Shack-Hartmann multiple-beam optical tweezers

Peter John Rodrigo; René Lynge Eriksen; Vincent Ricardo Daria; Jesper Glückstad

doi:10.1364/OE.11.000208

Abstract

We introduce a new method for generating an array of programmable optical tweezers based on the principle of the Shack-Hartmann wave front sensor. In this approach, a lenslet array divides a laser beam into multiple point sources that are subsequently imaged onto the sample plane of an inverted microscope. This results in a matrix of tightly focused beams used for local confinement and manipulation of micron-sized dielectric particles in an aqueous solution. Using a spatial light-modulating device, the phase profile of the laser beam is computer-encoded providing for controlled spatial deflections of the trapping beams.

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References

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Publication

A. Ashikin, 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 (1986).
[Crossref]
R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).
S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514 (1989).
[Crossref] [PubMed]
M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]
A. Terray, J. Oakey, and D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841 (2002).
[Crossref] [PubMed]
J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).
J. D. Mansell, et al., “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor,” Appl. Opt. 40366 (2001).
[Crossref]
R. K. Tyson. Principles of Adaptive Optics 2nd Ed. (Academic Press, 1998).
J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949 (1994).
[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 (1999).
[Crossref]
R. L. Eriksen, V. R. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-597.
[Crossref] [PubMed]
P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1550.
[Crossref] [PubMed]
Y. Ogura, K. Kagawa, and J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430 (2001).
[Crossref]
G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170 (1994).
[Crossref] [PubMed]
S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]
S. Sinzinger and J. Jahns. Microoptics (Wiley-VCH, 1991).
S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]
J. P. Hoogenboom, et al., “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828 (2002).
[Crossref]
R. Dumke, et al., “Micro-optical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits,” Phys. Rev. Lett.89, 097903 (2002).
[Crossref] [PubMed]

2002 (4)

A. Terray, J. Oakey, and D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841 (2002).
[Crossref] [PubMed]

R. L. Eriksen, V. R. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-597.
[Crossref] [PubMed]

P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1550.
[Crossref] [PubMed]

J. P. Hoogenboom, et al., “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828 (2002).
[Crossref]

2001 (2)

Y. Ogura, K. Kagawa, and J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430 (2001).
[Crossref]

J. D. Mansell, et al., “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor,” Appl. Opt. 40366 (2001).
[Crossref]

1999 (2)

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]

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 (1999).
[Crossref]

1997 (1)

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

1996 (1)

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

1994 (2)

G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170 (1994).
[Crossref] [PubMed]

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949 (1994).
[Crossref]

1989 (1)

S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514 (1989).
[Crossref] [PubMed]

1987 (1)

J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).

1986 (1)

A. Ashikin, 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 (1986).
[Crossref]

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Allen, J. G.

J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).

Ashikin, A.

A. Ashikin, 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 (1986).
[Crossref]

Berg, H. C.

S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514 (1989).
[Crossref] [PubMed]

Bille, J. F.

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949 (1994).
[Crossref]

Bjorkholm, J. E.

A. Ashikin, 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 (1986).
[Crossref]

Blair, H. C.

S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514 (1989).
[Crossref] [PubMed]

Block, S. M.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514 (1989).
[Crossref] [PubMed]

Chu, S.

A. Ashikin, 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 (1986).
[Crossref]

Daria, V. R.

R. L. Eriksen, V. R. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-597.
[Crossref] [PubMed]

P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1550.
[Crossref] [PubMed]

Dumke, R.

R. Dumke, et al., “Micro-optical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits,” Phys. Rev. Lett.89, 097903 (2002).
[Crossref] [PubMed]

Dziedzic, J. M.

A. Ashikin, 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 (1986).
[Crossref]

Eriksen, R. L.

R. L. Eriksen, V. R. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-597.
[Crossref] [PubMed]

P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1550.
[Crossref] [PubMed]

Fujioka, S.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

Gallet, F.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

Hénon, S.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]

Honma, M.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

Hoogenboom, J. P.

J. P. Hoogenboom, et al., “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828 (2002).
[Crossref]

Jahns, J.

S. Sinzinger and J. Jahns. Microoptics (Wiley-VCH, 1991).

Kagawa, K.

Y. Ogura, K. Kagawa, and J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430 (2001).
[Crossref]

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

Lenormand, G.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]

Liang, J.

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949 (1994).
[Crossref]

Love, G. D.

G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170 (1994).
[Crossref] [PubMed]

Major, J. V.

G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170 (1994).
[Crossref] [PubMed]

Mansell, J. D.

J. D. Mansell, et al., “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor,” Appl. Opt. 40366 (2001).
[Crossref]

Marr, D. W. M.

A. Terray, J. Oakey, and D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841 (2002).
[Crossref] [PubMed]

Masuda, S.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

Nose, T.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

Oakey, J.

A. Terray, J. Oakey, and D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841 (2002).
[Crossref] [PubMed]

Ogura, Y.

Y. Ogura, K. Kagawa, and J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430 (2001).
[Crossref]

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Purvis, A.

G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170 (1994).
[Crossref] [PubMed]

Reicherter, M.

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 (1999).
[Crossref]

Richert, A.

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]

Rodrigo, P. J.

P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1550.
[Crossref] [PubMed]

Sato, S.

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

Schmutz, L.

J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Sinzinger, S.

S. Sinzinger and J. Jahns. Microoptics (Wiley-VCH, 1991).

Tanida, J.

Y. Ogura, K. Kagawa, and J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430 (2001).
[Crossref]

Terray, A.

A. Terray, J. Oakey, and D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841 (2002).
[Crossref] [PubMed]

Tiziani, H. J.

