Abstract

We propose a new iterative algorithm for obtaining optimal holograms targeted to the generation of arbitrary three dimensional structures of optical traps. The algorithm basic idea and performance are discussed in conjunction to other available algorithms. We show that all algorithms lead to a phase distribution maximizing a specific performance quantifier, expressed as a function of the trap intensities. In this scheme we go a step further by introducing a new quantifier and the associated algorithm leading to unprecedented efficiency and uniformity in trap light distributions. The algorithms performances are investigated both numerically and experimentally.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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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] [PubMed]
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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]
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    [CrossRef] [PubMed]
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    [CrossRef]

2006

2005

2004

2003

D.G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

2002

M. Meister and R. J. Winfield, "Novel approaches to direct search algorithms for the design of diffractive optical elements," Opt. Commun. 203, 3949 (2002).
[CrossRef]

J. Curtis, B.A. Koss, D.G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175, (2002).
[CrossRef]

J. S. Liu and M. R. Taghizadeh, "Iterative algorithm for the design of diffractive phase elements for laser beam shaping," Opt. Lett. 27, 1463-1465, (2002).
[CrossRef]

2001

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

2000

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

1999

1997

E. Martn-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, "Complex modulation characterization of liquid crystal devices by interferometric data correlation," Meas. Sci. Technol. 8, 764-772 (1997).
[CrossRef]

T. Haist, M. Schönleber, H.J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

1986

1969

L.B. Lesem, P.M. Hirsch, J.A. Jordan "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Andilla, J.

Angelani, L.

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Carnicer, A.

E. Martn-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, "Complex modulation characterization of liquid crystal devices by interferometric data correlation," Meas. Sci. Technol. 8, 764-772 (1997).
[CrossRef]

Casetti, L.

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

Cooper, J.

Courtial, J.

Curtis, J.

J. Curtis, B.A. Koss, D.G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175, (2002).
[CrossRef]

Curtis, J.E.

Dearing, M.T.

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

Dufresne, E.R.

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

Dziedzic, J. M.

Gibson, G.

Grier, D.

Grier, D.G.

D.G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

J. Curtis, B.A. Koss, D.G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175, (2002).
[CrossRef]

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

Haist, T.

J. Liesener, M. Reicherter, T. Haist, 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, 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, M. Schönleber, H.J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

Hirsch, P.M.

L.B. Lesem, P.M. Hirsch, J.A. Jordan "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Jordan, J.A.

L.B. Lesem, P.M. Hirsch, J.A. Jordan "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Jordan, P.

Juvells, I.

E. Martn-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, "Complex modulation characterization of liquid crystal devices by interferometric data correlation," Meas. Sci. Technol. 8, 764-772 (1997).
[CrossRef]

Koss, B.A.

J. Curtis, B.A. Koss, D.G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175, (2002).
[CrossRef]

Laczik, Z.

Ladavac, K.

Leach, J.

Lee, S.H.

Lesem, L.B.

L.B. Lesem, P.M. Hirsch, J.A. Jordan "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Liesener, J.

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

Liu, J. S.

Martn-Badosa, E.

E. Martn-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, "Complex modulation characterization of liquid crystal devices by interferometric data correlation," Meas. Sci. Technol. 8, 764-772 (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, 3949 (2002).
[CrossRef]

Montes-Usategui, M.

Padgett, M.

Padgett, M. J.

Pettini, M.

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

Pleguezuelos, E.

Polin, M.

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, 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, H.J. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999).
[CrossRef]

Roichman, Y.

Ruocco, G.

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

Schmitz, C.H.J.

Schönleber, M.

T. Haist, M. Schönleber, H.J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

Sheets, S.A.

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

Sinclair, G.

Spalding, G.C.

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

Spatz, J.P.

Taghizadeh, M. R.

Tiziani, H.J.

J. Liesener, M. Reicherter, T. Haist, 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, 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, M. Schönleber, H.J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

Vallmitjana, S.

E. Martn-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, "Complex modulation characterization of liquid crystal devices by interferometric data correlation," Meas. Sci. Technol. 8, 764-772 (1997).
[CrossRef]

Wagemann, E.U.

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, 3949 (2002).
[CrossRef]

Yao, E.

Zamponi, F.

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

Europhys. Lett.

