Abstract

Computer-generated holograms in conjunction with spatial light modulators (SLMs) offer a way to dynamically generate holograms that are adapted to specific tasks. To use the full dynamic capability of the SLM, the hologram computation should be very fast. We present a method that uses the highly parallel architecture of a consumer graphics board to compute analytical holograms in video real time. A precice characterization of the SLM (Holoeye LC-R-2500) and the adaption of its settings to our near-infrared application is necessary to guarantee an efficient hologram reconstruction. The benefits of a fast computation of adapted holograms and the application of an efficient SLM are demonstrated by measuring the trapping forces of holographic tweezers.

© 2006 Optical Society of America

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    [CrossRef]
  27. 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, 608-610 (1999).
    [CrossRef]
  28. J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 77-82 (2000).
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  29. K. Lavadac and D. G. Grier, "Microoptomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
    [CrossRef]
  30. L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
    [CrossRef]
  31. K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  33. E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2005

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

M. Polin, K. Lavadac, S.-H. Lee, Y. Roichman, and D. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

2004

2003

C. Petz and M. Magnor, "Fast hologram synthesis for 3D geometry models using graphics hardware," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 266-275 (2003).
[CrossRef]

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

2002

2001

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

2000

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

1999

T. Haist, E.-U. Wagemann, and H. J. Tiziani, "Pulsed-laser ablation using dynamic computer-generated holograms written into a liquid crystal display," J. Opt. A 1, 428-430 (1999).
[CrossRef]

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written in a liquid crystal display," Opt. Lett. 9, 508-510 (1999).

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, 608-610 (1999).
[CrossRef]

A. Ritter, J. Böttger, O. Deussen, M. König, and T. Strothotte, "Hardware-based rendering of full-parallax synthetic holograms," Appl. Opt. 38, 1364-1369 (1999).
[CrossRef]

1998

F. Gittes and C. F. Schmidt, "Interference model for back-focal-plane displacement detection in optical tweezers," Opt. Lett. 23, 7-9 (1998).
[CrossRef]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
[CrossRef]

1996

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

K. T. Gahagan and G. A. Schwartzlander, Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 821-823 (1996).
[CrossRef]

1995

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

E. G. Johnson and M. A. G. Abushagur, "Microgenetic algorithm optimization methods applied to dielectric gratings," J. Opt. Soc. Am. A 12, 1152-1160 (1995).
[CrossRef]

1994

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

1993

M. Lucente, "Interactive computation of holograms using a look-up table," J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

1992

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1991

C. C. Mao, K. M. Johnson, and G. Moddel, "Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators," Ferroelectrics 114, 45-53 (1991).
[CrossRef]

1987

Abushagur, M. A. G.

Allebach, J. P.

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Bannister, R. W.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Baumbach, T.

Block, S. M.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Böttger, J.

Bryngdahl, O.

O. Bryngdahl and F. Wyrowski, "Digital holography: computer-generated holograms," in Progress in Optics,E.Wolf, ed. (Elsevier 1990), Volak. 28, pp. 1-86.

Cameron, C. D.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Coomber, S. D.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Cresswell, I.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Cresswell, I. G.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Deussen, O.

DeVelis, J. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, 1989).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Eldeib, H.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Fernando, R.

R. Fernando and M. J. Kilgard, The Cg Tutorial (Addison-Wesley, 2003).

Florin, E.-L.

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
[CrossRef]

Gahagan, K. T.

Ghislain, L. P.

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Gittes, F.

Godo, H.

Goetz, G.

G. Goetz, "Real-time coherent light modulator," paper presented at the spring meeting of the Optical Society of America, Washington, D.C., May1970.

Grier, D.

Grier, D. G.

K. Lavadac and D. G. Grier, "Microoptomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optics," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Gross, H.

H. Gross, Handbook of Optical Systems Vol 1: Fundamentals of Technical Optics (Springer, 2005).

Hahn, S.

C. J. Thompson, S. Hahn, and M. Oskin, "Using modern graphics architectures for general-purpose computing: a framework and analysis," in Proceedings of the IEEE/ACM International Symposium on Microarchitecture MICRO-35 (Institute of Electrical and Electronics Engineers, 2002), pp. 306-317.

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 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, 608-610 (1999).
[CrossRef]

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written in a liquid crystal display," Opt. Lett. 9, 508-510 (1999).

T. Haist, E.-U. Wagemann, and H. J. Tiziani, "Pulsed-laser ablation using dynamic computer-generated holograms written into a liquid crystal display," J. Opt. A 1, 428-430 (1999).
[CrossRef]

Hallett, P. M.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

He, H.

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

Heckenberg, N. R.

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

Hörber, J. K. H.

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
[CrossRef]

Horiuchi, M.

Hughes, J. R.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Hui, V.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Ito, T.

