Abstract

The focus of an oil-immersion microscope objective is shifted because of the refractive-index mismatch between the cover glass and the aqueous sample. We present a procedure with which to determine the focal shift by use of an inverted microscope equipped with optical tweezers. As the position of the sample chamber is scanned vertically, we measure the axial displacement of an optically trapped bead; the relative motion of the bead with respect to the surface supplies the effective focal shift. Measurements of this quantity deviate from electromagnetic calculations of the focal shift, a discrepancy attributable to the depth-dependent decrease in axial trap stiffness that arises from spherical aberration.

© 2005 Optical Society of America

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    [CrossRef]

2004 (1)

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

2003 (3)

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

E. Fallman and O. Axner, Appl. Opt. 42, 3915 (2003).
[CrossRef]

1998 (1)

1997 (1)

1996 (2)

K. Visscher, S. P. Gross, and S. M. Block, IEEE J. Sel. Top. Quantum Electron. 2, 1066 (1996).
[CrossRef]

N. S. White, R. J. Errington, M. D. Fricker, and J. L. Wood, J. Microsc. 181, 99 (1996).
[CrossRef]

1994 (1)

1993 (1)

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, J. Microsc. 169, 391 (1993).
[CrossRef]

1991 (1)

Abbondanzieri, E. A.

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

Axner, O.

Block, S. M.

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

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, IEEE J. Sel. Top. Quantum Electron. 2, 1066 (1996).
[CrossRef]

Cremer, C.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, J. Microsc. 169, 391 (1993).
[CrossRef]

Errington, R. J.

N. S. White, R. J. Errington, M. D. Fricker, and J. L. Wood, J. Microsc. 181, 99 (1996).
[CrossRef]

Fallman, E.

Fricker, M. D.

N. S. White, R. J. Errington, M. D. Fricker, and J. L. Wood, J. Microsc. 181, 99 (1996).
[CrossRef]

Gelles, J.

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

Gittes, F.

Gouesbet, G.

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, IEEE J. Sel. Top. Quantum Electron. 2, 1066 (1996).
[CrossRef]

Hell, S.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, J. Microsc. 169, 391 (1993).
[CrossRef]

Joo, I. J.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Kim, H. I.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Kim, K. B.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Kim, P. S.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Landick, R.

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

Lock, J. A.

Neuman, K. C.

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

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

Oh, C. H.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Park, B. O.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, J. Microsc. 169, 391 (1993).
[CrossRef]

Schmidt, C. F.

Song, S. H.

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Stelzer, E. H. K.

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, J. Microsc. 169, 391 (1993).
[CrossRef]

Torok, P.

Varga, P.

Videen, G.

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, IEEE J. Sel. Top. Quantum Electron. 2, 1066 (1996).
[CrossRef]

Visser, T. D.

White, N. S.

N. S. White, R. J. Errington, M. D. Fricker, and J. L. Wood, J. Microsc. 181, 99 (1996).
[CrossRef]

Wiersma, S. H.

Wood, J. L.

N. S. White, R. J. Errington, M. D. Fricker, and J. L. Wood, J. Microsc. 181, 99 (1996).
[CrossRef]

Appl. Opt. (1)

Cell (1)

K. C. Neuman, E. A. Abbondanzieri, R. Landick, J. Gelles, and S. M. Block, Cell 115, 437 (2003).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Visscher, S. P. Gross, and S. M. Block, IEEE J. Sel. Top. Quantum Electron. 2, 1066 (1996).
[CrossRef]

J. Microsc. (2)

N. S. White, R. J. Errington, M. D. Fricker, and J. L. Wood, J. Microsc. 181, 99 (1996).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, and E. H. K. Stelzer, J. Microsc. 169, 391 (1993).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

K. B. Kim, H. I. Kim, I. J. Joo, C. H. Oh, S. H. Song, P. S. Kim, and B. O. Park, Opt. Commun. 226, 25 (2003).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Origin of the focal shift. Convergent light crosses the interface between n 1 and n 2 ( n 1 > n 2 ) and comes to a focus at position d rather than d , where the focus would occur in the absence of an index mismatch. The coordinate system defines the axes. Light propagates in the z direction. The immersion oil (lighter shading) and the cover glass (thick horizontal line) that form the bottom of the sample chamber have index n 1 ; the aqueous fluid in the chamber has index n 2 . (b) Axial position-dependent interference signal. The intensity of the forward-scattered light from a trapped bead is measured by a photodetector (PD, inset) located in a plane optically conjugate to the condenser back focal plane (CL, inset). As the stage is moved, the interference between the direct light (inset, darker curve) and the reflected light (inset, lighter, dashed curve) produces a periodic intensity modulation (lighter circles) that can be fitted by a sinusoidal function (darker curve).

Fig. 2
Fig. 2

(a) Dependence of interference signal on NA. The photodetector voltage was measured as a trapped bead and was moved relative to the cover glass for a series of decreasing iris aperture stops on the condenser; traces are arranged in order of decreasing NA from bottom to top and are displaced on the ordinate for clarity. (b) Computed position signals for collection NA estimated from the traces in (a). From bottom to top, the NA values are 1.16, 1.03, 0.71, 0.54, and 0.26.

Fig. 3
Fig. 3

Measured and calculated focal shift versus refractive index of the second medium. The effective focal shift was measured for both 1.064 - μ m (open circles) and 1.047 - μ m (filled circles) wavelengths. The refractive index of the first medium was 1.515 (immersion oil and cover glass). We varied the index of the second medium by mixing water and glycerol. The calculated focal shift (solid curve) was determined at 1.064 μ m as described in the text and is indistinguishable from the shift at 1.047 μ m . The focal shift calculated in the paraxial limit ( n 2 n 1 ; dashed curve) is included for comparison.

Fig. 4
Fig. 4

(a) Comparison of measured (open circles) and estimated (solid curve) axial trap stiffness versus stage position for a bead trapped in water. The stage position was measured relative to the point where the focus lies at the glass–water interface. The curve plots the second derivative of the axial intensity from theory (see text), rescaled. (b) Difference between calculated and measured focal shift versus index of the second medium (filled circles), compared with a model in which this difference is approximated by the depth-dependent drop in axial stiffness (solid curve). The rates of change of stiffness with depth were calculated for various indices as in (a); then each rate was fitted to a line over the relevant region of measurement ( 1 3.5 μ m ) . These slopes were then rescaled and plotted as shown.

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