Abstract

We describe a simple yet powerful technique of simultaneously measuring both translational and rotational motion of mesoscopic particles in optical tweezers by measuring the backscattered intensity on a quadrant photodiode (QPD). While the measurement of translational motion by taking the difference of the backscattered intensity incident on adjacent quadrants of a QPD is well known, we demonstrate that rotational motion can be measured very precisely by taking the difference between the diagonal quadrants. The latter measurement eliminates the translational component entirely and leads to a detection sensitivity of around 50 mdeg at S/N of 2 for angular motion of a driven microrod. The technique is also able to resolve the translational and rotational Brownian motion components of the microrod in an unperturbed trap and can be very useful in measuring translation–rotation coupling of micro-objects induced by hydrodynamic interactions.

© 2014 Optical Society of America

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  1. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
    [CrossRef]
  2. P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
    [CrossRef]
  3. S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
    [CrossRef]
  4. Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
    [CrossRef]
  5. G. Volpe and D. Petrov, Phys. Rev. Lett. 97, 210603 (2006).
    [CrossRef]
  6. B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).
  7. Y. Arita, M. Mazilu, and K. Dholakia, Nat. Commun. 4, 2374 (2013).
    [CrossRef]
  8. P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
    [CrossRef]
  9. J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).
  10. K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
    [CrossRef]
  11. V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
    [CrossRef]
  12. J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
    [CrossRef]
  13. S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
    [CrossRef]
  14. A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
    [CrossRef]
  15. A. R. Carter, G. M. King, and T. T. Perkins, Opt. Express 15, 13434 (2007).
    [CrossRef]

2013 (3)

Y. Arita, M. Mazilu, and K. Dholakia, Nat. Commun. 4, 2374 (2013).
[CrossRef]

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
[CrossRef]

2012 (2)

S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
[CrossRef]

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

2011 (1)

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

2010 (1)

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

2007 (1)

2006 (3)

S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

G. Volpe and D. Petrov, Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

2004 (1)

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

2001 (1)

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Alsayed, A. M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Arita, Y.

Y. Arita, M. Mazilu, and K. Dholakia, Nat. Commun. 4, 2374 (2013).
[CrossRef]

Banerjee, A.

S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
[CrossRef]

Bassetti, B.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

Baudisch, B.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Benett, J. S.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).

Block, S. M.

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

Brousse, E.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Carter, A. R.

Cicuta, P.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

Cooper, J. M.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

Curran, A.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

Dholakia, K.

Y. Arita, M. Mazilu, and K. Dholakia, Nat. Commun. 4, 2374 (2013).
[CrossRef]

Di Leonardo, R.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

Friedrich, B. F.

V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Galajda, P.

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Geyer, V. F.

V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
[CrossRef]

Gibson, L. J.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Gisler, T.

S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Haldar, A.

S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
[CrossRef]

Han, Y.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Heckenberg, N. R.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Howard, J.

V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
[CrossRef]

Julicher, F.

V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
[CrossRef]

Kelly, R. M.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

King, G. M.

Kotar, J.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

Lagomarsino, M. C.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

Lee, M. P.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

Leoni, M.

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

Lubensky, T. C.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Martin, S.

S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Mazilu, M.

Y. Arita, M. Mazilu, and K. Dholakia, Nat. Commun. 4, 2374 (2013).
[CrossRef]

Neuman, K. C.

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

Nicholson, T.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Nieminen, T. A.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Nobili, M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Ormos, P.

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Orrit, M.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

Padgett, M. J.

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

Pal, S. B.

S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
[CrossRef]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).

Perkins, T. T.

Petrov, D.

G. Volpe and D. Petrov, Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

Preece, D.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Reichert, M.

S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Roy, B.

S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
[CrossRef]

Rubinsztein-Dunlop, H.

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Ruijgrok, P. V.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

Stark, H.

S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

Tchebotareva, A. L.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

Verhart, N. R.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

Volpe, G.

