Abstract

We present a method for reducing intensity fluctuations that typically occur when a spatial light modulator is updated between consecutive computer generated holograms. The method is applicable to most iterative hologram generating algorithms and minimizes the average phase difference between consecutive holograms. Applications with high stability requirements, such as optical force measurement with holographic optical tweezers, should benefit from this improvement.

© 2010 OSA

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References

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  1. A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008).
    [CrossRef] [PubMed]
  2. C. O. Mejean, A. W. Schaefer, E. A. Millman, P. Forscher, and E. R. Dufresne, “Multiplexed force measurements on live cells with holographic optical tweezers,” Opt. Express 17(8), 6209–6217 (2009).
    [CrossRef] [PubMed]
  3. A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
    [CrossRef]
  4. D. Preece, R. Bowman, A. Linnenberger, G. Gibson, S. Serati, and M. Padgett, “Increasing trap stiffness with position clamping in holographic optical tweezers,” Opt. Express 17(25), 22718–22725 (2009).
    [CrossRef]
  5. M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers,” Appl. Opt. 45(5), 888–896 (2006).
    [CrossRef] [PubMed]
  6. M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24(9), 608–610 (1999).
    [CrossRef]
  7. E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
    [CrossRef]
  8. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [CrossRef] [PubMed]
  9. L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of piconewton forces using a simple optical force microscope,” Biophys. J. 66, A278 (1994).
  10. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000).
    [CrossRef]
  11. T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
    [CrossRef]
  12. D. Engström, A. Frank, J. Backsten, M. Goksör, and J. Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express 17(12), 9989–10000 (2009).
    [CrossRef] [PubMed]
  13. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
    [CrossRef]
  14. M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Proc. SPIE(1991), pp. 34–42.
  15. R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
    [CrossRef] [PubMed]
  16. E. Eriksson, S. Keen, J. Leach, M. Goksör, and M. J. Padgett, “The effect of external forces on discrete motion within holographic optical tweezers,” Opt. Express 15(26), 18268–18274 (2007).
    [CrossRef] [PubMed]
  17. E. Marom and N. Konforti, “Dynamic optical interconnections,” Opt. Lett. 12(7), 539–541 (1987).
    [CrossRef] [PubMed]
  18. M. Johansson, S. Hård, B. Robertson, I. Manolis, T. Wilkinson, and W. Crossland, “Adaptive beam steering implemented in a ferroelectric liquid-crystal spatial-light-modulator free-space, fiber-optic switch,” Appl. Opt. 41(23), 4904–4911 (2002).
    [CrossRef] [PubMed]
  19. E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
    [CrossRef]
  20. R. W. Gerchber and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).
  21. F. Wyrowski and O. Bryngdahl, “Iterative fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5(7), 1058–1065 (1988).
    [CrossRef]
  22. D. Engström, G. Milewski, J. Bengtsson, and S. Galt, “Diffraction-based determination of the phase modulation for general spatial light modulators,” Appl. Opt. 45(28), 7195–7204 (2006).
    [CrossRef] [PubMed]
  23. E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
    [CrossRef]
  24. J. L. Harriman, A. Linnenberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proceedings of the SPIE - The International Society for Optical Engineering 5553, 58–67 (2004).
  25. X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43(35), 6400–6406 (2004).
    [CrossRef] [PubMed]
  26. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46(23), 5667–5679 (2007).
    [CrossRef] [PubMed]
  27. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15(9), 5801–5808 (2007).
    [CrossRef] [PubMed]
  28. J. E. Curtis, C. H. J. Schmitz, and J. P. Spatz, “Symmetry dependence of holograms for optical trapping,” Opt. Lett. 30(16), 2086–2088 (2005).
    [CrossRef] [PubMed]

2010 (1)

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

2009 (3)

2008 (1)

2007 (4)

2006 (2)

2005 (2)

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

J. E. Curtis, C. H. J. Schmitz, and J. P. Spatz, “Symmetry dependence of holograms for optical trapping,” Opt. Lett. 30(16), 2086–2088 (2005).
[CrossRef] [PubMed]

2004 (2)

X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43(35), 6400–6406 (2004).
[CrossRef] [PubMed]

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

2000 (1)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000).
[CrossRef]

1999 (1)

1997 (1)

T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[CrossRef]

1994 (1)

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of piconewton forces using a simple optical force microscope,” Biophys. J. 66, A278 (1994).

1988 (1)

1987 (1)

1972 (1)

R. W. Gerchber and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Ågren, D.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Allard, L.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Ambs, P.

Backsten, J.

Bengtsson, J.

Bernet, S.

Blab, G. A.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

Bowman, R.

Bryngdahl, O.

Cohn, R. W.

Crossland, W.

Curtis, J. E.

J. E. Curtis, C. H. J. Schmitz, and J. P. Spatz, “Symmetry dependence of holograms for optical trapping,” Opt. Lett. 30(16), 2086–2088 (2005).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

Di Leonardo, R.

Downing, B. P. B.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

Dufresne, E. R.

