Abstract

In optical traps the position of a trapped bead is usually determined by measuring the intensity distribution of the forward-scattered light and the back-scattered light. In this paper we demonstrate that this position can be determined using the side-scattered light. A quadrant photodiode is used to monitor the position of an optically trapped object in a dual-beam fiber-optic trap by measurement of intensity shifts in the back focal plane of the objective that is perpendicular to the propagating beam. An approximated model based on ray optics is presented with numerical results that describe the use of the side-scattered light for position detection. The influences of system parameters, including fiber separations, the numerical apertures (NA), and the radii of microspheres, are discussed in details. We find out that the displacement sensitivity of the detector is null for some critical radii and numerical apertures. In addition, the noises in laser powers are analyzed, and one power difference regime is proposed to weaken the influences.

© 2017 Optical Society of America

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References

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
    [Crossref]
  2. P. Jones, O. Marago, and G. Volpe, Optical Tweezers: Principles and Applications (Cambridge University, 2015).
  3. J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
    [Crossref] [PubMed]
  4. N. Bellini, F. Bragheri, I. Cristiani, J. Guck, R. Osellame, and G. Whyte, “Validation and perspectives of a femtosecond laser fabricated monolithic optical stretcher,” Biomed. Opt. Express 3(10), 2658–2668 (2012).
    [Crossref] [PubMed]
  5. X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
    [Crossref] [PubMed]
  6. G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
    [Crossref]
  7. N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, “Visualization of optical binding of microparticles using a femtosecond fiber optical trap,” Opt. Express 14(8), 3677–3687 (2006).
    [Crossref] [PubMed]
  8. C. Jensen-McMullin, H. P. Lee, and E. R. Lyons, “Demonstration of trapping, motion control, sensing and fluorescence detection of polystyrene beads in a multi-fiber optical trap,” Opt. Express 13(7), 2634–2642 (2005).
    [Crossref] [PubMed]
  9. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
    [Crossref] [PubMed]
  10. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
    [Crossref] [PubMed]
  11. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998).
    [Crossref] [PubMed]
  12. J. Huisstede, K. van der Werf, M. Bennink, and V. Subramaniam, “Force detection in optical tweezers using backscattered light,” Opt. Express 13(4), 1113–1123 (2005).
    [Crossref] [PubMed]
  13. A. Rohrbacha and E. H. K. Stelze, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
    [Crossref]
  14. M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
    [Crossref] [PubMed]
  15. F. Gittes and C. F. Schmidt, “Back-focal-plane detection of force and motion in optical traps,” Biophys. J. 74, A183 (1998).
  16. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
    [Crossref] [PubMed]
  17. E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36(25), 6423–6433 (1997).
    [Crossref] [PubMed]

2016 (2)

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
[Crossref] [PubMed]

2012 (1)

2006 (1)

2005 (2)

2004 (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

2002 (1)

A. Rohrbacha and E. H. K. Stelze, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
[Crossref]

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

1998 (3)

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998).
[Crossref] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

F. Gittes and C. F. Schmidt, “Back-focal-plane detection of force and motion in optical traps,” Biophys. J. 74, A183 (1998).

1997 (2)

E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36(25), 6423–6433 (1997).
[Crossref] [PubMed]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

1992 (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Allersma, M. W.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Bellini, N.

Bennink, M.

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Bragheri, F.

Chen, X.

X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
[Crossref] [PubMed]

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

Collins, S. D.

Cristiani, I.

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

deCastro, M. J.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

Dholakia, K.

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Gittes, F.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

F. Gittes and C. F. Schmidt, “Back-focal-plane detection of force and motion in optical traps,” Biophys. J. 74, A183 (1998).

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998).
[Crossref] [PubMed]

Guck, J.

N. Bellini, F. Bragheri, I. Cristiani, J. Guck, R. Osellame, and G. Whyte, “Validation and perspectives of a femtosecond laser fabricated monolithic optical stretcher,” Biomed. Opt. Express 3(10), 2658–2668 (2012).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

Huisstede, J.

Jensen-McMullin, C.

Käs, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

Knoesen, A.

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Lee, H. P.

Luo, H.

X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
[Crossref] [PubMed]

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

Lyons, E. R.

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

Metzger, N. K.

Moon, T. J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

Osellame, R.

Rohrbacha, A.

A. Rohrbacha and E. H. K. Stelze, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
[Crossref]

Schmidt, C. F.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

F. Gittes and C. F. Schmidt, “Back-focal-plane detection of force and motion in optical traps,” Biophys. J. 74, A183 (1998).

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998).
[Crossref] [PubMed]

Sibbett, W.

Sidick, E.

Stelze, E. H. K.

A. Rohrbacha and E. H. K. Stelze, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
[Crossref]

Stewart, R. J.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

Subramaniam, V.

van der Werf, K.

Wang, M. D.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Whyte, G.

Wright, E. M.

Xiao, G.

X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
[Crossref] [PubMed]

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

Xiong, W.

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
[Crossref] [PubMed]

Yang, K.

X. Chen, G. Xiao, K. Yang, W. Xiong, and H. Luo, “Characteristics of the orbital rotation in dual-beam fiber-optic trap with transverse offset,” Opt. Express 24(15), 16952–16960 (2016).
[Crossref] [PubMed]

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

Yin, H.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Appl. Opt. (1)

Biomed. Opt. Express (1)

Biophys. J. (5)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The Optical stretcher: a Novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74(2), 1074–1085 (1998).
[Crossref] [PubMed]

F. Gittes and C. F. Schmidt, “Back-focal-plane detection of force and motion in optical traps,” Biophys. J. 74, A183 (1998).

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

IEEE Photonics J. (1)

G. Xiao, K. Yang, H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics J. 8(1), 1–8 (2016).
[Crossref]

J. Appl. Phys. (1)

A. Rohrbacha and E. H. K. Stelze, “Three-dimensional position detection of optically trapped dielectric particles,” J. Appl. Phys. 91(8), 5474–5488 (2002).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

Other (1)

P. Jones, O. Marago, and G. Volpe, Optical Tweezers: Principles and Applications (Cambridge University, 2015).

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Figures (9)

Fig. 1
Fig. 1

Geometry for calculating the light power due to the scattering of a single incident ray by a microsphere.

Fig. 2
Fig. 2

Isignal versus the axial offset of the particle.

Fig. 3
Fig. 3

Schematic of the position detection system of dual-beam fiber-optic trap.

Fig. 4
Fig. 4

(a) Displacement of the particle as a function of time detected by QPD and CCD. (b) Isignal versus the axial offset.

Fig. 5
Fig. 5

(a) Isignal versus the axial offset of the particle for varying r. (b) The slope of the curve versus r.

Fig. 6
Fig. 6

(a) Isignal versus the axial offset of the particle for varying S. (b) The slope of the curve versus S.

Fig. 7
Fig. 7

(a) Isignal versus particle axial offset for varying NA. (b) The slope of the curve versus NA.

Fig. 8
Fig. 8

(a) Qaxial as a function of axial offset of the particle for varying S when r = ω0. (b) Qaxial as a function of axial offset of the particle for varying r when S = 5ω0.

Fig. 9
Fig. 9

δIsignal caused by single power change.

Equations (5)

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I signal = I + - I - I + + I - ,
ΔI Δz = I signal ( z 0 +Δz) I signal (Δz) Δz
F 1 =Q( s 1 ) P 1 F 2 =Q( s 2 ) P 2 ,
Q( s 1 ) P 0 =Q( s 2 )( P 0 +δ P 2 ) .
Q( s 1 ) Q( s 2 ) = s 1 s 2 =1+ δ P 2 P 0 .

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