Abstract

We report the extension to a multi-axes exploration of the potential well reconstruction method against drag force to simultaneously characterize the potential wells of several trapping sites generated with holographic optical tweezers. The final result is a robust, fast and automatic procedure we use to characterize holographic tweezers. We mainly focus on the reliability of the method and its application to address the dependence of the diffraction efficiency with the trap position in a given holographic traps pattern.

© 2008 Optical Society of America

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  1. P. N. Lebedev, "Experimental examination of light pressure," Annalen der Physik 6, 433 (1901).
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  3. G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
    [CrossRef] [PubMed]
  4. K. Svoboda and S. M. Block, "Force and velocity measured for single kinesin molecules," Cell 77, 773-784 (1994).
    [CrossRef] [PubMed]
  5. R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
    [CrossRef] [PubMed]
  6. J. C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended dna molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
    [CrossRef] [PubMed]
  7. M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005)
    [CrossRef] [PubMed]
  8. N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
    [CrossRef]
  9. E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instr. 69, 1974-1977 (1998).
    [CrossRef]
  10. D. G. Grier, "A revolution in optical manipulation," Nature (London) 424, 810-816 (2003).
    [CrossRef] [PubMed]
  11. A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
    [CrossRef] [PubMed]
  12. M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
    [CrossRef]
  13. K. Berg-Sorensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
    [CrossRef]
  14. M. Klein, M. Andersson, O. Axner, and E. Fallman, "Dual-trap technique for reduction of low-frequency noise in force measuring optical tweezers," Appl. Opt. 46, 405-412 (2007).
    [CrossRef] [PubMed]
  15. H. Faxen, "Die Bewegung einer starren Kugel langs der Achse eines mit zahrer Flbsigkeit gefiillten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).
  16. S. Keen, J. Leach, G. Gibson, and M. J. Padgett, "Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers," J. Opt. A Pure Appl. Opt. 9, S264-S266 (2007).
    [CrossRef]
  17. W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).
  18. Y. K. Nahmias, B. Zhi Gao, and D. J. Odde, "Dimensionless parameters for the design of optical traps and laser guidance Ssstems," Appl. Opt. 43, 3999-4006 (2004).
    [CrossRef] [PubMed]
  19. F. Belloni and S. Monneret, "Quadrant kinoform: an approach to multiplane dynamic three-dimensional holographic trapping," Appl. Opt. 46, 4587-4593 (2007).
    [CrossRef] [PubMed]
  20. S. Monneret, F. Belloni, and O. Soppera. "Combining fluidic reservoirs and optical tweezers to control beads/living cells contacts," Microfluid. Nanofluid. (2007).
    [CrossRef]

2007 (3)

2005 (1)

2004 (2)

2003 (1)

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

2002 (3)

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

2001 (1)

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

2000 (2)

J. C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended dna molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

1998 (1)

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

1996 (1)

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

1994 (1)

K. Svoboda and S. M. Block, "Force and velocity measured for single kinesin molecules," Cell 77, 773-784 (1994).
[CrossRef] [PubMed]

1986 (1)

1923 (1)

H. Faxen, "Die Bewegung einer starren Kugel langs der Achse eines mit zahrer Flbsigkeit gefiillten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).

1901 (1)

P. N. Lebedev, "Experimental examination of light pressure," Annalen der Physik 6, 433 (1901).

Andersson, M.

Arimondo, E.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Ashkin, A.

Axner, O.

Ballerini, R.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Belloni, F.

Berg-Sorensen, K.

K. Berg-Sorensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Bernet, S.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Bjorkholm, J. E.

Block, S. M.

K. Svoboda and S. M. Block, "Force and velocity measured for single kinesin molecules," Cell 77, 773-784 (1994).
[CrossRef] [PubMed]

Capitanio, M.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Chu, S.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

Dufresne, E. R.

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

Dunlap, D.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Dziedzic, J. M.

Fallman, E.

Faxen, H.

H. Faxen, "Die Bewegung einer starren Kugel langs der Achse eines mit zahrer Flbsigkeit gefiillten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).

Finer, J. T.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Finzi, L.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Flyvbjerg, H.

K. Berg-Sorensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Gallet, F.

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

Gibson, G.

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

Giuntini, M.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Grier, D.

Grier, D. G.

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

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

Hecker, N.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Henon, S.

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

Keen, S.

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

Klein, M.

Ladavac, K.

Leach, J.

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

Lebedev, P. N.

P. N. Lebedev, "Experimental examination of light pressure," Annalen der Physik 6, 433 (1901).

Lee, S.-H.

Lenormand, G.

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

Malagnino, N.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Meiners, J. C.

J. C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended dna molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

Monneret, S.

Nahmias, Y. K.

Odde, D. J.

Padgett, M. J.

