Abstract

Back-focal-plane interferometry is a method capable of determining the three-dimensional position of a particle with high precision (<3 nm) at high sampling rates (1 MHz). We investigated theoretically the performance of such a system for dielectric spheres with diameters D=0.533 µm and for metallic spheres with D300 nm. Good sensitivity and linearity were achieved for a detection angular aperture sinα of no more than 0.5. A value of sinα>0.7 should be used only for dielectric spheres with diameters approximately equal to the laser wavelength. Harmonic optical traps can be calibrated by measurement of the thermal motion of the sphere. We performed Brownian dynamics simulations and subsequent thermal noise analyses to prove that the wrong sinα incorrectly suggests an increased and nonharmonic axial trapping potential.

© 2003 Optical Society of America

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2002

A. Rohrbach and E. H. K. Stelzer, J. Appl. Phys. 91, 5474 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, Appl. Opt. 41, 2494 (2002).
[CrossRef] [PubMed]

2001

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

1999

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

1998

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

F. Gittes and C. F. Schmidt, Methods Cell Biol. 55, 129 (1998).
[CrossRef]

1994

L. Ghislain, N. Switz, and W. Webb, Rev. Sci. Instrum. 65, 2762 (1994).
[CrossRef]

1993

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

1990

Altmann, S.

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

Block, S. M.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Denk, W.

Fisinger, S.

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

Florin, E.-L.

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

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

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Ghislain, L.

L. Ghislain, N. Switz, and W. Webb, Rev. Sci. Instrum. 65, 2762 (1994).
[CrossRef]

Gittes, F.

F. Gittes and C. F. Schmidt, Methods Cell Biol. 55, 129 (1998).
[CrossRef]

Hörber, J. K. H.

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

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

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Pralle, A.

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

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Prummer, M.

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

Rohrbach, A.

A. Rohrbach and E. H. K. Stelzer, J. Appl. Phys. 91, 5474 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, Appl. Opt. 41, 2494 (2002).
[CrossRef] [PubMed]

Schmidt, C. F.

F. Gittes and C. F. Schmidt, Methods Cell Biol. 55, 129 (1998).
[CrossRef]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Stelzer, E. H. K.

A. Rohrbach and E. H. K. Stelzer, J. Appl. Phys. 91, 5474 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, Appl. Opt. 41, 2494 (2002).
[CrossRef] [PubMed]

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

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

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Switz, N.

L. Ghislain, N. Switz, and W. Webb, Rev. Sci. Instrum. 65, 2762 (1994).
[CrossRef]

Tischer, C.

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

Webb, W.

L. Ghislain, N. Switz, and W. Webb, Rev. Sci. Instrum. 65, 2762 (1994).
[CrossRef]

Webb, W. W.

Appl. Opt.

Appl. Phys. A

E.-L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Appl. Phys. Lett.

C. Tischer, S. Altmann, S. Fisinger, J. K. H. Hörber, E. H. K. Stelzer, and E.-L. Florin, Appl. Phys. Lett. 79, 3878 (2001).
[CrossRef]

J. Appl. Phys.

A. Rohrbach and E. H. K. Stelzer, J. Appl. Phys. 91, 5474 (2002).
[CrossRef]

Methods Cell Biol.

F. Gittes and C. F. Schmidt, Methods Cell Biol. 55, 129 (1998).
[CrossRef]

Microsc. Res. Tech.

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

Nature

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, Nature 365, 721 (1993).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

L. Ghislain, N. Switz, and W. Webb, Rev. Sci. Instrum. 65, 2762 (1994).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Principle of the tracking setup: OL, objective lens; DL, detection lens; QPD, quadrant photodiode; stop, aperture stop; sinα, angular aperture.

Fig. 2
Fig. 2

Relative diode signals for (left) lateral x displacement and (right) axial z displacement for various spheres. Capture angles of the detection lens are plotted for sinα=0.10.9. The shaded areas indicate how the focus intensity profile relates to the position of the bead. Signals at sinα=0.5 are plotted with thick curves.

Fig. 3
Fig. 3

Imaging of a particle track (xz projections) with different detection angles sinα. The particle position track pr (top right) corresponds to the Brownian motion of a 0.53-µm latex bead captured in an optical trap at 10-mW laser power (for 50 ms at 100 kHz). This distribution is transferred to intensity signal tracks pSr (aspect ratio maintained) by three different imaging maps Sr [for sinα=0.3, 0.5, 0.7]. The maps SXx,0,z and SZx,0,z (shown as contour plots; dashed lines and solid curves, respectively) are superimposed and indicate lines of a constant diode signal. The gray scale of all four particle tracks indicates the sampling time within 50 ms.

Fig. 4
Fig. 4

Trapping potential profiles describing the stiffnesses kX, kY, and kZ of the optical trap for a 0.53-µm bead at sinα=0.9. The sampling was 100 kHz over 2.0 s (200,000 points). The solid curves correspond to parabolic fits.

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