Abstract

No iterative algorithm is necessary to calculate holograms for most holographic optical trapping patterns. Instead, holograms may be produced by a simple extension of the prisms-and-lenses method. This formulaic approach yields the same diffraction efficiency as iterative algorithms for any asymmetric or symmetric but nonperiodic pattern of points while requiring less calculation time. A slight spatial disordering of periodic patterns significantly reduces intensity variations between the different traps without extra calculation costs. Eliminating laborious hologram calculations should greatly facilitate interactive holographic trapping.

© 2005 Optical Society of America

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    [CrossRef]
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  5. E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
    [CrossRef]
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    [CrossRef]
  7. J. E. Curtis and J. P. Spatz, Proc. SPIE 5514, 455 (2004).
    [CrossRef]
  8. M. Konrad, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
    [CrossRef]
  9. K. Ladavac, K. Kasza, and D. G. Grier, Phys. Rev. E 70, 010901 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  11. M. Pelton, K. Ladavac, and D. G. Grier, Phys. Rev. E 70, 031108 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. Laczik, Opt. Express 12, 5475 (2004).
    [CrossRef]
  18. G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. Laczik, M. J. Padgett, and J. Courtial, Opt. Express 12, 1665 (2004).
    [CrossRef] [PubMed]
  19. G. Sinclair, P. Jordan, J. Courtial, and M. Padgett, Opt. Express 12, 5475 (2004).
    [CrossRef] [PubMed]
  20. G. Sinclair, P. Jordan, J. Leach, and M. Padgett, J. Mod. Opt. 51, 409 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. In general, ?j can be extended to ?j*=?j+?xj with, for example, a lens phase ?Lj for 3D positioning[3] or a helical phase ??j to change the trap’s mode.[6]

2005

S. Lee, K. Ladavac, M. Polin, and D. G. Grier, Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef]

2004

W. Losert, C. Poole, P. Bradford, and D. English, Proc. SPIE 5514, 197 (2004).
[CrossRef]

C. H.J. Schmitz, J. E. Curtis, and J. P. Spatz, Proc. SPIE 5514, 446 (2004).
[CrossRef]

G. Sinclair, P. Jordan, J. Leach, and M. Padgett, J. Mod. Opt. 51, 409 (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, Phys. Rev. E 70, 031108 (2004).
[CrossRef]

J. E. Curtis and J. P. Spatz, Proc. SPIE 5514, 455 (2004).
[CrossRef]

K. Ladavac, K. Kasza, and D. G. Grier, Phys. Rev. E 70, 010901 (2004).
[CrossRef]

G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. Laczik, M. J. Padgett, and J. Courtial, Opt. Express 12, 1665 (2004).
[CrossRef] [PubMed]

G. Sinclair, P. Jordan, J. Courtial, and M. Padgett, Opt. Express 12, 5475 (2004).
[CrossRef] [PubMed]

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. Laczik, Opt. Express 12, 5475 (2004).
[CrossRef]

2003

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef] [PubMed]

M. Konrad, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef]

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

P. T. Korda, M. B. Taylor, and D. G. Grier, Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

2001

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

K. L. Tan, S. T. Warr, I. G. Manolis, T. D. Wilkinson, M. M. Redmond, W. A. Crossland, R. J. Mears, and B. Robertson, J. Opt. Soc. Am. A 18, 205 (2001).
[CrossRef]

2000

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, Opt. Commun. 185, 77 (2000).
[CrossRef]

1999

1998

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

1997

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

1986

1969

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Ashkin, A.

Bechinger, C.

M. Konrad, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef]

Bjorkholm, J.

Bradford, P.

W. Losert, C. Poole, P. Bradford, and D. English, Proc. SPIE 5514, 197 (2004).
[CrossRef]

Chu, S.

Cooper, J.

Courtial, J.

Crossland, W. A.

Curtis, J. E.

C. H.J. Schmitz, J. E. Curtis, and J. P. Spatz, Proc. SPIE 5514, 446 (2004).
[CrossRef]

J. E. Curtis and J. P. Spatz, Proc. SPIE 5514, 455 (2004).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef] [PubMed]

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

Dziedzic, J. M.

English, D.

W. Losert, C. Poole, P. Bradford, and D. English, Proc. SPIE 5514, 197 (2004).
[CrossRef]

Gibson, G.

Grier, D. G.

S. Lee, K. Ladavac, M. Polin, and D. G. Grier, Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef]

K. Ladavac, K. Kasza, and D. G. Grier, Phys. Rev. E 70, 010901 (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, Phys. Rev. E 70, 031108 (2004).
[CrossRef]

P. T. Korda, M. B. Taylor, and D. G. Grier, Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, Opt. Commun. 185, 77 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jordan, P.

Kasza, K.

K. Ladavac, K. Kasza, and D. G. Grier, Phys. Rev. E 70, 010901 (2004).
[CrossRef]

Konrad, M.

M. Konrad, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef]

Korda, P. T.

P. T. Korda, M. B. Taylor, and D. G. Grier, Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Laczik, Z.

Ladavac, K.

S. Lee, K. Ladavac, M. Polin, and D. G. Grier, Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef]

K. Ladavac, K. Kasza, and D. G. Grier, Phys. Rev. E 70, 010901 (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, Phys. Rev. E 70, 031108 (2004).
[CrossRef]

Leach, J.