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

Pavone, F. S.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Pesce, G.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Polin, M.

Quake, S. R.

J. C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended dna molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

Richert, A.

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

Ritsch-Marte, M.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Rohrbach, A.

Roichman, Y.

Romano, G.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Sasso, A.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Simeon, J.

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

Simmons, R. M.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Singer, W.

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

Spudich, J. A.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Svoboda, K.

K. Svoboda and S. M. Block, "Force and velocity measured for single kinesin molecules," Cell 77, 773-784 (1994).
[CrossRef] [PubMed]

Zhi Gao, B.

Annalen der Physik (1)

P. N. Lebedev, "Experimental examination of light pressure," Annalen der Physik 6, 433 (1901).

Appl. Opt. (4)

Ark. Mat. Astron. Fys. (1)

H. Faxen, "Die Bewegung einer starren Kugel langs der Achse eines mit zahrer Flbsigkeit gefiillten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).

Biophys. J. (2)

G. Lenormand, S. Henon, A. Richert, J. Simeon, and F. Gallet, "Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton," Biophys. J. 81, 43-56 (2001).
[CrossRef] [PubMed]

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813-1822 (1996).
[CrossRef] [PubMed]

Cell (1)

K. Svoboda and S. M. Block, "Force and velocity measured for single kinesin molecules," Cell 77, 773-784 (1994).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

W. Singer, S. Bernet, N. Hecker, and M. Ritsch-Marte, "Three-dimensional force calibration of optical tweezers," J. Mod. Opt. 47, 2921-2931 (2000).

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

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

Nature (London) (1)

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

Opt. Commun. (1)

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, "Measurements of trapping efficiency and stiffness in optical tweezers," Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. C. Meiners and S. R. Quake, "Femtonewton force spectroscopy of single extended dna molecules," Phys. Rev. Lett. 84, 5014-5017 (2000).
[CrossRef] [PubMed]

Rev. Sci. Instr. (1)

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

Rev. Sci. Instrum. (2)

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

K. Berg-Sorensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004).
[CrossRef]

Other (1)

S. Monneret, F. Belloni, and O. Soppera. "Combining fluidic reservoirs and optical tweezers to control beads/living cells contacts," Microfluid. Nanofluid. (2007).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Calibration technique basic steps. (a) Uniform speed motions are applied along two orthogonal axes in four different directions imparting a calibrated drag force onto the trapped object; (b) Time-Lapse fluorescent imaging provides a stack of raw images where we select one or more regions of interest; (c) Matlab tracking algorithm performs an image segmentation and (d) evaluates the position of the bead center.

Fig. 2.
Fig. 2.

Tracking algorithm calibration. Left, the position of a bead attached to the coverslip is tracked when the stage translates along the x axis in steps of 35nm. Right, a zoom shows the algorithm accuracy to be approximately ten nanometers

Fig. 3.
Fig. 3.

Algorithm output 1. Left, the scattering plot of the x,y bead coordinates evaluated by the image processing algorithm. Right, the conceptual image of a trapped bead climbing up the walls of a potential well as the result of an imparted external force, in our case a calibrated drag force represented by the black arrows.

Fig. 4.
Fig. 4.

Algorithm output 2. Left, the x,y bead coordinates are plotted separately versus the image counter, i.e. time. The black dots show the selected values, usually tens per peak, which are averaged to extract the equilibrium position corresponding to a specific drag force. This mean values are then used to perform a linear regression and extract the stiffness of the selected trap, right figure.

Fig. 5.
Fig. 5.

Left, trap stiffness versus the total laser power in the sample, for two beads trapped simultaneously. Right the traps pattern used during the experiment. Distance to coverslip is 10µm.

Fig. 6.
Fig. 6.

The normalized stiffness of an holographic trap is reported as a function of the distance with respect to the zero order. Distance to coverslip is 10µm.

Fig. 7.
Fig. 7.

Multiple trap characterization. Left, the trap stiffness mainly depends on the trap position relative to the optical axis, or zero order (bead 2), because of variations in the diffraction efficiency. Right the traps pattern used during the experiment. Distance to coverslip is 10µm.

Fig. 8.
Fig. 8.

Ghost traps characterization. The distance of the first order from the center is ≈5.5µm.

Fig. 9.
Fig. 9.

(a) Principle of beads confinement. (b) Picture of the chamber with detail of the entrance. (c) Picture taken in working conditions but with a 4× objective, low white light to see the microstereolitographic structure and fluorescence light to image the beads confined outside the chamber.

Tables (1)

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Table 1. Characterization of an holographic trap and its residual diffraction orders.

Equations (2)

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F s p r i n g ( r ) = k · r
U s p r i n g ( r ) = 1 2 k · r 2 = 1 2 F s p r i n g r

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