Abstract

We demonstrate a new method for measuring the sedimentation of a single colloidal bead by using a combination of optical tweezers and a stereo microscope based on a spatial light modulator. We use optical tweezers to raise a micron-sized silica bead to a fixed height and then release it to observe its 3D motion while it sediments under gravity. This experimental procedure provides two independent measurements of bead diameter and a measure of Faxén’s correction, where the motion changes due to presence of the boundary.

© 2014 Optical Society of America

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  1. C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics 5(1), 81–101 (2011).
    [CrossRef]
  2. Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19(2), 1016–1026 (2011).
    [CrossRef] [PubMed]
  3. S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
    [CrossRef] [PubMed]
  4. S. R. P. Pavani, R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
    [CrossRef] [PubMed]
  5. J. S. Dam, I. R. Perch-Nielsen, D. Palima, J. Glückstad, “Three-dimensional imaging in three-dimensional optical multi-beam micromanipulation,” Opt. Express 16(10), 7244–7250 (2008).
    [CrossRef] [PubMed]
  6. R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
    [CrossRef]
  7. M. Lee, G. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. Phillips, M. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21(14), 16541–16551 (2013).
    [CrossRef] [PubMed]
  8. S. Quirin, D. S. Peterka, R. Yuste, “Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging,” Opt. Express 21(13), 16007–16021 (2013).
    [CrossRef] [PubMed]
  9. G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
    [CrossRef] [PubMed]
  10. S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
    [CrossRef] [PubMed]
  11. R. Blazejewski, “Apparent viscosity and settling velocity of suspensions of rigid monosized spheres in stokes flow,” Int. J. Multiphase Flow. 39, 179–185 (2012).
    [CrossRef]
  12. J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
    [CrossRef] [PubMed]
  13. A. T. Juhl, D.-K. Yang, V. P. Tondiglia, L. V. Natarajan, T. J. White, T. J. Bunning, “Ordering of glass rods in nematic and cholesteric liquid crystals,” Opt. Mater. Express 1(8), 1536–1547 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
    [CrossRef]
  17. G. M. Gibson, J. Leach, S. Keen, A. J. Wright, M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16(19), 14561–14570 (2008).
    [CrossRef] [PubMed]
  18. M. Hasler, T. Haist, W. Osten, “Stereo vision in spatial-light-modulator–based microscopy,” Opt. Lett. 37(12), 2238–2240 (2012).
    [CrossRef] [PubMed]
  19. R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
    [CrossRef]
  20. C. Gosse, V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
    [CrossRef] [PubMed]
  21. X. Michalet, “Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium,” Phys. Rev. E 82(4), 041914 (2010).
    [CrossRef]

2014

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

2013

2012

R. Blazejewski, “Apparent viscosity and settling velocity of suspensions of rigid monosized spheres in stokes flow,” Int. J. Multiphase Flow. 39, 179–185 (2012).
[CrossRef]

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

M. Hasler, T. Haist, W. Osten, “Stereo vision in spatial-light-modulator–based microscopy,” Opt. Lett. 37(12), 2238–2240 (2012).
[CrossRef] [PubMed]

2011

A. T. Juhl, D.-K. Yang, V. P. Tondiglia, L. V. Natarajan, T. J. White, T. J. Bunning, “Ordering of glass rods in nematic and cholesteric liquid crystals,” Opt. Mater. Express 1(8), 1536–1547 (2011).
[CrossRef]

R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
[CrossRef]

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics 5(1), 81–101 (2011).
[CrossRef]

Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19(2), 1016–1026 (2011).
[CrossRef] [PubMed]

2010

J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
[CrossRef] [PubMed]

X. Michalet, “Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium,” Phys. Rev. E 82(4), 041914 (2010).
[CrossRef]

2009

G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
[CrossRef] [PubMed]

A. Yao, M. Tassieri, M. Padgett, J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[CrossRef] [PubMed]

2008

2006

2002

C. Gosse, V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[CrossRef] [PubMed]

1986

Ashkin, A.

Bailey, N. J.

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

Bernet, S.

Bjorkholm, J.

Blazejewski, R.

R. Blazejewski, “Apparent viscosity and settling velocity of suspensions of rigid monosized spheres in stokes flow,” Int. J. Multiphase Flow. 39, 179–185 (2012).
[CrossRef]

Bocquet, L.

J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
[CrossRef] [PubMed]

Bowman, R.

