Abstract

Holographic optical traps use the forces exerted by computer-generated holograms to trap, move and otherwise transform mesoscopically textured materials. This article introduces methods for optimizing holographic optical traps’ efficiency and accuracy, and an optimal statistical approach for characterizing their performance. This combination makes possible real-time adaptive optimization.

© 2005 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu. “Observation of a single-beam gradient force optical trap for dielectric particles.” Opt. Lett. 11, 288–290 (1986).
    [Crossref] [PubMed]
  2. E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
    [Crossref]
  3. 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]
  4. 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]
  5. E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier. “Computer-generated holographic optical tweezer arrays.” Rev. Sci. Instr. 72, 1810–1816 (2001).
    [Crossref]
  6. J. E. Curtis, B. A. Koss, and D. G. Grier. “Dynamic holographic optical tweezers.” Opt. Commun. 207, 169–175 (2002).
    [Crossref]
  7. D. G. Grier. “A revolution in optical manipulation.” Nature 424, 810–816 (2003).
    [Crossref] [PubMed]
  8. P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
    [Crossref]
  9. P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
    [Crossref] [PubMed]
  10. A. Jesacher, S. Furhpater, S. Bernet, and M. Ritsch-Marte. “Size selective trapping with optical “cogwheel” tweezers.” Opt. Express 12, 4129–4135 (2004).
    [Crossref] [PubMed]
  11. K. Ladavac, K. Kasza, and D. G. Grier. “Sorting by periodic potential energy landscapes: Optical fractionation.” Phys. Rev. E 70, 010901(R) (2004).
  12. M. Pelton, K. Ladavac, and D. G. Grier. “Transport and fractionation in periodic potential-energy landscapes.” Phys. Rev. E 70, 031108 (2004).
    [Crossref]
  13. S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
    [Crossref] [PubMed]
  14. S.-H. Lee and D. G. Grier. “Flux reversal in a two-state symmetric optical thermal ratchet.” Phys. Rev. E 71, 060102(R) (2005).
    [Crossref]
  15. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte. “Size selective trapping with optical “cogwheel” tweezers.” Opt. Express 12, 4129–4135 (2004).
    [Crossref] [PubMed]
  16. V. Soifer, V. Kotlyar, and L. Doskolovich. Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, Bristol, PA, 1997).
  17. H. He, N. R. Heckenberg, and 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]
  18. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
    [Crossref] [PubMed]
  19. K. T. Gahagan and G. A. Swartzlander. “Optical vortex trapping of particles.” Opt. Lett. 21, 827–829 (1996).
    [Crossref] [PubMed]
  20. N. B. Simpson, L. Allen, and M. J. Padgett. “Optical tweezers and optical spanners with Laguerre-Gaussian modes.” J. Mod. Opt. 43, 2485–2491 (1996).
    [Crossref]
  21. M. Meister and R. J. Winfield. “Novel approaches to direct search algorithms for the design of diffractive optical elements.” Opt. Commun. 203, 39–49 (2002).
    [Crossref]
  22. J. L. Aragón, G. G. Naumis, and M. Torres. “A multigrid approach to the average lattices of quasicrystals.” Acta Cryst. A58, 352–360 (2002).
  23. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
    [Crossref] [PubMed]
  24. L. P. Ghislain, N. A. Switz, and W. W. Webb. “Measurement of small forces using an optical trap.” Rev. Sci. Instr. 65, 2762–2768 (1994).
    [Crossref]
  25. F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
    [Crossref]
  26. 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, S75–S78 (1998).
    [Crossref]
  27. K. Berg-Sørensen and H. Flyvbjerg. “Power spectrum analysis for optical tweezers.” Rev. Sci. Instr. 75, 594–612 (2004).
    [Crossref]
  28. F. Gittes and C. F. Schmidt. “Interference model for back-focal-plane displacement detection in optical tweezers.” Opt. Lett. 23, 7–9 (1998).
    [Crossref]
  29. J. C. Crocker and D. G. Grier. “Methods of digital video microscopy for colloidal studies.” J. Colloid Interface Sci. 179, 298–310 (1996).
    [Crossref]
  30. G. E. P. Box and G. M. Jenkins. Time Series Analysis: Forecasting and Control (Holden-Day, San Francisco, 1976).
  31. H. Risken. The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989), 2nd ed.
    [Crossref]
  32. M. Polin, D. G. Grier, and S. Quake. “Anomalous vibrational dispersion in holographically trapped colloidal arrays.” Phys. Rev. Lett. submitted for publication (2005).
    [PubMed]
  33. P. T. Korda, G. C. Spalding, and D. G. Grier. “Evolution of a colloidal critical state in an optical pinning potential.” Phys. Rev. B 66, 024504 (2002).
    [Crossref]

