Abstract

For optical tweezers, especially when used in biological studies, optimizing the trapping efficiency reduces photo damage or enables the generation of larger trapping forces. One important, yet not-well understood, tuning parameter is how much the laser beam needs to be expanded before coupling it into the trapping objective. Here, we measured the trap stiffness for 0.5–2 μm-diameter microspheres for various beam expansions. We show that the highest overall trapping efficiency is achieved by slightly under-filling a high-numerical aperture objective when using microspheres with a diameter corresponding to about the trapping-laser wavelength in the medium. The optimal filling ratio for the lateral direction depended on the microsphere size, whereas for the axial direction it was nearly independent. Our findings are in agreement with Mie theory calculations and suggest that apart from the choice of the optimal microsphere size, slightly under-filling the objective is key for the optimal performance of an optical trap.

© 2011 OSA

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References

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  1. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [CrossRef] [PubMed]
  2. N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
    [CrossRef]
  3. V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
    [CrossRef] [PubMed]
  4. A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
    [CrossRef]
  5. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
    [CrossRef] [PubMed]
  6. H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).
  7. M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
    [CrossRef]
  8. A. Samadi and N. S. Reihani, “Optimal beam diameter for optical tweezers,” Opt. Lett. 35, 1494–1496 (2010).
    [CrossRef] [PubMed]
  9. M. Jahnel, M. Behrndt, A. Jannasch, E. Schäffer, and S. Grill, “Measuring the complete force field of an optical trap,” Opt. Lett. 36, 1260–1262 (2011).
    [CrossRef] [PubMed]
  10. M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17, 17190–17199 (2009).
    [CrossRef] [PubMed]
  11. 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]
  12. V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
    [CrossRef] [PubMed]
  13. D. R. Skinner and R. E. Whitcher “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E: J. Sci. Instrum . 5, 237–238 (1972).
    [CrossRef]
  14. E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
    [CrossRef] [PubMed]
  15. S. F. Tolić-Nørrelykke, 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]
  16. S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007).
    [CrossRef] [PubMed]
  17. N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, and P. A. M. Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263–4269 (2006).
    [CrossRef] [PubMed]
  18. H. van de HulstLight Scattering by Small Particles (Dover Puplications, Inc., 1981).
  19. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
    [CrossRef]
  20. V. N. Mahajan, “Uniform versus Gaussian beams - a comparison of the effects of diffraction, obscuration, and aberrations,” J. Opt. Soc. Am. A 3, 470–485 (1986).
    [CrossRef]
  21. S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
    [CrossRef]
  22. A. Rohrbach, “Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
    [CrossRef] [PubMed]
  23. Note that version 1.0 of the optical tweezers computational toolbox (Ref. [19]) contained a power scaling error in the code which was corrected in version 1.1.
  24. J. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).
    [CrossRef]
  25. T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf . 79–80, 1005–1017 (2003).

2011 (1)

2010 (1)

2009 (1)

2008 (2)

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[CrossRef] [PubMed]

2007 (4)

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[CrossRef] [PubMed]

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[CrossRef] [PubMed]

S. N. S. Reihani and L. B. Oddershede, “Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations,” Opt. Lett. 32, 1998–2000 (2007).
[CrossRef] [PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

2006 (2)

N. B. Viana, M. S. Rocha, O. N. Mesquita, A. Mazolli, and P. A. M. Neto, “Characterization of objective transmittance for optical tweezers,” Appl. Opt. 45, 4263–4269 (2006).
[CrossRef] [PubMed]

S. F. Tolić-Nørrelykke, 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]

2005 (1)

A. Rohrbach, “Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

2003 (2)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf . 79–80, 1005–1017 (2003).

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

1999 (1)

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]

1998 (1)

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

1994 (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

1993 (1)

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

1992 (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

1986 (1)

1972 (1)

D. R. Skinner and R. E. Whitcher “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E: J. Sci. Instrum . 5, 237–238 (1972).
[CrossRef]

Allen, L.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

Ander, M.

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[CrossRef] [PubMed]

Behrndt, M.

Bing-Huan, M.

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

Block, S. M.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Bormuth, V.