M. Lee, G. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. Phillips, M. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21(14), 16541–16551 (2013).
[CrossRef] [PubMed]

R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
[CrossRef]

Bowman, R. W.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Bunning, T. J.

Carberry, D. M.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Chu, S.

Cooper, J.

A. Yao, M. Tassieri, M. Padgett, J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[CrossRef] [PubMed]

Cooper, J. M.

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

Cottin-Bizonne, C.

J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
[CrossRef] [PubMed]

Croquette, V.

C. Gosse, V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[CrossRef] [PubMed]

Dam, J. S.

Ding, H.

Dziedzic, J.

Evans, R.

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

Fürhapter, S.

Gibson, G.

M. Lee, G. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. Phillips, M. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21(14), 16541–16551 (2013).
[CrossRef] [PubMed]

R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
[CrossRef]

Gibson, G. M.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16(19), 14561–14570 (2008).
[CrossRef] [PubMed]

Gillette, M. U.

Glückstad, J.

Gosse, C.

C. Gosse, V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[CrossRef] [PubMed]

Grieve, J. A.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Haist, T.

Hasler, M.

Heitkam, S.

S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
[CrossRef] [PubMed]

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics 5(1), 81–101 (2011).
[CrossRef]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
[CrossRef] [PubMed]

Juhl, A. T.

Kang, B.-H.

G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
[CrossRef] [PubMed]

Keen, S.

Langevin, D.

S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
[CrossRef] [PubMed]

Leach, J.

Lee, M.

Leitz, G.

G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
[CrossRef] [PubMed]

Linnenberger, A.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics 5(1), 81–101 (2011).
[CrossRef]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
[CrossRef] [PubMed]

Michalet, X.

X. Michalet, “Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium,” Phys. Rev. E 82(4), 041914 (2010).
[CrossRef]

Miles, M. J.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Millet, L.

Mir, M.

Natarajan, L. V.

Osten, W.

Padgett, M.

M. Lee, G. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. Phillips, M. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21(14), 16541–16551 (2013).
[CrossRef] [PubMed]

R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
[CrossRef]

A. Yao, M. Tassieri, M. Padgett, J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[CrossRef] [PubMed]

Padgett, M. J.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16(19), 14561–14570 (2008).
[CrossRef] [PubMed]

Palacci, J.

J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
[CrossRef] [PubMed]

Palima, D.

Pavani, S. R. P.

Perch-Nielsen, I. R.

Peterka, D. S.

Phillips, D.

Phillips, D. B.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Piestun, R.

Popescu, G.

Preece, D.

R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
[CrossRef]

Quirin, S.

Ritsch-Marte, M.

Rogers, J.

Salonen, A.

S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
[CrossRef] [PubMed]

Schoenwaelder, M. E.

G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
[CrossRef] [PubMed]

Serati, S.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Staehelin, L. A.

G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
[CrossRef] [PubMed]

Tassieri, M.

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

A. Yao, M. Tassieri, M. Padgett, J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[CrossRef] [PubMed]

Tondiglia, V. P.

Toquet, F.

S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
[CrossRef] [PubMed]

Unarunotai, S.

Wang, Z.

Warren, R. L.

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

White, T. J.

Wright, A. J.

Yang, D.-K.

Yao, A.

A. Yao, M. Tassieri, M. Padgett, J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[CrossRef] [PubMed]

Ybert, C.

J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
[CrossRef] [PubMed]

Yoshitake, Y.

S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
[CrossRef] [PubMed]

Yuste, R.

Biophys. J.

C. Gosse, V. Croquette, “Magnetic tweezers: micromanipulation and force measurement at the molecular level,” Biophys. J. 82(6), 3314–3329 (2002).
[CrossRef] [PubMed]

Comput. Phys. Commun.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, M. J. Padgett, “Red tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185(1), 268 (2014).
[CrossRef]

Int. J. Multiphase Flow.

R. Blazejewski, “Apparent viscosity and settling velocity of suspensions of rigid monosized spheres in stokes flow,” Int. J. Multiphase Flow. 39, 179–185 (2012).
[CrossRef]

J. Opt.

R. Bowman, D. Preece, G. Gibson, M. Padgett, “Stereoscopic particle tracking for 3D touch, vision and closed-loop control in optical tweezers,” J. Opt. 13(4), 044003 (2011).
[CrossRef]

Lab Chip

A. Yao, M. Tassieri, M. Padgett, J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[CrossRef] [PubMed]

Laser Photonics

C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics 5(1), 81–101 (2011).
[CrossRef]

New J. Phys.