2005 (2)

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
[Crossref] [PubMed]

S.-H. Lee and D. G. Grier. “Flux reversal in a two-state symmetric optical thermal ratchet.” Phys. Rev. E 71, 060102(R) (2005).
[Crossref]

2004 (5)

K. Ladavac, K. Kasza, and D. G. Grier. “Sorting by periodic potential energy landscapes: Optical fractionation.” Phys. Rev. E 70, 010901(R) (2004).

M. Pelton, K. Ladavac, and D. G. Grier. “Transport and fractionation in periodic potential-energy landscapes.” Phys. Rev. E 70, 031108 (2004).
[Crossref]

K. Berg-Sørensen and H. Flyvbjerg. “Power spectrum analysis for optical tweezers.” Rev. Sci. Instr. 75, 594–612 (2004).
[Crossref]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte. “Size selective trapping with optical “cogwheel” tweezers.” Opt. Express 12, 4129–4135 (2004).
[Crossref] [PubMed]

A. Jesacher, S. Furhpater, S. Bernet, and M. Ritsch-Marte. “Size selective trapping with optical “cogwheel” tweezers.” Opt. Express 12, 4129–4135 (2004).
[Crossref] [PubMed]

2003 (1)

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

2002 (6)

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

M. Meister and R. J. Winfield. “Novel approaches to direct search algorithms for the design of diffractive optical elements.” Opt. Commun. 203, 39–49 (2002).
[Crossref]

J. L. Aragón, G. G. Naumis, and M. Torres. “A multigrid approach to the average lattices of quasicrystals.” Acta Cryst. A58, 352–360 (2002).

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

P. T. Korda, G. C. Spalding, and D. G. Grier. “Evolution of a colloidal critical state in an optical pinning potential.” Phys. Rev. B 66, 024504 (2002).
[Crossref]

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. Instr. 72, 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, 77–82 (2000).
[Crossref]

1999 (1)

1998 (3)

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.-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, S75–S78 (1998).
[Crossref]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[Crossref]

1997 (1)

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

1996 (3)

J. C. Crocker and D. G. Grier. “Methods of digital video microscopy for colloidal studies.” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

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

N. B. Simpson, L. Allen, and M. J. Padgett. “Optical tweezers and optical spanners with Laguerre-Gaussian modes.” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

1995 (2)

H. He, N. R. Heckenberg, and 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]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

1994 (1)

L. P. Ghislain, N. A. Switz, and W. W. Webb. “Measurement of small forces using an optical trap.” Rev. Sci. Instr. 65, 2762–2768 (1994).
[Crossref]

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

1986 (1)

Allen, L.

N. B. Simpson, L. Allen, and M. J. Padgett. “Optical tweezers and optical spanners with Laguerre-Gaussian modes.” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Aragón, J. L.

J. L. Aragón, G. G. Naumis, and M. Torres. “A multigrid approach to the average lattices of quasicrystals.” Acta Cryst. A58, 352–360 (2002).

Ashkin, A.

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg. “Power spectrum analysis for optical tweezers.” Rev. Sci. Instr. 75, 594–612 (2004).
[Crossref]

Bernet, S.

