Abstract

For most optical tweezer applications, precise and reliable tracking of the trapped particle is an important requirement. Backfocal-plane interferometry is the fastest and most accurate tracking technique if the particle displacements are limited to half of the focal width. Especially for positive axial displacements, the nonlinear detector response can lead to incorrect tracking results. Here we show how the linear detection range around the trap center can be extended by a factor of 2 to 4 in the axial direction using a second frequency-detuned tracking focus that is generated by the same laser as the optical trap. Additionally, we show how the noise in the axial signal can be decreased significantly using a second detector.

© 2010 Optical Society of America

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  1. A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
    [CrossRef] [PubMed]
  2. P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
    [CrossRef] [PubMed]
  3. H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
    [CrossRef] [PubMed]
  4. K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
    [CrossRef]
  5. P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, Appl. Opt. 45, 7309 (2006).
    [CrossRef] [PubMed]
  6. A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
    [CrossRef]
  7. A. Rohrbach, H. Kress, and E. H. K. Stelzer, Opt. Lett. 28, 411 (2003).
    [CrossRef] [PubMed]
  8. J. K. Dreyer, K. Berg-Sorensen, and L. Oddershede, Appl. Opt. 43, 1991 (2004).
    [CrossRef] [PubMed]
  9. H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
    [CrossRef]
  10. M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
    [CrossRef] [PubMed]

2009 (1)

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

2007 (1)

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
[CrossRef]

2004 (3)

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

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

J. K. Dreyer, K. Berg-Sorensen, and L. Oddershede, Appl. Opt. 43, 1991 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
[CrossRef] [PubMed]

1999 (1)

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Asbury, C. L.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
[CrossRef] [PubMed]

Berg-Sorensen, K.

Block, S. M.

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

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
[CrossRef] [PubMed]

Buss, F.

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

Dreyer, J. K.

Florin, E. L.

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Griffiths, G.

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
[CrossRef]

Holzer, D.

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

Horber, J. K. H.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Huang, R. X.

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

Jonas, A.

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

Kress, H.

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
[CrossRef]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, Opt. Lett. 28, 411 (2003).
[CrossRef] [PubMed]

Lang, M. J.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
[CrossRef] [PubMed]

Neuman, K. C.

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

Neumayer, D.

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

Oddershede, L.

Pralle, A.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Prummer, M.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Rohrbach, A.

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, Appl. Opt. 45, 7309 (2006).
[CrossRef] [PubMed]

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
[CrossRef]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, Opt. Lett. 28, 411 (2003).
[CrossRef] [PubMed]

Seitz, P. C.

Shaevitz, J. W.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
[CrossRef] [PubMed]

Stelzer, E. H. K.

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

P. C. Seitz, E. H. K. Stelzer, and A. Rohrbach, Appl. Opt. 45, 7309 (2006).
[CrossRef] [PubMed]

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
[CrossRef]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, Opt. Lett. 28, 411 (2003).
[CrossRef] [PubMed]

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Tischer, C.

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

Wu, P. Y.

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

Appl. Opt. (2)

Biophys. J. (1)

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, Biophys. J. 83, 491 (2002).
[CrossRef] [PubMed]

Microsc. Res. Tech. (1)

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. E (1)

H. Kress, E. H. K. Stelzer, G. Griffiths, and A. Rohrbach, Phys. Rev. E 71, 061927 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

P. Y. Wu, R. X. Huang, C. Tischer, A. Jonas, and E. L. Florin, Phys. Rev. Lett. 103, 108101 (2009).
[CrossRef] [PubMed]

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

H. Kress, E. H. K. Stelzer, D. Holzer, F. Buss, G. Griffiths, and A. Rohrbach, Proc. Natl. Acad. Sci. USA 104, 11633 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

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

A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, and E. H. K. Stelzer, Rev. Sci. Instrum. 75, 2197 (2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. Zeroth (blue / dark gray) and first (red / light gray) order diffracted beams of the AOM are combined by a polarizing beam splitter (PBS). Trapping lens (TL), scanning mirror (SM).

Fig. 2
Fig. 2

Low-NA single beam signals (blue / dark gray) and signals with separate tracking beam (red / light gray) for PS beads with different diameters. Dotted traces show signals S z ( b z 0 ) generated while fixing the bead to the coverslip, revealing the trap center b z 0 . Straight lines indicate linear fits, and gray rectangles show the linear detection range.

Fig. 3
Fig. 3

Axial signals for a PS bead, diameter 200 nm. The upper graphs show the signals for different detection NAs ( NA 1 = 0.9 and NA 2 = 0.45 ), both for single beam detection. Intensity reductions cancel in the ratio q ( b z ) (red, lower graphs) of the two signals. A larger linear and unique detection region is obtained.

Equations (4)

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S z ( b , NA ) = 1 S 0 NA | E ˜ i + E ˜ s ( b ) | 2 d A S o s + g z ( NA ) · b z .
S z ( b z ) = 1 S 0 NA ( | E ˜ i ( ω tp ) + E ˜ s ( ω tp ) | 2 + | E ˜ i ( ω tk ) + E ˜ s ( ω tk ) | 2 ) d A ,
I D = I i + I s + 2 I i I s cos ( Δ φ ) .
I D ( b z ) I i ( t ) ( 1 + η + 2 η cos ( Δ φ b + β b z ) ) .

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