C. O. Mejean, A. W. Schaefer, E. A. Millman, P. Forscher, and E. R. Dufresne, “Multiplexed force measurements on live cells with holographic optical tweezers,” Opt. Express 17(8), 6209–6217 (2009).
[CrossRef] [PubMed]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

Engström, D.

Eriksson, E.

Farré, A.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

Forde, N. R.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008).
[CrossRef] [PubMed]

Forscher, P.

Frank, A.

Fürhapter, S.

Galt, S.

Gerchber, R. W.

R. W. Gerchber and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Ghislain, L. P.

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of piconewton forces using a simple optical force microscope,” Biophys. J. 66, A278 (1994).

Gibson, G.

Goksör, M.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

Haist, T.

M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers,” Appl. Opt. 45(5), 888–896 (2006).
[CrossRef] [PubMed]

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24(9), 608–610 (1999).
[CrossRef]

T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[CrossRef]

Hällstig, E.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Hård, S.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

M. Johansson, S. Hård, B. Robertson, I. Manolis, T. Wilkinson, and W. Crossland, “Adaptive beam steering implemented in a ferroelectric liquid-crystal spatial-light-modulator free-space, fiber-optic switch,” Appl. Opt. 41(23), 4904–4911 (2002).
[CrossRef] [PubMed]

Ianni, F.

Jesacher, A.

Johansson, M.

Junique, S.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Keen, S.

Kohler, C.

Konforti, N.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Leach, J.

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000).
[CrossRef]

Lindgren, M.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Linnenberger, A.

Manolis, I.

Marom, E.

Martin, T.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Maurer, C.

Mejean, C. O.

Milewski, G.

Millán, M. S.

Millman, E. A.

Noharet, B.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Öhgren, J.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Osten, W.

Otón, J.

Padgett, M.

Padgett, M. J.

Pérez-Cabré, E.

Preece, D.

Reicherter, M.

Ritsch-Marte, M.

Robertson, B.

Ruocco, G.

Saxton, W. O.

R. W. Gerchber and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Schaefer, A. W.

Schmitz, C. H. J.

Schonleber, M.

T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[CrossRef]

Schwaighofer, A.

Serati, S.

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

Sjöqvist, L.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

Spatz, J. P.

Stigwall, J.

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

Switz, N. A.

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of piconewton forces using a simple optical force microscope,” Biophys. J. 66, A278 (1994).

Tiziani, H.

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, “Optical particle trapping with computer-generated holograms written on a liquid-crystal display,” Opt. Lett. 24(9), 608–610 (1999).
[CrossRef]

T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[CrossRef]

van der Horst, A.

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16(25), 20987–21003 (2008).
[CrossRef] [PubMed]

Wagemann, E. U.

Wang, Q.

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Webb, W. W.

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of piconewton forces using a simple optical force microscope,” Biophys. J. 66, A278 (1994).

Wilkinson, T.

Wyrowski, F.

Xun, X.

Zwick, S.

Appl. Opt. (5)

Biophys. J. (1)

L. P. Ghislain, N. A. Switz, and W. W. Webb, “Measurement of piconewton forces using a simple optical force microscope,” Biophys. J. 66, A278 (1994).

J. Biophoton. (1)

A. Farré, A. van der Horst, G. A. Blab, B. P. B. Downing, and N. R. Forde, “Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers,” J. Biophoton. 3(4), 224–233 (2010), doi:.
[CrossRef]

J. Mod. Opt. (1)

E. Hällstig, J. Stigwall, T. Martin, L. Sjöqvist, and M. Lindgren, “Fringing fields in a liquid crystal spatial light modulator for beam steering,” J. Mod. Opt. 51(8), 1233–1247 (2004).
[CrossRef]

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

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Opt. Commun. (3)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, “Multi-functional optical tweezers using computer-generated holograms,” Opt. Commun. 185(1-3), 77–82 (2000).
[CrossRef]

T. Haist, M. Schonleber, and H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140(4-6), 299–308 (1997).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1-6), 169–175 (2002).
[CrossRef]

Opt. Eng. (1)

E. Hällstig, J. Öhgren, L. Allard, L. Sjöqvist, D. Engström, S. Hård, D. Ågren, S. Junique, Q. Wang, and B. Noharet, “Retrocommunication utilizing electroabsorption modulators and nonmechanical beam steering,” Opt. Eng. 44(4), 045001 (2005).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Optik (Stuttg.) (1)

R. W. Gerchber and W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Rev. Sci. Instrum. (1)

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72(3), 1810–1816 (2001).
[CrossRef]

Other (2)

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” in Proc. SPIE(1991), pp. 34–42.

J. L. Harriman, A. Linnenberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proceedings of the SPIE - The International Society for Optical Engineering 5553, 58–67 (2004).

Supplementary Material (3)

» Media 1: AVI (1545 KB)     
» Media 2: AVI (1498 KB)     
» Media 3: AVI (1487 KB)     

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Figures (10)

Fig. 1
Fig. 1

Measured far field intensity during update of the SLM (Hamamatsu) with a sequence of ten CGHs (Media 1). Spots were positioned on a 5x5 grid centered on the optical axis. In every second CGH one spot, marked with a circle, at varying positions were removed from the grid and then replaced in the following CGH. Snapshots of the far field are extracted at (a) t = 3.0 s (stable CGH #3), (b) t = 3.26 s (worst case for this specific SLM update), and (c) t = 4.0 s (stable CGH #4), respectively. (d) Examples of normalized spot power as function of time for the specific SLM update shown in (a)–(c).