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Box, G. E. P.

G. E. P. Box and G. M. Jenkins. Time Series Analysis: Forecasting and Control (Holden-Day, San Francisco, 1976).

Chu, S.

Crocker, J. C.

J. C. Crocker and D. G. Grier. “Methods of digital video microscopy for colloidal studies.” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier. “Dynamic holographic optical tweezers.” Opt. Commun. 207, 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. Instr. 72, 1810–1816 (2001).
[Crossref]

Doskolovich, L.

V. Soifer, V. Kotlyar, and L. Doskolovich. Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, Bristol, PA, 1997).

Dufresne, E. R.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (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. Instr. 72, 1810–1816 (2001).
[Crossref]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[Crossref]

Dziedzic, J. M.

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, S75–S78 (1998).
[Crossref]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg. “Power spectrum analysis for optical tweezers.” Rev. Sci. Instr. 75, 594–612 (2004).
[Crossref]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Fürhapter, S.

Furhpater, S.

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. Instr. 65, 2762–2768 (1994).
[Crossref]

Gittes, F.

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

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

Grier, D. G.

S.-H. Lee and D. G. Grier. “Flux reversal in a two-state symmetric optical thermal ratchet.” Phys. Rev. E 71, 060102(R) (2005).
[Crossref]

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
[Crossref] [PubMed]

M. Pelton, K. Ladavac, and D. G. Grier. “Transport and fractionation in periodic potential-energy landscapes.” Phys. Rev. E 70, 031108 (2004).
[Crossref]

K. Ladavac, K. Kasza, and D. G. Grier. “Sorting by periodic potential energy landscapes: Optical fractionation.” Phys. Rev. E 70, 010901(R) (2004).

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

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

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

P. T. Korda, G. C. Spalding, and D. G. Grier. “Evolution of a colloidal critical state in an optical pinning potential.” Phys. Rev. B 66, 024504 (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. Instr. 72, 1810–1816 (2001).
[Crossref]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[Crossref]

J. C. Crocker and D. G. Grier. “Methods of digital video microscopy for colloidal studies.” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

M. Polin, D. G. Grier, and S. Quake. “Anomalous vibrational dispersion in holographically trapped colloidal arrays.” Phys. Rev. Lett. submitted for publication (2005).
[PubMed]

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]

He, H.

H. He, N. R. Heckenberg, and 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]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and 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]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

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, S75–S78 (1998).
[Crossref]

Jenkins, G. M.

G. E. P. Box and G. M. Jenkins. Time Series Analysis: Forecasting and Control (Holden-Day, San Francisco, 1976).

Jesacher, A.

Kasza, K.

K. Ladavac, K. Kasza, and D. G. Grier. “Sorting by periodic potential energy landscapes: Optical fractionation.” Phys. Rev. E 70, 010901(R) (2004).

Korda, P. T.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

P. T. Korda, G. C. Spalding, and D. G. Grier. “Evolution of a colloidal critical state in an optical pinning potential.” Phys. Rev. B 66, 024504 (2002).
[Crossref]

Koss, B. A.

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

Kotlyar, V.

V. Soifer, V. Kotlyar, and L. Doskolovich. Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, Bristol, PA, 1997).

Ladavac, K.

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
[Crossref] [PubMed]

K. Ladavac, K. Kasza, and D. G. Grier. “Sorting by periodic potential energy landscapes: Optical fractionation.” Phys. Rev. E 70, 010901(R) (2004).

M. Pelton, K. Ladavac, and D. G. Grier. “Transport and fractionation in periodic potential-energy landscapes.” Phys. Rev. E 70, 031108 (2004).
[Crossref]

Lee, S.-H.

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
[Crossref] [PubMed]

S.-H. Lee and D. G. Grier. “Flux reversal in a two-state symmetric optical thermal ratchet.” Phys. Rev. E 71, 060102(R) (2005).
[Crossref]

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]

MacKintosh, F. C.

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

Meister, M.

