Yamaguchi, �??Three-dimensional microscopy with phase-shifting digital holography,�?? Opt. Lett. 23, 1221-1223 (1998).
    [CrossRef]
  8. S. Lai, Brian King and M. A. Neifeld, �??Wave front reconstruction by means of phase-shifting digital inline holography,�?? Opt. Commun. 173, 155-160 (2000).
    [CrossRef]
  9. I. Yamaguchi, J. Kato, S. Ohta and J. Mizuno, �??Image Formation in Phase-Shifting Digital Holography and Applications to Microscopy,�?? Appl. Opt. 40, 6177-6186 (2001).
    [CrossRef]
  10. L. Z. Cai, Q. Liu and X. L. Yang, �??Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects,�?? Opt. Lett. 29, 182-185(2004).
    [CrossRef]
  11. L. Z. Cai, Q. Liu, Y. R. Wang, and X. L. Yang, �??Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase errors,�?? Opt. Commun. 233, 21-26 (2004).
    [CrossRef]
  12. Y. Y. Cheng and James C. Wyant, �??Phase shifter calibration in phase-shifting interferometry,�?? Appl.Opt. 24, 3049-3052 (1985).
    [CrossRef] [PubMed]
  13. C. S. Guo, L. Zhang, H. T. Wang, J. Liao and Y.Y. Zhu, �??Phase-Shifting Error and Its Elimination in Phase- Shifting Digital Holography,�?? Opt. Lett. 27, 1-3 (2002).
    [CrossRef]
  14. C. C. Jin, N. K. Bao and P. S. Chung, �??Application of a novel phase-shift method using a computer-controlled polarization mechanism,�?? Opt. Eng. 33, 2733-2737 (1994).
    [CrossRef]
  15. M. B. North-Morris, J. VanDelden, and J. C. Wyant, �??Phaseshifting birefringent scatterplate interferometer,�?? Appl. Opt. 41, 668�??677 (2002).
    [CrossRef] [PubMed]
  16. C. S. Guo, Z. Y. Rong, H. T. Wang, Y. R. Wang and L.Z.Cai; �??Phase-Shifting with Computer-Generated Holograms Written on a Spatial Light Modulator,�?? Appl. Opt. 42, 6975-6979 (2003).
    [CrossRef] [PubMed]
  17. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen and J. P. Woerdman, �??Helical-wavefront laser beam produced with a spiral phase plate,�?? Opt. Commun. 112, 321-327 (1994).
    [CrossRef]
  18. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, �??Generation of optical-phase singularities by computer-generated holograms,�?? Opt. Lett. 17, 221-223(1992).
    [CrossRef] [PubMed]
  19. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, �??The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,�?? J. Modern Opt. 45, 1231-1237 (1998).
    [CrossRef]
  20. J. C. Wyant and V. P. Bennett, �??Using Computer Generated Holograms to Test Aspheric Wavefronts,�?? Appl. Opt. 9, 2833-2839(1972).
    [CrossRef]
  21. J. C. Wyant and P. K. O�??Neill, �??Computer Generated Hologram: Null Lens Test of Aspheric Wavefronts,�?? Appl. Opt. 13, 2762-2765(1974).
    [CrossRef] [PubMed]
  22. K. A. Goldberg and J. Bokor, �??Fourier-transform method of phase-shift determination,�?? Appl. Opt. 40, 2886�??2894 (2001).
    [CrossRef]
  23. C. S. Guo, Z. Y. Rong, J. L. He, L. Z. Cai and Y. R. Wang, �??Determination of global phase shifts between interferograms by use of an energy-minimum algorithm,�?? Appl. Opt. 42, 6514-6519(2003).
    [CrossRef] [PubMed]
  24. L. Allen, M. P. Padgett, and M. Babiker, �??The orbital angular momentum of light,�?? Progress in Optics 39, 291-372 (1999).
    [CrossRef]
  25. J. K. Yang, Z. H. Musslimani, �??Fundamental and vortex solitons in a two-dimensional optical lattice,�?? Opt. Lett. 28, 2094-2096 (2003).
    [CrossRef] [PubMed]
  26. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, �??Anisotropic Enhancement of Discrete Diffraction and Formation of Two-Dimensional Discrete-Soliton Trains,�?? Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef] [PubMed]
  27. K. Ladavac and D. G. Grier, �??Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,�?? Opt. Express 12, 1144-1149 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1144">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1144</a>
    [CrossRef] [PubMed]

Appl. Opt. (9)

U. Schnars and W. Juptner, �??Direct recording of holograms by a CCD target and numerical reconstruction,�?? Appl. Opt. 33, 179-181 (1994)
[CrossRef] [PubMed]

J. Pomarico, U. Schnars, H.-J. Hartmann and W. Juptner, �??Digital recording and numerical reconstruction of holograms: a new method for displaying light in flight,�?? Appl. Opt. 34, 8095-8099 (1995).
[CrossRef] [PubMed]