G. Volpe and D. Petrov, Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

Yodh, A. G.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Zhang, J.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Zijlstra, P.

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Nat. Commun. (1)

Y. Arita, M. Mazilu, and K. Dholakia, Nat. Commun. 4, 2374 (2013).
[CrossRef]

Nature (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (4)

A. Curran, M. P. Lee, M. J. Padgett, J. M. Cooper, and R. Di Leonardo, Phys. Rev. Lett. 108, 240601 (2012).
[CrossRef]

P. V. Ruijgrok, N. R. Verhart, P. Zijlstra, A. L. Tchebotareva, and M. Orrit, Phys. Rev. Lett. 107, 037401 (2011).
[CrossRef]

S. Martin, M. Reichert, H. Stark, and T. Gisler, Phys. Rev. Lett. 97, 248301 (2006).
[CrossRef]

G. Volpe and D. Petrov, Phys. Rev. Lett. 97, 210603 (2006).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

V. F. Geyer, F. Julicher, J. Howard, and B. F. Friedrich, Proc. Natl. Acad. Sci. USA 110, 18058 (2013).
[CrossRef]

J. Kotar, M. Leoni, B. Bassetti, M. C. Lagomarsino, and P. Cicuta, Proc. Natl. Acad. Sci. USA 107, 7669 (2010).
[CrossRef]

Rev. Sci. Instrum. (2)

S. B. Pal, A. Haldar, B. Roy, and A. Banerjee, Rev. Sci. Instrum. 83, 023108 (2012).
[CrossRef]

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

Sci. Rep. (1)

J. S. Benett, L. J. Gibson, R. M. Kelly, E. Brousse, B. Baudisch, D. Preece, T. A. Nieminen, T. Nicholson, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Sci. Rep. 3, 1759 (2013).

Science (1)

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, Science 314, 626 (2006).
[CrossRef]

Other (1)

B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

(a) (1), (2), and (3) show a rod of dimension 4×1μm, illuminated at the center by a laser beam of diameter 1 μm, oriented at (1) 0 deg, (2) 45 deg, and (3) 90 deg to the polarization direction (x axis) of the beam. Corresponding scatter patterns showing scattered field intensity are shown adjacent to the rod (x and y axes are in μm). (b) Net signal from a QPD as the rod is translated by 1 μm across the laser beam. The blue curve shows Strans, while the red curve shows Srot. (c) The net signal from a QPD as the rod is rotated by 90 deg across the laser beam.

Fig. 2.
Fig. 2.

Schematic of the experiment. ML, microscope lamp; GS, glass slide; CS, coverslip; MO, microscope objective; DBS, dichroic beam splitter; BS, 50–50 beam splitter; TB, trapping beam; DB, detection beam; QPD, quadrant photodiode; AOM, acousto-optic modulator.

Fig. 3.
Fig. 3.

(a) Rotational motion of a rod (4×1μm) using two traps: one near the top serving as a pivot point, and the other lower down that was spatially modulated by the AOM (dimensions in microns). (b) QPD signal for Srot. (c) Power spectra (PSD, power spectral density) for Strans and Srot. Srot shows peaks at the rod rotation frequency and higher harmonics generated due to the square wave. (d) Exponential response of the rod due to the square-wave excitation (shown below the response). The time constants of the rising and falling exponentials are different due to the different trap stiffnesses at the two end locations.

Fig. 4.
Fig. 4.

(a) Power spectrum of Strans with double Lorentzian fit. (b) Power spectrum of Srot with Lorentzian fit. (c) Power spectrum of Strans with Lorentzian fit from x=5Hz so as to completely eliminate the rotational component whose corner frequency is 1.5 Hz. (d) Variation of fcrot with laser beam power (intensity).

Equations (3)

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Drdθdt+kr(θθ0)=Cη(t).
dx+k1xdt+k2θdt=2Dtdtη1,
dθ+k3θdt+k4xdt=2Drdtη2,

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