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[CrossRef] [PubMed]

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[CrossRef] [PubMed]

A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
[CrossRef]

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

Cremer, C.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Dholakia, K.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

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. Tolić-Nørrelykke, 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]

Grill, S.

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf . 79–80, 1005–1017 (2003).

Hell, S.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Hong-Liang, R.

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[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.

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[CrossRef] [PubMed]

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[CrossRef] [PubMed]

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[CrossRef] [PubMed]

S. F. Tolić-Nørrelykke, 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]

A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
[CrossRef]

IM, K.-B.

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

Jahnel, M.

Jannasch, A.

Jian-Guang, W.

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

Jin-Hua, Z.

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

Joo, I.-J.

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

Jülicher, F.

S. F. Tolić-Nørrelykke, 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]

Kim, H.-I.

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

Kim, P.-S.

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

Knöner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

Mahajan, V. N.

Mahamdeh, M.

Mazolli, A.

McGloin, D.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

Mesquita, O. N.

Min-Cheng, Z.

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

Neto, P. A. M.

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf . 79–80, 1005–1017 (2003).

Nørrelykke, S. F.

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[CrossRef] [PubMed]

Oddershede, L. B.

Oh, C.-H.

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

Padgett, M. J.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

Pavone, F. S.

S. F. Tolić-Nørrelykke, 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]

Pawley, J.

J. Pawley, Handbook of Biological Confocal Microscopy (Springer, 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]

Reihani, N. S.

Reihani, S. N. S.

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Rocha, M. S.

Rohrbach, A.

A. Rohrbach, “Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf . 79–80, 1005–1017 (2003).

Samadi, A.

Schäffer, E.

M. Jahnel, M. Behrndt, A. Jannasch, E. Schäffer, and S. Grill, “Measuring the complete force field of an optical trap,” Opt. Lett. 36, 1260–1262 (2011).
[CrossRef] [PubMed]

M. Mahamdeh and E. Schäffer, “Optical tweezers with millikelvin precision of temperature-controlled objectives and base-pair resolution,” Opt. Express 17, 17190–17199 (2009).
[CrossRef] [PubMed]

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[CrossRef] [PubMed]

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[CrossRef] [PubMed]

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[CrossRef] [PubMed]

S. F. Tolić-Nørrelykke, 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]

A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
[CrossRef]

Simpson, N. B.

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

Skinner, D. R.

D. R. Skinner and R. E. Whitcher “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E: J. Sci. Instrum . 5, 237–238 (1972).
[CrossRef]

Song, S.-H.

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

Stelzer, E. H. K.

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]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[CrossRef] [PubMed]

Tolic-Nørrelykke, S. F.

S. F. Tolić-Nørrelykke, 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]

van Blaaderen, A.

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
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A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
[CrossRef]

van de Hulst, H.

H. van de HulstLight Scattering by Small Particles (Dover Puplications, Inc., 1981).

van Kats, C. M.

V. Bormuth, A. Jannasch, M. Ander, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Optical trapping of coated microspheres,” Opt. Express 16, 13831–13844 (2008).
[CrossRef] [PubMed]

A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
[CrossRef]

Viana, N. B.

Whitcher, R. E.

D. R. Skinner and R. E. Whitcher “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E: J. Sci. Instrum . 5, 237–238 (1972).
[CrossRef]

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M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

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Appl. Opt. (1)

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A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
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Chin. Phys. Lett. (1)

M. Bing-Huan, Z. Jin-Hua, Z. Min-Cheng, L. Yin-Mei, W. Jian-Guang, and R. Hong-Liang, “Improvement of transverse trapping efficiency of optical tweezers,” Chin. Phys. Lett. 25, 2300–2302 (2008).
[CrossRef]

J. Korean Phys. Soc. (1)

H.-I. Kim, I.-J. Joo, S.-H. Song, P.-S. Kim, K.-B. IM, and C.-H. Oh, “Dependence of the optical trapping efficiency on the ratio of the beam radius-to-the aperture radius,” J. Korean Phys. Soc. 43(3), 348–351 (2003).

