Abstract

We firstly demonstrate the three-dimensional (3D) measurement of a nanometer-sized sphere held in optical tweezers in water using an in-line digital holographic microscope with a green light emitting diode. Suppressing the movement with optical tweezers enabled us to detect the three-dimensional position of a polystyrene sphere with a diameter of 200nm. The positioning resolutions of the microscope were 3.2nm in the transverse direction and 3.4nm in the axial direction, from the standard deviation of measurements of the 200nm sphere fixed on glass. Changes in the Brownian motion in response to a change in the trapping laser power were measured. We also demonstrated that this holographic measurement is an effective method for determining the threshold power of the optical trapping.

© 2011 Optical Society of America

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  36. S. Keen, J. Leach, G. Gibson, and M. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” Pure Appl. Opt. 9, S264–S266(2007).
    [CrossRef]

2011

2010

2009

2008

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[CrossRef] [PubMed]

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

2007

S. H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007).
[CrossRef] [PubMed]

S. Keen, J. Leach, G. Gibson, and M. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” Pure Appl. Opt. 9, S264–S266(2007).
[CrossRef]

2006

F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, and O. Monnom, “Digital holographic microscopy with reduced spatial coherence for three dimensional particle flow analysis,” Appl. Opt. 45, 864–871 (2006).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
[CrossRef] [PubMed]

S. F. Tolic-Norrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

I. Tinoco, Jr., D. Collin, and P. T. X. Li, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2006).
[CrossRef]

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801–803 (2006).
[CrossRef] [PubMed]

2005

2004

K. Ladavac, K. Kasza, and D. G. Grier, “Sorting mesoscopic objects with periodic potential landscapes: optical fractionation,” Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

2003

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[CrossRef] [PubMed]

1999

Y. Hayasaki, M. Itoh, T. Yatagai, and N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[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]

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

J. S. Meiners and S. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

1998

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

1996

B. Skarman, K. Wozniac, and J. Becker, “Simultaneous 3D-PIV and temperature measurement using a new CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6, (1996).
[CrossRef]

1994

1993

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of 18 kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef] [PubMed]

1990

1987

L. Onural and P. D. Scott, “Digital recording of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

1986

Agarwal, R.

Ashkin, A.

Becker, J.

B. Skarman, K. Wozniac, and J. Becker, “Simultaneous 3D-PIV and temperature measurement using a new CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6, (1996).
[CrossRef]

Bennink, M. L.

Bjorkholm, J. E.

Block, S. M.

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801–803 (2006).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of 18 kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), Chap. 4.

Bowman, R.

Callens, N.

Cheong, F. C.

Chu, S.

Clare, H.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

Collin, D.

I. Tinoco, Jr., D. Collin, and P. T. X. Li, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2006).
[CrossRef]

Cooper, J.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

Denk, W.

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[CrossRef] [PubMed]

Dixon, L.

Dubois, F.

Dufresne, E. R.

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

Dziedzic, J. M.

Flendrig, L.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

Florin, E. L.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

Flyvbjerg, H.

S. F. Tolic-Norrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Garcia-Sucerquia, J.

Gibson, G.

R. Bowman, G. Gibson, and M. Padgett, “Particle tracking stereomicroscopy in optical tweezers: control of trap shape,” Opt. Express 18, 11785–11790 (2010).
[CrossRef] [PubMed]

S. Keen, J. Leach, G. Gibson, and M. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” Pure Appl. Opt. 9, S264–S266(2007).
[CrossRef]

Gibson, G. M.

Gittes, F.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 3.10.

Greenleaf, W. J.

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801–803 (2006).
[CrossRef] [PubMed]

Grier, D. G.

Gutsche, C.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Haist, T.

Hajizadeh, F.

Hayasaki, Y.

M. Miyazaki and Y. Hayasaki, “Motion control of low-index microspheres in liquid based on optical repulsive force of a focused beam array,” Opt. Lett. 34, 821–823 (2009).
[CrossRef] [PubMed]

Y. Hayasaki, M. Itoh, T. Yatagai, and N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Hörber, J. K. H.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

Howard, J.

S. F. Tolic-Norrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Hoyos, M.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), Chap. 4.

Huisstede, J. H. G.

Itoh, M.

Y. Hayasaki, M. Itoh, T. Yatagai, and N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Jericho, M. H.

Jericho, S. K.

Jordan, P.

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

Jülicher, F.

S. F. Tolic-Norrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Jüptner, W.

Kasza, K.

K. Ladavac, K. Kasza, and D. G. Grier, “Sorting mesoscopic objects with periodic potential landscapes: optical fractionation,” Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

Keen, S.

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[CrossRef] [PubMed]

S. Keen, J. Leach, G. Gibson, and M. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” Pure Appl. Opt. 9, S264–S266(2007).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), Chap. 3.

Keyser, U. F.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Klages, P.

Kremer, F.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Kreuzer, H. J.

Krishnatreya, B. J.

Kurowski, P.

Ladavac, K.