L. Angelani, L. Casetti,M. Pettini, G. Ruocco, F. Zamponi, "Topological signature of first-order phase transitions in a mean-field model," Europhys. Lett. 6, 775-781 (2003).
[CrossRef]

IBM J. Res. Dev.

L.B. Lesem, P.M. Hirsch, J.A. Jordan "The kinoform: a new wavefront reconstruction device," IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Meas. Sci. Technol.

E. Martn-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, "Complex modulation characterization of liquid crystal devices by interferometric data correlation," Meas. Sci. Technol. 8, 764-772 (1997).
[CrossRef]

Nature

D.G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Opt. Commun.

J. Curtis, B.A. Koss, D.G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175, (2002).
[CrossRef]

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

T. Haist, M. Schönleber, H.J. Tiziani, "Computer-generated holograms from 3D-objects written on twistednematic liquid crystal displays," Opt. Commun. 140, 299-308 (1997).
[CrossRef]

M. Meister and R. J. Winfield, "Novel approaches to direct search algorithms for the design of diffractive optical elements," Opt. Commun. 203, 3949 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

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

Other

J.W. Goodman, "Introduction to Fourier Optics," McGraw-Hill (1996).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic representation of Fourier optics propagation from SLM plane (back focal plane) to the front focal plane of the optical system.

Fig. 2.
Fig. 2.

Optimization progress for GSW algorithm.

Fig. 3.
Fig. 3.

Experimental setup for holographic optical trapping: L1,L2,L3,L4: lenses; P, A: linear polarizers; M1: dichroic mirror; M2: dielectric mirror; MO: microscope objective.

Fig. 4.
Fig. 4.

Experimental determination of light distribution on trapping plane. For each algorithm we report the raw image of laser spots (left) together with the corrected (see text) values for trap intensities (Im ) represented in the gray level of square tiles centered at the corresponding lattice site.

Tables (2)

Tables Icon

Table 1. Summary of theoretical performances of investigated algorithms. The target trap structure is a 10 × 10 square grid. Column 2 contains a 100 × 100 detail of the total 768 × 768 hologram. Performance parameters after K (column 6) iterations are reported in columns 3,4,5. Computational cost scaling is reported in column 6 where: M=number of traps, N=number of pixels in hologram, K=number of iterations, P=number of gray levels (256 here).

Tables Icon

Table 2. Summary of experimental performances of investigated algorithms.

Equations (20)

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

v m = e i 2 π ( 2 f + z m ) λ i d 2 λ f j = 1 , N u e i ( ϕ j Δ j m )
Δ j m = π z m λ f 2 ( x j 2 + y j 2 ) + 2 π λ f ( x j x m + y j y m )
V m = j = 1 , N 1 N e i ( ϕ j Δ j m )
e = m I m , u = 1 max [ I m ] min [ I m ] max [ I m ] + min [ I m ] , σ = 100 ( I I ) 2 I
ϕ j = Δ j m j
ϕ j m Re { V m } = Re { i e i ϕ j N m e i Δ j m } = 0
ϕ j ¯ = arg [ m e i Δ j m ] + n j π , n j = 0,1
2 ϕ j ϕ k m Re { V m } | ϕ j = ϕ j ¯ = δ j k ( 1 ) n j 1 N m e i Δ j m
ϕ j = arg [ m e i Δ j m ]
ϕ j = arg [ m e i ( Δ j m + θ m ) ) ]
ϕ j m V m = Re { i e i ϕ j N m e i Δ j m V m * V m } = 0
ϕ j ¯ = arg [ m e i Δ j m V m V m ] + n j π , n j = 0,1
2 ϕ j ϕ k m V m | ϕ j = ϕ j ¯ = δ j k ( 1 ) n j 1 N m e i Δ j m V m * V m + o ( 1 N 2 )
ϕ j = arg [ m e i Δ j m V m V m ]
ϕ j [ ( 1 ξ ) m V m + ξ m log V m ] = Re { i e i ϕ j N m e i Δ j m V m * V m ( 1 ξ + ξ V m ) } = 0
ϕ j = arg [ m e i Δ j m V m V m ( 1 ξ + ξ V m ) ]
I f σ
ϕ j = arg [ m e i Δ j m w m V m V m ]
0 th step w m 0 = 1 , ϕ j 0 = ϕ j S R
kth step w m k = w m k 1 V m k 1 V m k 1 , ϕ j k = arg [ m e i Δ j m w m k V m k 1 V m k 1 ]

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