M. Meister and R. J. Winfield. “Novel approaches to direct search algorithms for the design of diffractive optical elements.” Opt. Commun. 203, 39–49 (2002).
[Crossref]

Naumis, G. G.

J. L. Aragón, G. G. Naumis, and M. Torres. “A multigrid approach to the average lattices of quasicrystals.” Acta Cryst. A58, 352–360 (2002).

Olmsted, P. D.

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

Padgett, M. J.

N. B. Simpson, L. Allen, and M. J. Padgett. “Optical tweezers and optical spanners with Laguerre-Gaussian modes.” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Pelton, M.

M. Pelton, K. Ladavac, and D. G. Grier. “Transport and fractionation in periodic potential-energy landscapes.” Phys. Rev. E 70, 031108 (2004).
[Crossref]

Polin, M.

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
[Crossref] [PubMed]

M. Polin, D. G. Grier, and S. Quake. “Anomalous vibrational dispersion in holographically trapped colloidal arrays.” Phys. Rev. Lett. submitted for publication (2005).
[PubMed]

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, S75–S78 (1998).
[Crossref]

Quake, S.

M. Polin, D. G. Grier, and S. Quake. “Anomalous vibrational dispersion in holographically trapped colloidal arrays.” Phys. Rev. Lett. submitted for publication (2005).
[PubMed]

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]

Risken, H.

H. Risken. The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989), 2nd ed.
[Crossref]

Ritsch-Marte, M.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

H. He, N. R. Heckenberg, and 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]

Schmidt, C. F.

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

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Schnurr, B.

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

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. Instr. 72, 1810–1816 (2001).
[Crossref]

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett. “Optical tweezers and optical spanners with Laguerre-Gaussian modes.” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Soifer, V.

V. Soifer, V. Kotlyar, and L. Doskolovich. Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, Bristol, PA, 1997).

Spalding, G. C.

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

P. T. Korda, G. C. Spalding, and D. G. Grier. “Evolution of a colloidal critical state in an optical pinning potential.” Phys. Rev. B 66, 024504 (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. Instr. 72, 1810–1816 (2001).
[Crossref]

Stelzer, E. H. K.

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, S75–S78 (1998).
[Crossref]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Swartzlander, G. A.

Switz, N. A.

L. P. Ghislain, N. A. Switz, and W. W. Webb. “Measurement of small forces using an optical trap.” Rev. Sci. Instr. 65, 2762–2768 (1994).
[Crossref]

Taylor, M. B.

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

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]

Torres, M.

J. L. Aragón, G. G. Naumis, and M. Torres. “A multigrid approach to the average lattices of quasicrystals.” Acta Cryst. A58, 352–360 (2002).

Wagemann, E. U.

Webb, W. W.

L. P. Ghislain, N. A. Switz, and W. W. Webb. “Measurement of small forces using an optical trap.” Rev. Sci. Instr. 65, 2762–2768 (1994).
[Crossref]

Winfield, R. J.

M. Meister and R. J. Winfield. “Novel approaches to direct search algorithms for the design of diffractive optical elements.” Opt. Commun. 203, 39–49 (2002).
[Crossref]

Acta Cryst. (1)

J. L. Aragón, G. G. Naumis, and M. Torres. “A multigrid approach to the average lattices of quasicrystals.” Acta Cryst. A58, 352–360 (2002).

Appl. Phys. A (1)

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, S75–S78 (1998).
[Crossref]

J. Colloid Interface Sci. (1)

J. C. Crocker and D. G. Grier. “Methods of digital video microscopy for colloidal studies.” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

J. Mod. Opt. (2)

H. He, N. R. Heckenberg, and 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. B. Simpson, L. Allen, and M. J. Padgett. “Optical tweezers and optical spanners with Laguerre-Gaussian modes.” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Nature (2)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block. “Direct observation of kinesin stepping by optical trapping interferometry.” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

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

Opt. Commun. (3)