Lee, S.

S. Lee, K. Ladavac, M. Polin, and D. G. Grier, Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef]

Leiderer, P.

M. Konrad, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef]

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, Opt. Commun. 185, 77 (2000).
[CrossRef]

Losert, W.

W. Losert, C. Poole, P. Bradford, and D. English, Proc. SPIE 5514, 197 (2004).
[CrossRef]

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef] [PubMed]

Manolis, I. G.

Mears, R. J.

Padgett, M.

Padgett, M. J.

Pelton, M.

M. Pelton, K. Ladavac, and D. G. Grier, Phys. Rev. E 70, 031108 (2004).
[CrossRef]

Polin, M.

S. Lee, K. Ladavac, M. Polin, and D. G. Grier, Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef]

Poole, C.

W. Losert, C. Poole, P. Bradford, and D. English, Proc. SPIE 5514, 197 (2004).
[CrossRef]

Redmond, M. M.

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, Opt. Commun. 185, 77 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

Robertson, B.

Schmitz, C. H.J.

C. H.J. Schmitz, J. E. Curtis, and J. P. Spatz, Proc. SPIE 5514, 446 (2004).
[CrossRef]

Schönleber, M.

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Sinclair, G.

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef] [PubMed]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Spatz, J. P.

J. E. Curtis and J. P. Spatz, Proc. SPIE 5514, 455 (2004).
[CrossRef]

C. H.J. Schmitz, J. E. Curtis, and J. P. Spatz, Proc. SPIE 5514, 446 (2004).
[CrossRef]

Tan, K. L.

Taylor, M. B.

P. T. Korda, M. B. Taylor, and D. G. Grier, Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, Opt. Commun. 185, 77 (2000).
[CrossRef]

M. Reicherter, T. Haist, E. U. Wagemann, and H. J. Tiziani, Opt. Lett. 24, 608 (1999).
[CrossRef]

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Wagemann, E. U.

Warr, S. T.

Wilkinson, T. D.

Yao, E.

IBM J. Res. Dev.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Mod. Opt.

G. Sinclair, P. Jordan, J. Leach, and M. Padgett, J. Mod. Opt. 51, 409 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nature

M. P. MacDonald, G. C. Spalding, and K. Dholakia, Nature 426, 421 (2003).
[CrossRef] [PubMed]

Opt. Commun.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, Opt. Commun. 185, 77 (2000).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

T. Haist, M. Schönleber, and H. J. Tiziani, Opt. Commun. 140, 299 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

K. Ladavac, K. Kasza, and D. G. Grier, Phys. Rev. E 70, 010901 (2004).
[CrossRef]

M. Pelton, K. Ladavac, and D. G. Grier, Phys. Rev. E 70, 031108 (2004).
[CrossRef]

Phys. Rev. Lett.

S. Lee, K. Ladavac, M. Polin, and D. G. Grier, Phys. Rev. Lett. 94, 110601 (2005).
[CrossRef]

P. T. Korda, M. B. Taylor, and D. G. Grier, Phys. Rev. Lett. 89, 128301 (2002).
[CrossRef]

M. Konrad, P. Leiderer, and C. Bechinger, Phys. Rev. Lett. 90, 158302 (2003).
[CrossRef]

Proc. SPIE

W. Losert, C. Poole, P. Bradford, and D. English, Proc. SPIE 5514, 197 (2004).
[CrossRef]

C. H.J. Schmitz, J. E. Curtis, and J. P. Spatz, Proc. SPIE 5514, 446 (2004).
[CrossRef]

J. E. Curtis and J. P. Spatz, Proc. SPIE 5514, 455 (2004).
[CrossRef]

Rev. Sci. Instrum.

E. R. Dufresne and D. G. Grier, Rev. Sci. Instrum. 69, 1974 (1998).
[CrossRef]

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, Rev. Sci. Instrum. 72, 1810 (2001).
[CrossRef]

Other

In general, ?j can be extended to ?j*=?j+?xj with, for example, a lens phase ?Lj for 3D positioning[3] or a helical phase ??j to change the trap’s mode.[6]

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Figures (5)

Fig. 1
Fig. 1

Comparison of the typical efficiencies achieved by hologram calculation methods for (a) N × N arrays of points and (b) random configurations of points. Squares, GS; circles, GAA; diamonds, S; triangles, SR.

Fig. 2
Fig. 2

Convergence of the GS and GAA algorithms for (a) N × N patterns, L = 50 px and (b) asymmetric configurations, N = 2 , 10, 20, 50, 100. Filled, GS; open, GAA.

Fig. 3
Fig. 3

(a) Histogram of efficiencies achieved by the SR method for a 5 × 5 array with L = 50 px and η = 84.7 ± 2.1 . (b) Improvement of the traps’ intensity variation by randomized shifts to N × N patterns, L = 50 px .

Fig. 4
Fig. 4

(a) Comparison of hologram efficiencies for a circle of N points. (b) Standard deviation in the intensities.

Fig. 5
Fig. 5

Comparison of the standard deviation in intensity for (a) N × N arrays and (b) random point configurations.

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