Abstract

Weak optical fields cause less damage to active cells and are easier to realize than traditional and tightly focused optical fields. While these fields are promising for biomedical science and particle manipulation applications, they lack a method for precise particle diffusion measurement because the weak fields cause the small changes in particle motion caused by weak fields. In this paper, we present a coaxial differential dynamic microscopy (CDDM) technique that uses a differential dynamic microscopy system, combined with an adjustable optical field. We use this technique to study Brownian motion of colloidal particles in weak optical fields. CDDM can quantitatively measure both the intensity and the pattern of the weak optical field and the diffusion coefficient of the particles. While the light paths of both the weak optical field and the illumination are coaxially incident on the sample cell, they remain independent. The optical field can be designed to have any pattern and adjusted to any intensity, while the measurements’ sample illumination requirements are also satisfied. To verify the accuracy of the technique, we measured particle diffusion in weak Gaussian optical fields of different strengths. The diffusion coefficient was found to decrease with increasing field strength. These experimental results agree well with those results predicted using the Fokker-Planck equation and Euler algorithm simulations. This technique is expected to provide an efficient tool for research into particle manipulation by using weak optical fields, particularly for delicate systems, such as colloidal particles and biological cells.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. Brown, The miscellaneous botanical works of Robert Brown (The Ray Society, 1866).
  2. A. Einstein, Investigations on the Theory of Brownian movement (New York: Dover Publications, 1956).
  3. M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
    [Crossref]
  4. P. Langevin, “Sur la théorie du mouvement brownien,” Acad. Sci. 146, 530–533 (1908).
  5. J. Perrin, Brownian movements and molecular reality (New York: Courier Dover. Publications, 2005).
  6. E. Frey and K. Kroy, “Brownian motion: a paradigm of soft matter and biological physics,” Ann. Phys. 14(1–3), 20–50 (2005).
    [Crossref]
  7. X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9(1), 28–37 (2013).
    [Crossref] [PubMed]
  8. P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys. 81(1), 387–442 (2009).
    [Crossref]
  9. M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
    [Crossref]
  10. J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers-single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78(5), 056601 (2015).
    [Crossref] [PubMed]
  11. P. Cicuta and A. M. Donald, “Microrheology: a review of the method and applications,” Soft Matter 3(12), 1449–1455 (2007).
    [Crossref]
  12. T. M. Squires and T. G. Mason, “Fluid Mechanics of Microrheology,” Annu. Rev. Fluid Mech. 42(1), 413–438 (2010).
    [Crossref]
  13. M. Campisi, P. Talkner, and P. Hänggi, “Influence of measurements on the statistics of work performed on a quantum system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041114 (2011).
    [Crossref] [PubMed]
  14. C. Gardiner and P. Zoller, Quantum Noise, a Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer-Verlag, 2000).
  15. J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
    [Crossref] [PubMed]
  16. M. C. Jenkins and S. U. Egelhaaf, “Colloidal suspensions in modulated light fields,” J. Phys. Condens. Matter 20(40), 404220 (2008).
    [Crossref]
  17. I. Golding and E. C. Cox, “Physical nature of bacterial cytoplasm,” Phys. Rev. Lett. 96(9), 098102 (2006).
    [Crossref] [PubMed]
  18. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288 (1986).
    [Crossref] [PubMed]
  19. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
    [Crossref] [PubMed]
  20. M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
    [Crossref] [PubMed]
  21. C. S. Guo, Y. N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
    [Crossref]
  22. R. Dasgupta, S. Ahlawat, and P. K. Gupta, “Microfluidic sorting with a moving array of optical traps,” Appl. Opt. 51(19), 4377–4387 (2012).
    [Crossref] [PubMed]
  23. X. Qi, D. M. Carberry, C. Cai, S. Hu, Z. Yuan, H. Rubinsztein-Dunlop, and J. Guo, “Optical sorting and cultivation of denitrifying anaerobic methane oxidation archaea,” Biomed. Opt. Express 8(2), 934–942 (2017).
    [Crossref] [PubMed]
  24. R. Cerbino and V. Trappe, “Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope,” Phys. Rev. Lett. 100(18), 188102 (2008).
    [Crossref] [PubMed]
  25. F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
    [Crossref] [PubMed]
  26. M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
    [Crossref] [PubMed]
  27. K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
    [Crossref] [PubMed]
  28. D. M. Wulstein, K. E. Regan, R. M. Robertson-Anderson, and R. McGorty, “Light-sheet microscopy with digital Fourier analysis measures transport properties over large field-of-view,” Opt. Express 24(18), 20881–20894 (2016).
    [Crossref] [PubMed]
  29. L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
    [Crossref] [PubMed]
  30. M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
    [Crossref] [PubMed]
  31. H. Risken, The Fokker–Planck equation: Methods of Solution and Applications (Springer-Verlag, 1984).
  32. A. M. Horowitz, “The second order Langevin equation and numerical simulations,” Nucl. Phys. B 280, 510–522 (1987).
    [Crossref]
  33. E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
    [Crossref]
  34. H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