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

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. Meister and R. J. Winfield. “Novel approaches to direct search algorithms for the design of diffractive optical elements.” Opt. Commun. 203, 39–49 (2002).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. B (1)

P. T. Korda, G. C. Spalding, and D. G. Grier. “Evolution of a colloidal critical state in an optical pinning potential.” Phys. Rev. B 66, 024504 (2002).
[Crossref]

Phys. Rev. E (3)

S.-H. Lee and D. G. Grier. “Flux reversal in a two-state symmetric optical thermal ratchet.” Phys. Rev. E 71, 060102(R) (2005).
[Crossref]

K. Ladavac, K. Kasza, and D. G. Grier. “Sorting by periodic potential energy landscapes: Optical fractionation.” Phys. Rev. E 70, 010901(R) (2004).

M. Pelton, K. Ladavac, and D. G. Grier. “Transport and fractionation in periodic potential-energy landscapes.” Phys. Rev. E 70, 031108 (2004).
[Crossref]

Phys. Rev. Lett. (4)

S.-H. Lee, K. Ladavac, M. Polin, and D. G. Grier. “Observation of flux reversal in a symmetric optical thermal ratchet.” Phys. Rev. Lett. 94, 110601 (2005).
[Crossref] [PubMed]

P. T. Korda, M. B. Taylor, and D. G. Grier. “Kinetically locked-in colloidal transport in an array of optical tweezers.” Phys. Rev. Lett. 89, 128301 (2002).
[Crossref] [PubMed]

F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt. “Microscopic viscoelasticity: Shear moduli of soft materials determined from thermal fluctuations.” Phys. Rev. Lett. 79, 3286–3289 (1997).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop. “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity.” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Rev. Sci. Instr. (5)

L. P. Ghislain, N. A. Switz, and W. W. Webb. “Measurement of small forces using an optical trap.” Rev. Sci. Instr. 65, 2762–2768 (1994).
[Crossref]

K. Berg-Sørensen and H. Flyvbjerg. “Power spectrum analysis for optical tweezers.” Rev. Sci. Instr. 75, 594–612 (2004).
[Crossref]

P. T. Korda, G. C. Spalding, E. R. Dufresne, and D. G. Grier. “Nanofabrication with holographic optical tweezers.” Rev. Sci. Instr. 73, 1956–1957 (2002).
[Crossref]

E. R. Dufresne and D. G. Grier. “Optical tweezer arrays and optical substrates created with diffractive optical elements.” Rev. Sci. Instr. 69, 1974–1977 (1998).
[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. Instr. 72, 1810–1816 (2001).
[Crossref]

Other (4)

V. Soifer, V. Kotlyar, and L. Doskolovich. Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, Bristol, PA, 1997).

G. E. P. Box and G. M. Jenkins. Time Series Analysis: Forecasting and Control (Holden-Day, San Francisco, 1976).

H. Risken. The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989), 2nd ed.
[Crossref]

M. Polin, D. G. Grier, and S. Quake. “Anomalous vibrational dispersion in holographically trapped colloidal arrays.” Phys. Rev. Lett. submitted for publication (2005).
[PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Simplified schematic of a holographic optical tweezer optical train before and after modification. (a) A collimated beam is split into multiple beams by the DOE, each of which is shown here as being collimated. The diffracted beams pass through the input pupil of an objective lens and are focused into optical traps in the objective’s focal plane. The undiffracted portion of the beam, shown here with the darkest shading, also focuses into the focal plane. (b) The input beam is converging as it passes through the DOE. The DOE collimates the diffracted beams, so that they focus into the focal plane, as in (a). The undiffracted beam comes to a focus within the coverslip bounding the sample. (c) A beam block can eliminate the undiffracted beam without substantially degrading the optical traps.

Fig. 2.
Fig. 2.

