Abstract

The random mask encoding technique of multiplexing phase-only filters can be easily adapted to the generation of holographic optical tweezers. The result is a direct, non-iterative and extremely fast algorithm that can be used for computing arbitrary arrays of optical traps. Additional benefits include the possibility of modifying any existing hologram to quickly add more trapping sites and the inexistence of ghost traps or replicas.

© 2006 Optical Society of America

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References

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  1. A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
    [CrossRef] [PubMed]
  2. M. J. Lang and S. M. Block, "Resource letter: LBOT-1: Laser-based optical tweezers," Am. J. Phys. 71, 201-215 (2003).
    [CrossRef]
  3. K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  4. W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
    [CrossRef]
  5. S. M. Block, "Constructing optical tweezers," in Cell Biology: A Laboratory Manual, D. Spector, R. Goldman, and L. Leinward, eds. (Cold Spring Harbor Press, Cold Spring Harbor, NY, 1998).
  6. E. Fällman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=ao-36-10-2107
    [CrossRef] [PubMed]
  7. M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, "Optical particle trapping with computer-generated holograms written on a liquid-crystal display," Opt. Lett. 24, 608-610 (1999), http://www.opticsinfobase.org/abstract.cfm?URI=ol-24-9-608
    [CrossRef]
  8. D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
    [CrossRef] [PubMed]
  9. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  10. R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
    [CrossRef]
  11. K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
    [CrossRef]
  12. E. Martín-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]
  13. L. Neto, D. Roberge, and Y. Sheng, "Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television," Appl. Opt. 34, 1944- (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-11-1944
    [CrossRef] [PubMed]
  14. N. Konforti, E. Marom, and S. Wu, "Phase-only modulation with twisted nematic liquid-crystal spatial light modulators," Opt. Lett. 13, 251- (1996), http://www.opticsinfobase.org/abstract.cfm?URI=ol-13-3-251
    [CrossRef]
  15. G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. J. Laczik, M. J. Padgett, and J. Courtial, "Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping," Opt. Express 12,1665-1670 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1665
    [CrossRef] [PubMed]
  16. M. Polin, K. Ladavac, S. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13,5831-5845 (2005),
    [CrossRef] [PubMed]
  17. http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5831
    [CrossRef] [PubMed]
  18. J. Curtis, C. Schmitz, and J. Spatz, "Symmetry dependence of holograms for optical trapping," Opt. Lett. 30, 2086-2088 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-16-2086
    [CrossRef]
  19. K. Visscher, S. P. Gross, and S. M. Block "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
    [CrossRef]
  20. R. Eriksen, P. Mogensen, and J. Glückstad, "Multiple-beam optical tweezers generated by the generalized phase-contrast method," Opt. Lett. 27, 267-269 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=ol-27-4-267
    [CrossRef]
  21. P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
    [CrossRef] [PubMed]
  22. J. Davis and D. Cottrell, "Random mask encoding of multiplexed phase-only and binary phase-only filters," Opt. Lett. 19, 496- (1994), http://www.opticsinfobase.org/abstract.cfm?URI=ol-19-7-496
  23. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

2005 (3)

2004 (2)

2003 (3)

M. J. Lang and S. M. Block, "Resource letter: LBOT-1: Laser-based optical tweezers," Am. J. Phys. 71, 201-215 (2003).
[CrossRef]

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

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

2002 (3)

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

W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

R. Eriksen, P. Mogensen, and J. Glückstad, "Multiple-beam optical tweezers generated by the generalized phase-contrast method," Opt. Lett. 27, 267-269 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=ol-27-4-267
[CrossRef]

1999 (1)

1997 (3)

E. Fällman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=ao-36-10-2107
[CrossRef] [PubMed]

E. Martín-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]

A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
[CrossRef] [PubMed]

1996 (1)

K. Visscher, S. P. Gross, and S. M. Block "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

1990 (1)

K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Ashkin, A.

A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
[CrossRef] [PubMed]

Axner, O.

Block, S. M.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

M. J. Lang and S. M. Block, "Resource letter: LBOT-1: Laser-based optical tweezers," Am. J. Phys. 71, 201-215 (2003).
[CrossRef]

K. Visscher, S. P. Gross, and S. M. Block "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Carnicer, A.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

E. Martín-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]

Courtial, J.

Curtis, J.

Curtis, J. E.

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

Daria, V. R.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef] [PubMed]

Eriksen, R.

Fällman, E.

Gibson, G.

Glückstad, J.

Grange, W.

W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Grier, D. G.

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

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

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

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Güntherodt, H.