Fig. 2
Fig. 2

General flowchart of a GS algorithm utilizing amplitude weighting in the spot positions and a random phase distribution as initial guess for ϕ ( x , y ) .

Fig. 3
Fig. 3

General flowchart of a GS–RPC algorithm utilizing amplitude weighting in the spot positions and reusing the previous CGH as initial guess for ϕ ( x , y ) . The operation at position (e) is added in order to limit the maximum phase difference for each pixel in the new CGH compared to the previous one.

Fig. 4
Fig. 4

Schematic of the free space setup described in section 3.1. Lenses L1 and L2 expand the laser beam to match the used area of the SLM (BNS). The far field intensity distribution is imaged onto the CMOS camera using L3. Inset shows a typical CGH used in the experiments.

Fig. 6
Fig. 6

Spot intensities during SLM (BNS) update of the free space setup described in Section 3.1. The first and second CGHs each forms 9 spots located among 10 equally separated positions on a circle with radius of 70 spot sizes centered around the optical axis; the position of the missing spot being different for the two CGHs. (a) Simulated and (d) measured spot intensities using GS-Rand. (b) Simulated and (e) measured spot intensities using GS-CGH1. (c) Simulated and (f) measured spot intensities using GS-RPC.

Fig. 5
Fig. 5

Schematic of the HOT setup described in Sections 3.2 and 3.3. Lenses L1 and L2 expand the laser beam to match the width of the SLM (Hamamatsu). The SLM plane is then imaged to the back focal plane of the microscope objective using lenses L3 and L4. The trapping plane coincides with the imaging plane of the microscope. Brightfield images of the trapped bead are captured by a CMOS camera (Prosilica). To allow for the free space experiments described in Section 3.3, a mirror and a second CMOS camera (Photonfocus) was inserted in the optical path as indicated by the dashed box. Inset shows a typical CGH used in the experiments.

Fig. 7
Fig. 7

Measured position for a trapped bead exposed to drag force induced by moving the microscope stage at a speed of (a)–(c) 20 µm/s and (d)–(e) 150 µm/s. The dotted lines represent approximate times for the SLM (Hamamatsu) updates. The CGHs were optimized using (a) GS–Rand, (b),(d) GS–CGH1, and (c),(e) GS–RPC.

Fig. 8
Fig. 8

Measured far field intensity during update of the SLM (Hamamatsu) with a sequence of ten CGHs optimized using GS-CGH1 (Media 2, (a)-(d) shows data from one update) and GS-RPC (Media 3, (e)-(h) shows data from one update), respectively. Spots were positioned on a 5x5 grid centered on the optical axis. In every second CGH one spot at varying positions, marked with a circle, was removed from the grid and then replaced in the following CGH. Snapshots of the far field are extracted at (a),(e) t = 3.0 s (stable CGH #3), (b),(f) t = 3.26 s (worst case for this specific SLM update), and (c),(g) t = 4.0 s (stable CGH #4), respectively. Normalized spot power for a selection of spots during the specific SLM update shown in (a)–(c) and (e)–(g) are shown in (d) and (h), respectively. Note that the results obtained when using CGHs optimized with GS-Rand is given in Fig. 1.

Fig. 9
Fig. 9

Simulated diffraction efficiency after SLM update (black), maximum intensity loss (red) and maximum intensity increase (blue) of stationary spots during update as functions of the restriction parameter (α). In (a)–(c), 4 spots were randomly positioned and one spot moved 1000 steps in random directions. In (d)–(f), 4 spots were positioned on a square grid centered on the optical axis and the lower left spot was moved 100 spot sizes to the left. In (g)–(i), 25 spots were positioned on a square grid centered on the optical axis and the lower left spot was moved 100 spot sizes to the left. The step size was 1 spot size in (a), (d) and (g), 0.5 spot sizes in (b), (e) and (h) and 0.25 spot sizes in (c), (f) and (i). The simulation sequence was repeated 100 times. Each plotted data point is the average along with the standard deviation of all steps and all simulation sequences.

Fig. 10
Fig. 10

Total computation time for generation of 512 × 512 pixels holograms in 10 iterations using a Fresnel propagation based version of the Gerchberg—Saxton algorithm implemented in CUDA with and without RPC.

Equations (3)

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u = 1 I max I min I max + I min ,
ϕ n ( x , y ) = { ϕ n ( x , y ) i f | ϕ n ( x , y ) ϕ 0 ( x , y ) | 2 π α ϕ 0 ( x , y ) e l s e α [ 0 , 1 ] ,
ϕ ( x , y , t ) = ϕ C G H 1 ( x , y ) + t T ( ϕ C G H 2 ( x , y ) ϕ C G H 1 ( x , y ) ) , 0 t T .

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