M. Tassieri, R. Evans, R. L. Warren, N. J. Bailey, J. M. Cooper, “Microrheology with optical tweezers: data analysis,” New J. Phys. 14(11), 115032 (2012).
[CrossRef]

Opt. Express

G. M. Gibson, J. Leach, S. Keen, A. J. Wright, M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Opt. Express 16(19), 14561–14570 (2008).
[CrossRef] [PubMed]

Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19(2), 1016–1026 (2011).
[CrossRef] [PubMed]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
[CrossRef] [PubMed]

S. R. P. Pavani, R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16(26), 22048–22057 (2008).
[CrossRef] [PubMed]

J. S. Dam, I. R. Perch-Nielsen, D. Palima, J. Glückstad, “Three-dimensional imaging in three-dimensional optical multi-beam micromanipulation,” Opt. Express 16(10), 7244–7250 (2008).
[CrossRef] [PubMed]

M. Lee, G. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. Phillips, M. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21(14), 16541–16551 (2013).
[CrossRef] [PubMed]

S. Quirin, D. S. Peterka, R. Yuste, “Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging,” Opt. Express 21(13), 16007–16021 (2013).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Mater. Express

Phys. Rev. E

X. Michalet, “Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium,” Phys. Rev. E 82(4), 041914 (2010).
[CrossRef]

Phys. Rev. Lett.

S. Heitkam, Y. Yoshitake, F. Toquet, D. Langevin, A. Salonen, “Speeding up of sedimentation under confinement,” Phys. Rev. Lett. 110(17), 178302 (2013).
[CrossRef] [PubMed]

J. Palacci, C. Cottin-Bizonne, C. Ybert, L. Bocquet, “Sedimentation and effective temperature of active colloidal suspensions,” Phys. Rev. Lett. 105(8), 088304 (2010).
[CrossRef] [PubMed]

Plant Cell

G. Leitz, B.-H. Kang, M. E. Schoenwaelder, L. A. Staehelin, “Statolith sedimentation kinetics and force transduction to the cortical endoplasmic reticulum in gravity-sensing arabidopsis columella cells,” Plant Cell 21(3), 843–860 (2009).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

a) Schematic view of the experimental setup. The red shaded area shows the path of the trapping laser, while the two red lines show the paths of the light from the two illumination fibres. The bottom-left image shows the SLM pattern that diffracts the light at a different angle for each illumination. The bottom-right image shows an example of a stereo image taken by the camera, from which the 3D position is obtained. b) The full position trace of a bead’s centre recorded during sedimentation. The green (dashed), blue (dash-dot) and red (dot) lines show positions recorded from a single sedimentation run. We recorded up to 50 runs. The averaged result, shown in grey (solid line), is normalised with z = 0 being the bead on the coverslip, its centre being one particle radius higher. We measured this bead’s diameter to be 4.84μm.

Fig. 2
Fig. 2

a) The average initial part of sedimentation shown for three different beads. Over this range, the viscosity is nearly constant. With a linear fit, knowing the viscosity, we can extract the bead size or vice versa. b) The effective viscosity experienced by a sedimenting bead (diameter = 4.84μm) approaching a boundary.

Fig. 3
Fig. 3

During each sedimentation run, we also record the x and y position of the bead. Shown in a) is the x (blue, dashed) and y (green, solid) for an example run using a particle with diameter of 4.84μm. We then calculate the Mean Square Displacement (MSD) of this trajectory. By averaging the MSD for 50 repeats, we obtain the data shown in b). Here, the error bars are the standard error of the mean. The MSD(x) data (▿) from the MSD(y) data (□) has been shifted for clarity. The fits do not intercept zero owing to the tracking error and finite exposure time in the acquisition [21]. From the slopes of the linear fits of MSD(x) (blue, dashed) and MSD(y) (green, solid) we obtain a particle size of 4.77μm and 4.90μm respectively

Tables (1)

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Table 1 Results comparing the diffusion method with the sedimentation method for particle sizing. The beads used come from a population with mean diameter of 4.72μm. For each particle, the standard deviation in sizes from the different methods is on average 3.5%.

Equations (2)

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dz dt = 2 gr 2 ( ρ s ρ f ) 9 η ,
η ( z ) = 2 gr 2 ( ρ s ρ f ) / 9 dz dt .

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