W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Haist, T.

Hegner, M.

W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Husale, S.

W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Jordan, P.

Juvells, I.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

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

Labastida, I.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

Laczik, Z. J.

Ladavac, K.

Lang, M. J.

M. J. Lang and S. M. Block, "Resource letter: LBOT-1: Laser-based optical tweezers," Am. J. Phys. 71, 201-215 (2003).
[CrossRef]

Leach, J.

Lee, S.

Lu, K.

K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Martín-Badosa, E.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

E. Martín-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]

Mogensen, P.

Neuman, K. C.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Padgett, M. J.

Polin, M.

Reicherter, M.

Rodrigo, P. J.

P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef] [PubMed]

Roichman, Y.

Saleh, B. E. A.

K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Schmitz, C.

Sinclair, G.

Spatz, J.

Tiziani, H.

Tudela, R.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

Vallmitjana, S.

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

E. Martín-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]

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Wagemann, E.

Yao, E.

Am. J. Phys. (1)

M. J. Lang and S. M. Block, "Resource letter: LBOT-1: Laser-based optical tweezers," Am. J. Phys. 71, 201-215 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Visscher, S. P. Gross, and S. M. Block "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

R. Tudela, E. Martín-Badosa, I. Labastida, S. Vallmitjana, I. Juvells, and A. Carnicer, "Full complex Fresnel holograms displayed on liquid crystal devices," J. Opt. A: Pure Appl. Opt. 5, S189-S194 (2003).
[CrossRef]

Meas. Sci. Technol. (1)

E. Martín-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 (1)

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

Opt. Commun. (1)

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

Opt. Eng. (1)

K. Lu and B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Opt. Eng. 29, 240-246 (1990).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Proc. Natl. Acad. Sci. USA (1)

A. Ashkin, "Optical trapping and manipulation of neutral particles using lasers," Proc. Natl. Acad. Sci. USA 94, 4853-4860 (1997).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

W. Grange, S. Husale, H. Güntherodt, and M. Hegner, "Optical tweezers system measuring the change in light momentum flux," Rev. Sci. Instrum. 73, 2308-2316 (2002).
[CrossRef]

Other (6)

S. M. Block, "Constructing optical tweezers," in Cell Biology: A Laboratory Manual, D. Spector, R. Goldman, and L. Leinward, eds. (Cold Spring Harbor Press, Cold Spring Harbor, NY, 1998).

http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-15-5831
[CrossRef] [PubMed]

L. Neto, D. Roberge, and Y. Sheng, "Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television," Appl. Opt. 34, 1944- (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-11-1944
[CrossRef] [PubMed]

N. Konforti, E. Marom, and S. Wu, "Phase-only modulation with twisted nematic liquid-crystal spatial light modulators," Opt. Lett. 13, 251- (1996), http://www.opticsinfobase.org/abstract.cfm?URI=ol-13-3-251
[CrossRef]

J. Davis and D. Cottrell, "Random mask encoding of multiplexed phase-only and binary phase-only filters," Opt. Lett. 19, 496- (1994), http://www.opticsinfobase.org/abstract.cfm?URI=ol-19-7-496

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

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1.

Optical setup for generating holographic optical tweezers.

Fig. 2.
Fig. 2.

Encoding two linear phases by complementary random binary masks.

Fig. 3.
Fig. 3.

(a) Binary mask, 256×256 pixels. (b) Magnitude squared of its Fourier transform in logarithmic scale.

Fig. 4.
Fig. 4.

(a) Hologram encoding an array of 4 optical traps and b) resulting traps.

Fig. 5.
Fig. 5.

New trapping site added to a Gerchberg-Saxton hologram.

Fig. 6.
Fig. 6.

(2.21 MB) Real-time, interactive manipulation of two yeast cells by means of tweezers generated with the algorithm.

Equations (7)

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

E ( x , y ) = ∫∫ R ( u , v ) e i 2 π λf ' ( ux + vy ) dudv .
R ( u , v ) = k = 1 N e i 2 π λf ' ( x k u + y k v ) ,
E ( x , y ) = k = 1 N ∫∫ e i 2 π λf ' [ ( x x k ) u + ( y y k ) v ] dudv = k = 1 N δ ( x x k , y y k ) .
R ( u , v ) = k = 1 N h k ( u , v ) e i 2 π λf ' ( x k u + y k v ) ,
h k ( u , v ) = { 1 iff ( u , v ) I k 0 otherwise ,
I l I m = l , m l m and k = 1 N I k = 2 .
E ( x , y ) = k = 1 N H k ( x x k , y y k ) ,

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