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

T. Ito, T. Shimobaba, H. Godo, and M. Horiuchi, "Holographic reconstruction with a 10-µm pixel-pitch reflective liquid-crystal display by use of a light-emitting diode reference light," Opt. Lett. 27, 1406-1408 (2002).
[CrossRef]

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Jackson, P. O.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Johnson, E. G.

Johnson, K. M.

C. C. Mao, K. M. Johnson, and G. Moddel, "Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators," Ferroelectrics 114, 45-53 (1991).
[CrossRef]

Jones, J. C.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Jüptner, W.

Kilgard, M. J.

R. Fernando and M. J. Kilgard, The Cg Tutorial (Addison-Wesley, 2003).

König, M.

Kunugi, T.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Lavadac, K.

Lee, S.-H.

Liesener, J.

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

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written in a liquid crystal display," Opt. Lett. 9, 508-510 (1999).

Lucente, M.

M. Lucente, "Interactive computation of holograms using a look-up table," J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

Magnor, M.

C. Petz and M. Magnor, "Fast hologram synthesis for 3D geometry models using graphics hardware," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 266-275 (2003).
[CrossRef]

Mao, C. C.

C. C. Mao, K. M. Johnson, and G. Moddel, "Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators," Ferroelectrics 114, 45-53 (1991).
[CrossRef]

Masuda, N.

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

Milham, K. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Miller, R.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Miller, R. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Minter, V.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Moddel, G.

C. C. Mao, K. M. Johnson, and G. Moddel, "Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators," Ferroelectrics 114, 45-53 (1991).
[CrossRef]

Oskin, M.

C. J. Thompson, S. Hahn, and M. Oskin, "Using modern graphics architectures for general-purpose computing: a framework and analysis," in Proceedings of the IEEE/ACM International Symposium on Microarchitecture MICRO-35 (Institute of Electrical and Electronics Engineers, 2002), pp. 306-317.

Osten, W.

Parrent, G. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, 1989).
[CrossRef]

Payne, D. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Petz, C.

C. Petz and M. Magnor, "Fast hologram synthesis for 3D geometry models using graphics hardware," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 266-275 (2003).
[CrossRef]

Polin, M.

Pralle, A.

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
[CrossRef]

Quarrel, J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Quentmeyer, T.

T. Quentmeyer, "Delivering real-time holographic video content with off-the-shelf PC hardware," masters thesis (Massachusetts Institute of Technology, Cambridge, Massachusetts, (2004).

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 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, 608-610 (1999).
[CrossRef]

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written in a liquid crystal display," Opt. Lett. 9, 508-510 (1999).

Reynolds, G. O.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, 1989).
[CrossRef]

Ritter, A.

Rohrbach, A.

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optically trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

Roichman, Y.

Rubinsztein-Dunlop, H.

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

Scattergood, D. C.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Schmidt, C. F.

Schwartzlander, G. A.

Seldowitz, M. A.

Sheerin, D. T.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Shimobaba, T.

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

T. Ito, T. Shimobaba, H. Godo, and M. Horiuchi, "Holographic reconstruction with a 10-µm pixel-pitch reflective liquid-crystal display by use of a light-emitting diode reference light," Opt. Lett. 27, 1406-1408 (2002).
[CrossRef]

Shirai, T.

Shiraki, A.

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

Slinger, C. W.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Smith, A. P.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Smith, M. A.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Stanley, M.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Payne, D. C. Scattergood, D. T. Sheerin, M. A. Smith, and M. Stanley, "Progress and prospects for practical electroholographic display systems," in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Stevenson, and T. J. Trout, eds., Proc. SPIE 4296, 18-32 (2001).
[CrossRef]

Stelzer, E. H. K.

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optically trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
[CrossRef]

Strothotte, T.

Sugie, T.

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

Svoboda, K.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Sweeney, D. W.

Switz, N. A.

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Takahashi, S.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Thompson, B. J.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (SPIE, 1989).
[CrossRef]

Thompson, C. J.

C. J. Thompson, S. Hahn, and M. Oskin, "Using modern graphics architectures for general-purpose computing: a framework and analysis," in Proceedings of the IEEE/ACM International Symposium on Microarchitecture MICRO-35 (Institute of Electrical and Electronics Engineers, 2002), pp. 306-317.

Tipton, D. L.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computer-generated holograms," Opt. Commun. 185, 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, 608-610 (1999).
[CrossRef]

T. Haist, E.-U. Wagemann, and H. J. Tiziani, "Pulsed-laser ablation using dynamic computer-generated holograms written into a liquid crystal display," J. Opt. A 1, 428-430 (1999).
[CrossRef]

M. Reicherter, J. Liesener, T. Haist, and H. J. Tiziani, "Optical particle trapping with computer-generated holograms written in a liquid crystal display," Opt. Lett. 9, 508-510 (1999).

Wagemann, E. U.

Wagemann, E.-U.

T. Haist, E.-U. Wagemann, and H. J. Tiziani, "Pulsed-laser ablation using dynamic computer-generated holograms written into a liquid crystal display," J. Opt. A 1, 428-430 (1999).
[CrossRef]

Watson, P. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Webb, W. W.