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 (1999).
[Crossref]

Tyson, R. K.

R. K. Tyson. Principles of Adaptive Optics 2nd Ed. (Academic Press, 1998).

Vankevics, A.

J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).

Wagemann, E. U.

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 (1999).
[Crossref]

Wang, M. D.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

Wormell, D.

J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).

Yin, H.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

Appl. Opt. (2)

J. D. Mansell, et al., “Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a Shack-Hartmann wave-front sensor,” Appl. Opt. 40366 (2001).
[Crossref]

Y. Ogura, K. Kagawa, and J. Tanida, “Optical manipulation of microscopic objects by means of vertical-cavity surface-emitting laser array sources,” Appl. Opt. 40, 5430 (2001).
[Crossref]

Appl. Phys. Lett. (1)

J. P. Hoogenboom, et al., “Patterning surfaces with colloidal particles using optical tweezers,” Appl. Phys. Lett. 80, 4828 (2002).
[Crossref]

Biophys. J. (1)

S. Hénon, G. Lenormand, A. Richert, and F. Gallet, “A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers,” Biophys. J. 76, 1145 (1999).
[Crossref] [PubMed]

Biophysics J. (1)

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophysics J. 72, 1335 (1997).
[Crossref]

J. Opt. Soc. Am. (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

J. Opt. Soc. Am. A (1)

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949 (1994).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Masuda, S. Fujioka, M. Honma, T. Nose, and S. Sato, “Dependence of optical properties on the device and material parameters in liquid crystal microlenses,” Jpn. J. Appl. Phys. 35, 4668 (1996).
[Crossref]

Nature (1)

S. M. Block, H. C. Blair, and H. C. Berg, “Compliance of bacterial flagella measured with optical tweezers,” Nature 338, 514 (1989).
[Crossref] [PubMed]

Opt. Express (2)

R. L. Eriksen, V. R. Daria, and J. Glückstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10, 597 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-597.
[Crossref] [PubMed]

P. J. Rodrigo, R. L. Eriksen, V. R. Daria, and J. Glückstad, “Interactive light-driven and parallel manipulation of inhomogeneous particles,” Opt. Express 10, 1550 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1550.
[Crossref] [PubMed]

Opt. Lett. (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 (1999).
[Crossref]

G. D. Love, J. V. Major, and A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170 (1994).
[Crossref] [PubMed]

A. Ashikin, 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 (1986).
[Crossref]

Proc. SPIE (1)

J. G. Allen, A. Vankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation”, Proc. SPIE, 739, 124, (1987).

Science (1)

A. Terray, J. Oakey, and D. W. M. Marr, “Microfluidic control using colloidal devices,” Science 296, 1841 (2002).
[Crossref] [PubMed]

Other (3)

R. K. Tyson. Principles of Adaptive Optics 2nd Ed. (Academic Press, 1998).

S. Sinzinger and J. Jahns. Microoptics (Wiley-VCH, 1991).

R. Dumke, et al., “Micro-optical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits,” Phys. Rev. Lett.89, 097903 (2002).
[Crossref] [PubMed]

Supplementary Material (2)

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» Media 2: MPG (1888 KB)

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Fig. 1. Block diagram for the proposed Shack-Hartmann-based optical tweezing methodology. The resulting xyz-deflectable beam spots are scaled onto the sample plane of a microscope.

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Fig. 2. Shack-Hartmann-type multiple-beam optical tweezers. Spatial Fourier-transforms of programmable phase gratings are imaged onto the tweezer plane for parallel particle trapping with fine positioning modality. In this case, the computer addresses the SLM in four quadrants for independent encoding of grating period and orientation. At the tweezer plane, this corresponds to a control in the magnitude and direction of each trapping beam deflection.

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Fig. 3. (MPEG, 1,739KB) Simultaneous trapping of four microspheres (encircled in the first frame) using a 2×2 Shack-Hartmann optical tweezer system. The white cross indicates one microsphere located at the bottom surface. During displacement of the sample stage, the out-of-focus particle moved to the left while the trapped microspheres remained in their respective trapping positions.

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Fig. 4. Wrapping of a linear phase function into an equivalent blazed phase grating (Modulo-2π). This blazing technique also applies in two-dimensions where ϕ=ϕ (x, y).

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Fig. 5. An example of computer-generated gray level pattern forming a 2×2 array of blazed phase gratings on the SLM. This defines the horizontal and vertical deflections of each of the four optical traps.

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Fig. 6. (MPEG, 1,889KB) Parallel trapping of polystyrene microspheres with independent deflection control. Shown at the right is a sequence of magnified images of one trapped particle (encircled in the left frame) illustrating different directions of deflection (magnitude ~ 1.5 µm).

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Equations (3)

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

Δ r_{ij} = \frac{λ f_{1}}{2 π} {(\frac{\partial ϕ}{\partial r})}_{ij}

θ_{ij} = \tan^{- 1} [\frac{{(\frac{\partial ϕ}{\partial y})}_{ij}}{{(\frac{\partial ϕ}{\partial x})}_{ij}}],

Δ r_{ij} = \frac{λ f_{l}}{T_{ij}} .

Abstract

References

2002 (4)

2001 (2)

1999 (2)

1997 (1)

1996 (1)

1994 (2)

1989 (1)

1987 (1)

1986 (1)

1971 (1)

Allen, J. G.

Ashikin, A.

Berg, H. C.

Bille, J. F.

Bjorkholm, J. E.

Blair, H. C.

Block, S. M.

Chu, S.

Daria, V. R.

Dumke, R.

Dziedzic, J. M.

Eriksen, R. L.

Fujioka, S.

Gallet, F.

Gelles, J.

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