(a) Design for 119 identical optical traps in a two-dimensional quasiperiodic array. (b) Trapping pattern projected without optimizations using the adaptive-additive algorithm. (c) Trapping pattern projected with optimized optics and adaptively corrected direct search algorithm. (d) Bright-field image of colloidal silica spheres 1.53 μm in diameter dispersed in water and organized in the optical trap array. The scale bar indicates 10 μm

Fig. 3.
Fig. 3.

A three-dimensional multifunctional holographic optical trap array created with the direct search algorithm. (a) Refined DOE phase pattern. (b), (c) and (d) The projected optical trap array at z = -10 μm, 0 μm and +10 μm. Traps are spaced by 1.2 μm in the plane, and the 12 traps in the middle plane consist of ℓ = 8 optical vortices. (e) Performance metrics for the hologram in (a) as a function of the number of accepted single-pixel changes. Data include the DOE’s overall diffraction efficiency as defined by Eq. (15), the projected pattern’s RMS error from Eq. (16), and its uniformity, 1 - u, where u is defined in Eq. (17).

Fig. 4.
Fig. 4.

Power dependence of (a) the trap stiffness, (b) the viscous drag coefficient and (c) the viscous relaxation time for a 1.53 μm diameter silica sphere trapped by an optical tweezer in water.

Equations (48)