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Webber, P. J.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, "100 mega-pixel computer generated holographic images from active tiling--a dynamic and scalable electro-optic modulator system," in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., Proc. SPIE 5005, 247-258 (2003).
[CrossRef]

Wyrowski, F.

O. Bryngdahl and F. Wyrowski, "Digital holography: computer-generated holograms," in Progress in Optics,E.Wolf, ed. (Elsevier 1990), Volak. 28, pp. 1-86.

Yabe, T.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Yoshida, K.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Yoshimura, K.

T. Ito, N. Masuda, K. Yoshimura, A. Shiraki, T. Shimobaba, and T. Sugie, "Special-purpose computer HORN-5 for a real-time electroholography," Opt. Express 13, 1932-1932 (2005).
[CrossRef]

Annu. Rev. Biophys. Biomol. Struct.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. A

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998).
[CrossRef]

Biophys. J.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Comp. Phys. Commun.

T. Ito, H. Eldeib, K. Yoshida, S. Takahashi, T. Yabe, and T. Kunugi, "Special-purpose computer for holography HORN-2," Comp. Phys. Commun. 93, 13-20 (1996).
[CrossRef]

Ferroelectrics

C. C. Mao, K. M. Johnson, and G. Moddel, "Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators," Ferroelectrics 114, 45-53 (1991).
[CrossRef]

J. Appl. Phys.

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optically trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

J. Electron. Imaging

M. Lucente, "Interactive computation of holograms using a look-up table," J. Electron. Imaging 2, 28-34 (1993).
[CrossRef]

J. Mod. Opt.

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

J. Opt. A

T. Haist, E.-U. Wagemann, and H. J. Tiziani, "Pulsed-laser ablation using dynamic computer-generated holograms written into a liquid crystal display," J. Opt. A 1, 428-430 (1999).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Amplitude modulation for the optimal settings of the LC-R-2500 (normalized to 1).

Fig. 2
Fig. 2

(Color online) Linearized phase modulation at 830 nm for the optimal settings (analyzer–polarizer, 19°–39°) of the LC-R-2500.

Fig. 3
Fig. 3

Comparison of the zeroth and first diffraction orders of a blazed phase grating.

Fig. 4
Fig. 4

Rendering pipeline of a modern GPU.

Fig. 5
Fig. 5

Hologram computation on the GPU: basic outline of the hologram.

Fig. 6
Fig. 6

Hologram computation on the GPU: computing two complex-valued hologram pixels with one GPU pixel.

Fig. 7
Fig. 7

Setup for the holographic tweezers.

Fig. 8
Fig. 8

(Color online) Calibration signal (y-position signal).

Fig. 9
Fig. 9

(Color online) Comparison of the measured potentials of a 3 μm bead along the y direction: left, measured by interference detection; right, measured by image processing.

Fig. 10
Fig. 10

(Color online) Corrected and astigmatic trapping potential (y direction, detected by interference detection).

Fig. 11
Fig. 11

Trapping of a disk-shaped particle (diameter, ∼3 μm): (a) untrapped, (b) erect and trapped with an astigmatic beam profile, (c) erect and aligned to elangated trapping potential.

Equations (55)

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( 13.6   Gflops )
1280 × 1024 pixels
13.7 μ m
90 %
1920 × 1200   pixels
9.5 μ m
92 %
1024 × 768   pixels
19 μ m
0.97   in .   ( 2 .46   cm )
93 %
830   nm
3.1 π   and   2 .1 π
830   nm
2.0 π
2 π
0.5   W / cm 2
75   Hz
h ( x , y )
U ( x , y )
U ( x , y ) = 1 N U i exp ( i k x x + i k y y ) × exp [ i β ( x 2 + y 2 ) ] exp [ i ϕ ( x , y ) ] ,
h ( x , y ) = atan [ Re ( U ) Im ( U ) ] .
( i k x x + i k y y )
( x , y )
exp [ i β ( x 2 + y 2 ) ]
exp ( i ϕ )
tan   ϕ ( x , y ) = y / x
30   Hz
N = 50   traps
1024 × 768   pixel
N = 14 × 30   Hz × 50 × 1024 × 768 = 16 .7 × 10 9  ( 1 / s )
( 16.7   Gflops )
5   Gflops
3.2   GHz,   6.4   Gflops )
400   MHz
50   Gflops
3.0   GHz
1024 × 768
25   ms
13.6 Gflops
13   Hz
( 10 12 )
830   nm, 150mW
( λ / 2 )
100 ×, 1.0   W
p ( x )
E ( x ) = k B T   ln   p ( x ) .
E ( x ) = ) α x 2 / 2 .
F ( x ) = α x .
E ( x )
3 μ m
α = 7.9 × 10 7 N ∕ m
α = 8.0 × 10 7 N ∕ m
75 %
13.6   Gflops

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