R. Agarwal, K. Ladavac, Y. Roichman, G. Yu, C. M. Lieber, and D. G. Grier, “Manipulation and assembly of nanowires with holographic optical traps,” Opt. Express 13, 8906–8912 (2005).
[CrossRef] [PubMed]

K. Ladavac, K. Kasza, and D. G. Grier, “Sorting mesoscopic objects with periodic potential landscapes: optical fractionation,” Phys. Rev. E 70, 010901(R) (2004).
[CrossRef]

Leach, J.

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, and M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16, 14561–14570 (2008).
[CrossRef] [PubMed]

S. Keen, J. Leach, G. Gibson, and M. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” Pure Appl. Opt. 9, S264–S266(2007).
[CrossRef]

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

Lee, S. H.

Li, P. T. X.

I. Tinoco, Jr., D. Collin, and P. T. X. Li, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2006).
[CrossRef]

Lieber, C. M.

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[CrossRef] [PubMed]

Meiners, J. S.

J. S. Meiners and S. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

Miyazaki, M.

Monnom, O.

Nishida, N.

Y. Hayasaki, M. Itoh, T. Yatagai, and N. Nishida, “Nonmechanical optical manipulation of microparticle using spatial light modulator,” Opt. Rev. 6, 24–27 (1999).
[CrossRef]

Onural, L.

L. Onural and P. D. Scott, “Digital recording of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Otto, O.

O. Otto, C. Gutsche, F. Kremer, and U. F. Keyser, “Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis,” Rev. Sci. Instrum. 79, 023710 (2008).
[CrossRef] [PubMed]

Padgett, M.

R. Bowman, G. Gibson, and M. Padgett, “Particle tracking stereomicroscopy in optical tweezers: control of trap shape,” Opt. Express 18, 11785–11790 (2010).
[CrossRef] [PubMed]

S. Keen, J. Leach, G. Gibson, and M. Padgett, “Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers,” Pure Appl. Opt. 9, S264–S266(2007).
[CrossRef]

P. Jordan, H. Clare, L. Flendrig, J. Leach, J. Cooper, and M. Padgett, “Permanent 3D microstructures in a polymeric host created using holographic optical tweezers,” J. Mod. Opt. 51, 627–632 (2004).

Padgett, M. J.

Pavone, F. S.

S. F. Tolic-Norrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[CrossRef]

Pralle, A.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

Prummer, M.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44, 378–386 (1999).
[CrossRef] [PubMed]

Quake, S.

J. S. Meiners and S. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[CrossRef]

Reicherter, M.

Reihani, S. N. S.

Roichman, Y.

Schäffer, E.

S. F. Tolic-Norrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77, 103101 (2006).
[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]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of 18 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 18 kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[CrossRef] [PubMed]

Schnars, U.

Scott, P. D.

L. Onural and P. D. Scott, “Digital recording of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Skarman, B.

B. Skarman, K. Wozniac, and J. Becker, “Simultaneous 3D-PIV and temperature measurement using a new CCD based holographic interferometer,” Flow Meas. Instrum. 7, 1–6, (1996).
[CrossRef]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426, 421–424 (2003).
[CrossRef] [PubMed]

Stelzer, E. H. K.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Flow chart.

Fig. 3
Fig. 3

(a) Hologram of a polystyrene sphere with a diameter of 200 nm and (b), (c), (d) its diffraction images at distances z = 429 nm , 689 nm , and 1300 nm , respectively. The square indicated in the dashed line in (c) is clipped as the template.

Fig. 4
Fig. 4

Three-dimensional position detection of a nanoparticle: (a) x direction, (b) y direction, and (c) z direction.

Fig. 5
Fig. 5

Movement of a sphere in the focal spot volume of a trapping laser beam at different powers: (a)  38 mW , (b)  48 mW , and (c)  128 mW .

Fig. 6
Fig. 6

Change of the Brownian motion with a change of the trapping laser power and the diameter of the sphere: (a)  200 nm and (b)  500 nm .

Equations (7)

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| u k ( x , y , z ) | 2 = | A k ( r ) exp ( i k z ) + A k ( s ) x 2 + y 2 exp ( i k x 2 + y 2 2 z ) | 2 = A k ( r ) 2 + A k ( s ) 2 x 2 + y 2 + 2 A k ( r ) A k ( s ) x 2 + y 2 cos k ( z x 2 + y 2 2 z ) ,
| u ( x , y , z ) | 2 = k | u k ( x , y , z ) | 2 d k .
u ( x , y , z ) = I 1 [ U ( u , v , 0 ) G ( u , v , z ) ] ,
U ( u , v , 0 ) = I [ u ( x , y , 0 ) ] ,
G ( u , v , z ) = exp ( 2 π j 1 / λ 2 u 2 v 2 z ) ,
D ( x , y , z ) = ζ = 0 M 1 ξ = 0 M 1 { I ( x + ξ , y + ζ , z ) T ( ξ , ζ , z 0 ) } 2 .
x sub = D ( x min + Δ x ) D ( x min Δ x ) 2 D ( x min Δ x ) 4 D ( x min ) + 2 D ( x min + Δ x ) ,

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