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E ( r ) = u ( ρ ) exp ( i φ ( ρ ) ) exp ( i kr ρ f ) d 2 ρ .
E ( r ) = j = 1 N u j exp ( i φ j ) T j ( r ) ,
T j ( r ) = exp ( i kr ρ j f ) .
E ( r ) = m = 1 M E m δ ( r r m ) , with
E m = α m exp ( i ξ m ) ,
E m = j = 1 N K j , m 1 T j , m exp ( i φ j ) ,
φ z ( ρ , z ) = k ρ 2 z 2 f 2 .
K j , m z = exp ( i φ z ( ρ j , z m ) ) .
φ ( ρ , ) = θ ,
K j , m = exp ( i φ ( ρ j , m ) )
Δ E m = K j , m 1 T j , m exp ( i φ j ) [ exp ( i Δ φ j ) 1 ] .
C = I + f σ ,
σ = 1 M m = 1 M ( I m γ I m ( D ) ) 2
γ = m = 1 M I m I m ( D ) m = 1 M ( I m ( D ) ) 2
= 1 M m = 1 M I m I m ( D ) ,
e rms = σ max ( I m ) .
u = max ( I m I m ( D ) ) min ( I m I m ( D ) ) max ( I m I m ( D ) ) + min ( I m I m ( D ) ) .
P ( r ) exp ( β V ( r ) ) ,
V ( r ) = 1 2 i = 1 3 κ i r i 2 ,
x ˙ ( t ) = x ( t ) τ + ξ ( t ) ,
ξ ( t ) ξ ( s ) = 2 k B T γ δ ( t s ) .
x ( t ) = x 0 exp ( t τ ) + 0 t ξ ( s ) exp ( t s τ ) ds .
x j + 1 = ϕ x j + a j + 1 ,
ϕ = exp ( Δ t τ ) ,
σ a 2 = k B T κ [ 1 exp ( 2 Δ t τ ) ] .
x j = ϕ x j 1 + a j and y j = x j + b j ,
p ( { x i } , { y i } ϕ , σ a 2 , σ b 2 ) = j = 2 N [ exp ( a j 2 2 σ a 2 ) 2 π σ a 2 ] j = 1 N [ exp ( b j 2 2 σ b 2 ) 2 π σ b 2 ] .
p ( { y j } ϕ , σ a 2 , σ b 2 ) = p ( { x j } , { y j } ϕ , σ a 2 , σ b 2 ) d x 1 d x N
= ( 2 π σ a 2 σ b 2 ) N 1 2 σ b 2 det ( A ϕ ) exp ( 1 2 σ b 2 ( y ) T [ I A σ 1 σ b 2 ] y ) ,
A ϕ = I σ b 2 + M ϕ σ a 2 ,
M ϕ = ( ϕ 2 ϕ 0 0 0 ϕ 1 + ϕ 2 ϕ 0 0 ϕ 1 + ϕ 2 ϕ 0 0 ϕ ϕ 1 + ϕ 2 ϕ 0 0 0 ϕ 1 ) .
det ( A ϕ ) = n = 1 N { 1 σ b 2 + 1 σ a 2 [ 1 + ϕ 2 2 ϕ cos ( 2 π n N ) ] }
( A ϕ 1 ) α β = 1 N n = 1 N σ a 2 σ b 2 exp ( i 2 π N n ( α β ) ) σ a 2 + σ b 2 [ 1 + ϕ 2 2 ϕ cos ( 2 π n N ) ] ,
p ( { y j } ϕ , σ a 2 , σ b 2 ) = ( 2 π ) N 2 n = 1 N { σ a 2 + σ b 2 [ 1 + ϕ 2 2 ϕ cos ( 2 π n N ) ] } 1 2
× exp ( 1 2 σ b 2 n = 1 N y n 2 ) exp ( 1 2 σ b 2 1 N m = 1 N y ˜ m 2 σ a 2 σ a 2 + σ b 2 [ 1 + ϕ 2 2 ϕ cos ( 2 π m N ) ] ) ,
L ( ϕ , σ a 2 , σ b 2 { y i } ) = N 2 ln 2 π 1 2 σ b 2 n = 1 N y n 2 + σ a 2 2 σ b 2 1 N n = 1 N y ˜ n 2 σ a 2 σ a 2 + σ b 2 [ 1 + ϕ 2 2 ϕ cos ( 2 π n N ) ]
1 2 n = 1 N ln ( σ a 2 + σ b 2 [ 1 + ϕ 2 2 ϕ cos ( 2 π n N ) ] ) .
L ϕ = L σ a 2 = L σ b 2 = 0 .
ϕ ̂ 0 = c 1 c 0 and σ ̂ a 0 2 = c 0 [ 1 ( c 1 c 0 ) 2 ] ,
c m = 1 N j = 1 N y j y ( j + m ) mod N
Δ ϕ ̂ 0 = σ ̂ a 0 2 N c 0 and Δ σ ̂ a 0 2 = σ ̂ a 0 2 2 N .
ϕ ̂ ϕ ̂ 0 { 1 + σ b 2 σ ̂ a 0 2 [ 1 ϕ ̂ 0 2 + c 2 c 0 ] } and σ ̂ a 2 σ ̂ a 0 2 σ b 2 σ ̂ a 0 2 c 0 [ 1 5 ϕ ̂ 0 4 + 4 ϕ ̂ 0 2 c 2 c 0 ] ,
κ k B T = 1 ϕ ̂ 2 σ ̂ a 2 and γ k B T Δ t = 1 ϕ ̂ 2 σ ̂ a 2 ln ϕ ̂ ,
( Δ κ κ ) 2 = ( Δ σ ̂ a 2 σ ̂ a 2 ) 2 + ( 2 ϕ ̂ 2 1 ϕ ̂ 2 ) 2 ( Δ ϕ ̂ ϕ ̂ ) 2 and
( Δγ γ ) 2 = ( Δ σ ̂ a 2 σ ̂ a 2 ) 2 + ( 2 ϕ ̂ 2 1 ϕ ̂ 2 + 1 ln ϕ ̂ ) 2 ( Δ ϕ ̂ ϕ ̂ ) 2 .
κ 0 k B T = 1 c 0 [ 1 ± 2 N ( 1 + 2 c 1 2 c 0 2 c 1 2 ) ] and γ 0 k B T Δ t = 1 c 0 ln ( c 0 c 1 ) ( 1 ± Δ γ 0 γ 0 )
N ( Δ γ 0 γ 0 ) 2 = 2 + 1 c 0 2 c 1 2 [ c 0 2 + 2 c 1 2 ln ( c 1 c 0 ) c 1 2 c 1 ln ( c 1 c 0 ) ] 2 .
α m α m i = 1 N κ i κ m .

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