Abstract

Optical tweezers have proven to be very useful in various scientific fields, from biology to nanotechnology. In this Letter we show, both by theory and experiment, that the interference intensity pattern at the back focal plane of the condenser consists of two distinguishable areas with anticorrelated intensity changes when the bead is moved in the axial direction. We show that the space angle defining the border of two areas linearly depends on the NA of the objective. We also propose a new octant photodiode, which could significantly improve the axial resolution compared to the commonly used quadrant photodiode technique.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
  3. T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
    [CrossRef] [PubMed]
  4. F. Hajizadeh and S. N. S. Reihani, Opt. Express 18, 551 (2010).
    [CrossRef] [PubMed]
  5. F. Gittes and C. H. Schmidt, Opt. Lett. 23, 7 (1998).
    [CrossRef]
  6. A. Pralle, M. Prummer, E.-L. Florin, E. H. K. Stelzer, and J. K. H. Hörber, Microsc. Res. Tech. 44, 378 (1999).
    [CrossRef] [PubMed]
  7. A. Rohrbach, H. Kress, and E. H. K. Stelzer, Opt. Lett. 28, 411 (2003).
    [CrossRef] [PubMed]
  8. G. Volpe, G. Kozyreff, and D. Petrov, J. Appl. Phys. 102, 084701 (2007).
    [CrossRef]
  9. J. K. Dreyer, K. Berg-Sørensen, and L. B. Oddershede, Appl. Opt. 43, 1991 (2004).
    [CrossRef] [PubMed]
  10. K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
    [CrossRef]

2010 (1)

2007 (2)

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef] [PubMed]

G. Volpe, G. Kozyreff, and D. Petrov, J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

2004 (2)

2003 (2)

1999 (1)

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 (1)

1986 (1)

Ashkin, A.

Berg-Sørensen, K.

Bjorkholm, J. E.

Bryant, Z.

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Bustamante, C.

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Chu, S.

Dreyer, J. K.

Dziedzic, J. M.

Florin, E.-L.

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

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Gittes, F.

Hajizadeh, F.

Hansen, T. M.

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef] [PubMed]

Hörber, J. K. H.

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

Kozyreff, G.

G. Volpe, G. Kozyreff, and D. Petrov, J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

Kress, H.

Oddershede, L.

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef] [PubMed]

Oddershede, L. B.

Petrov, D.

G. Volpe, G. Kozyreff, and D. Petrov, J. Appl. Phys. 102, 084701 (2007).
[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]

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]

Reihani, S. N. S.

F. Hajizadeh and S. N. S. Reihani, Opt. Express 18, 551 (2010).
[CrossRef] [PubMed]

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef] [PubMed]

Rohrbach, A.

Schmidt, C. H.

Smith, S. B.

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Sørensen, M.

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef] [PubMed]

Stelzer, E. H. K.

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. Hörber, Microsc. Res. Tech. 44, 378 (1999).
[CrossRef] [PubMed]

Volpe, G.

G. Volpe, G. Kozyreff, and D. Petrov, J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

G. Volpe, G. Kozyreff, and D. Petrov, J. Appl. Phys. 102, 084701 (2007).
[CrossRef]

Microsc. Res. Tech. (1)

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 (1)

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

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

T. M. Hansen, S. N. S. Reihani, L. Oddershede, and M. Sørensen, Proc. Natl. Acad. Sci. USA 104, 5830 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Theoretical photodiode signals when a 1.01 μm bead is scanned through the laser focus in the (a) lateral and (b) axial directions with NA as the parameter. The graph defined by δ represents the subtraction of graphs with NA C of 1.3 and 1.1. (b) Upper inset, sensitivity (the slope of photodiode signal) as a function of the NA of the condenser. (b) Lower inset, space angle defining the border of the anticorrelated areas at the BFP of the condenser as a function of objective NA.

Fig. 2
Fig. 2

Experimental results for the relevant photodiode signal when a 1.01 μm bead is scanned through the laser focus in the (a) lateral and (b) axial directions with NA as the parameter. Inset, variation of the sensitivity with the condenser NA.

Fig. 3
Fig. 3

(a) Typical PS graphs for lateral signal (black upper curve), and axial signals for small condenser NA (red middle curve) and large condenser NA (blue lower curve). (b) Results for the PS calibration method as a function of the condenser NA for lateral (black squares) and axial (red circles) signals. The NA of the objective is NA O = 1.3 .

Fig. 4
Fig. 4

Schematic of the proposed OPD. The formulas show how to calculate the position of the trapped bead from photodiode signals.

Equations (1)

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δ I ( r , r ) I tot = 2 k 3 α π r 2 exp ( ρ 2 w 2 ( z ) ( k w 0 θ ) 2 4 ) 1 + ( z z 0 ) 2 × sin [ k ( ζ ( z ) k ρ 2 2 R ( z ) + r cos θ cos θ ) + r sin θ sin θ cos ( ϕ ϕ ) z ] ,

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