J. Microsc. (2)

V. Bormuth, J. Howard, and E. Schäffer, “LED illumination for video-enhanced DIC imaging of single microtubules,” J. Microsc. 226, 1–5 (2007).
[CrossRef] [PubMed]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive-index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

J. Mod. Opt. (1)

N. B. Simpson, D. McGloin, K. Dholakia, L. Allen, and M. J. Padgett, “Optical tweezers with increased axial trapping efficiency,” J. Mod. Opt. 45, 1943–1949 (1998).
[CrossRef]

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

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt . 9, S196–S203 (2007).
[CrossRef]

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

J. Phys. E: J. Sci. Instrum (1)

D. R. Skinner and R. E. Whitcher “Measurement of the radius of a high-power laser beam near the focus of a lens,” J. Phys. E: J. Sci. Instrum . 5, 237–238 (1972).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf . 79–80, 1005–1017 (2003).

Langmuir (1)

E. Schäffer, S. F. Nørrelykke, and J. Howard, “Surface forces and drag coefficients of microspheres near a plane surface measured with optical tweezers,” Langmuir 23, 3654–3665 (2007).
[CrossRef] [PubMed]

Microsc. Res. Tech. (1)

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).
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Opt. Express (2)

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A. Rohrbach, “Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

S. F. Tolić-Nørrelykke, 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]

Other (4)

H. van de HulstLight Scattering by Small Particles (Dover Puplications, Inc., 1981).

A. Jannasch, V. Bormuth, C. M. van Kats, A. van Blaaderen, J. Howard, and E. Schäffer, “Coated microspheres as enhanced probes for optical trapping,” Proc. SPIE p. 70382B (2008).
[CrossRef]

Note that version 1.0 of the optical tweezers computational toolbox (Ref. [19]) contained a power scaling error in the code which was corrected in version 1.1.

J. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Exemplary laser profile measured by the knife-edge method. The power measurements (symbols) were fitted with an error function of width ω 0 = 1.71 ± 0.01 mm. Inset: Schematic objective with a hemispherical principal plane H 1. Zoom: Aberrations occurring at a glass-water interface when using oil-immersion objectives. The marginal rays correspond to NA ≈ 1.3, the next ones (spaced by 10°) to NA ≈ 1.15. (b) Trap stiffness as a function of immersion-oil refractive index for 0.46 μm-diameter microspheres. (c) Objective transmission through an annulus with outer diameter D centered on the optical axis. The line is a fit using T = T 0aD 10 with T 0 = 0.73 and a = 10−8 mm−10. Inset: Schematic of the measurement (see text for details). For (b) and (c) each symbol is the mean of three measurements. Error bars are standard deviations plotted only if larger than the symbol size. (d) Laser focus profile (α = 0.95). Scans (dotted lines) through 80 nm-diameter gold particles fitted to the derivative of a Gaussian (ω x ( y ) = 410(530) nm; dim solid lines) and compared to our calculations (ω x ( y ) = 400(470) nm; dashed lines). The insets show a CCD image of the laser focus and cross-sections (dotted lines; both in the same units) through the center fitted by Gaussians (ω x ( y ) = 340(570) nm; lines).

Fig. 2
Fig. 2

Trap stiffness measurements (symbols) and calculations (thick [thin] lines for NA = 1.2[1.3]) as a function of filling ratio α for four microsphere sizes in the lateral x- (a), y- (b), and axial z-direction (c). Inset in (c): Axial trap position relative to the center of the focus as a function of filling ratio (NA = 1.2). Symbols are averages obtained from ≥6 different microspheres for each size. Error bars are standard deviations plotted only if larger than the symbol size. For all measurements the laser power before the trapping objective was P = 250 mW. Due to a 4 % asymmetry in the laser profile, overfilling ratios in the y-axis were slightly larger than those in the x-axis. (d) To achieve a trap stiffness of κ x = 1 pN/nm, the power in the focus (using our fit parameters; thick lines [NA = 1.2]) and before the objective (assuming 100 % transmission; thin lines [NA = 1.2]) are plotted as a function of α.

Equations (3)

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α = 2 ω 0 D NA = ω 0 f NA
E = exp ( r ω 0 ) 2 = exp ( 2 f n medium sin θ α D NA ) 2
P trunc = T 0 [ 1 exp ( 2 [ D max α D NA ] 2 ) ]

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