I. Yamaguchi, J. Kato, S. Ohta and J. Mizuno, �??Image Formation in Phase-Shifting Digital Holography and Applications to Microscopy,�?? Appl. Opt. 40, 6177-6186 (2001).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, �??Phaseshifting birefringent scatterplate interferometer,�?? Appl. Opt. 41, 668�??677 (2002).
[CrossRef] [PubMed]

C. S. Guo, Z. Y. Rong, H. T. Wang, Y. R. Wang and L.Z.Cai; �??Phase-Shifting with Computer-Generated Holograms Written on a Spatial Light Modulator,�?? Appl. Opt. 42, 6975-6979 (2003).
[CrossRef] [PubMed]

J. C. Wyant and V. P. Bennett, �??Using Computer Generated Holograms to Test Aspheric Wavefronts,�?? Appl. Opt. 9, 2833-2839(1972).
[CrossRef]

J. C. Wyant and P. K. O�??Neill, �??Computer Generated Hologram: Null Lens Test of Aspheric Wavefronts,�?? Appl. Opt. 13, 2762-2765(1974).
[CrossRef] [PubMed]

K. A. Goldberg and J. Bokor, �??Fourier-transform method of phase-shift determination,�?? Appl. Opt. 40, 2886�??2894 (2001).
[CrossRef]

C. S. Guo, Z. Y. Rong, J. L. He, L. Z. Cai and Y. R. Wang, �??Determination of global phase shifts between interferograms by use of an energy-minimum algorithm,�?? Appl. Opt. 42, 6514-6519(2003).
[CrossRef] [PubMed]

Appl.Opt. (1)

Y. Y. Cheng and James C. Wyant, �??Phase shifter calibration in phase-shifting interferometry,�?? Appl.Opt. 24, 3049-3052 (1985).
[CrossRef] [PubMed]

J. Modern Opt. (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, �??The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,�?? J. Modern Opt. 45, 1231-1237 (1998).
[CrossRef]

Opt. Commun. (3)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen and J. P. Woerdman, �??Helical-wavefront laser beam produced with a spiral phase plate,�?? Opt. Commun. 112, 321-327 (1994).
[CrossRef]

S. Lai, Brian King and M. A. Neifeld, �??Wave front reconstruction by means of phase-shifting digital inline holography,�?? Opt. Commun. 173, 155-160 (2000).
[CrossRef]

L. Z. Cai, Q. Liu, Y. R. Wang, and X. L. Yang, �??Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase errors,�?? Opt. Commun. 233, 21-26 (2004).
[CrossRef]

Opt. Eng. (2)

C. Wagner, W. Osten, S. Seebacher, �??Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,�?? Opt. Eng. 39, 79-85 (2000).
[CrossRef]

C. C. Jin, N. K. Bao and P. S. Chung, �??Application of a novel phase-shift method using a computer-controlled polarization mechanism,�?? Opt. Eng. 33, 2733-2737 (1994).
[CrossRef]

Opt. Express (3)

Opt. Lett. (6)

Phys. Rev. Lett. (1)

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, �??Anisotropic Enhancement of Discrete Diffraction and Formation of Two-Dimensional Discrete-Soliton Trains,�?? Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Prog. Opt. (1)

L. Allen, M. P. Padgett, and M. Babiker, �??The orbital angular momentum of light,�?? Progress in Optics 39, 291-372 (1999).
[CrossRef]

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 (5)

Fig. 1.
Fig. 1.

The experimental geometry for in-line phase-shifting digital holography with optical vortices as the reference beam.

Fig. 2.
Fig. 2.

Phase distributions of the optical vortices. (a)–(d) are four optical vortices with topological charge of l = 1; each rotates 90 degree with respect to the former, respectively. (e)–(h) are the respective interferograms with a plane wave.

Fig. 3.
Fig. 3.

Dependence of the phase shift on the rotation angle of optical vortex with l = 1.

Fig. 4.
Fig. 4.

(a) Photo of the object recorded; (b) one of four phase-shifting digital holograms recorded by the CCD camera; (c) the image reconstructed directly by the hologram shown in Fig. 4(b); (d) the final reconstructed image after performing four-step phase-shifting algorithm.

Fig. 5.
Fig. 5.

(a)–(d) are the reconstructed images of the holograms involved in Fig. 4 when the location errors are set on purpose to 8 pixels, 12 pixels, 16 pixels and 32 pixels, respectively.

Equations (3)

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

U R = A ( r ) exp [ il ( ϕ + θ ) ] = A ( r ) exp ( ilϕ ) exp ( ilθ )
U h x y = exp ( ) 4 A R ( r ) { I 1 x y 0 I 3 x y π + i [ I 2 x y π 2 I 4 x y 3 π 2 ] }
U o ( x , y , z o ) = exp [ π λ z o ( x 2 + y 2 ) ] U h x y .

Metrics