2017 (1)

2016 (1)

2015 (2)

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers-single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78(5), 056601 (2015).
[Crossref] [PubMed]

2013 (4)

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9(1), 28–37 (2013).
[Crossref] [PubMed]

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

2012 (2)

M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
[Crossref] [PubMed]

R. Dasgupta, S. Ahlawat, and P. K. Gupta, “Microfluidic sorting with a moving array of optical traps,” Appl. Opt. 51(19), 4377–4387 (2012).
[Crossref] [PubMed]

2011 (2)

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

M. Campisi, P. Talkner, and P. Hänggi, “Influence of measurements on the statistics of work performed on a quantum system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041114 (2011).
[Crossref] [PubMed]

2010 (2)

T. M. Squires and T. G. Mason, “Fluid Mechanics of Microrheology,” Annu. Rev. Fluid Mech. 42(1), 413–438 (2010).
[Crossref]

C. S. Guo, Y. N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

2009 (2)

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys. 81(1), 387–442 (2009).
[Crossref]

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

2008 (3)

R. Cerbino and V. Trappe, “Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope,” Phys. Rev. Lett. 100(18), 188102 (2008).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

M. C. Jenkins and S. U. Egelhaaf, “Colloidal suspensions in modulated light fields,” J. Phys. Condens. Matter 20(40), 404220 (2008).
[Crossref]

2007 (1)

P. Cicuta and A. M. Donald, “Microrheology: a review of the method and applications,” Soft Matter 3(12), 1449–1455 (2007).
[Crossref]

2006 (1)

I. Golding and E. C. Cox, “Physical nature of bacterial cytoplasm,” Phys. Rev. Lett. 96(9), 098102 (2006).
[Crossref] [PubMed]

2005 (1)

E. Frey and K. Kroy, “Brownian motion: a paradigm of soft matter and biological physics,” Ann. Phys. 14(1–3), 20–50 (2005).
[Crossref]

2004 (1)

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

2003 (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

1998 (1)

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
[Crossref]

1987 (1)

A. M. Horowitz, “The second order Langevin equation and numerical simulations,” Nucl. Phys. B 280, 510–522 (1987).
[Crossref]

1986 (1)

1908 (1)

P. Langevin, “Sur la théorie du mouvement brownien,” Acad. Sci. 146, 530–533 (1908).

1906 (1)

M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
[Crossref]

Ahlawat, S.

Ashkin, A.

Babaye Khorasani, F.

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Bellini, T.

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

Bjorkholm, J. E.

Brogioli, D.

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

Bryant, G.

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Cai, C.

Campisi, M.

M. Campisi, P. Talkner, and P. Hänggi, “Influence of measurements on the statistics of work performed on a quantum system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041114 (2011).
[Crossref] [PubMed]

Carberry, D. M.

Cerbino, R.

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

R. Cerbino and V. Trappe, “Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope,” Phys. Rev. Lett. 100(18), 188102 (2008).
[Crossref] [PubMed]

Chaikin, P. M.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Chen, H.

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

Chu, S.

Cicuta, P.

P. Cicuta and A. M. Donald, “Microrheology: a review of the method and applications,” Soft Matter 3(12), 1449–1455 (2007).
[Crossref]

Conrad, J. C.

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Cox, E. C.

I. Golding and E. C. Cox, “Physical nature of bacterial cytoplasm,” Phys. Rev. Lett. 96(9), 098102 (2006).
[Crossref] [PubMed]

Dasgupta, R.

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Donald, A. M.

P. Cicuta and A. M. Donald, “Microrheology: a review of the method and applications,” Soft Matter 3(12), 1449–1455 (2007).
[Crossref]

Dziedzic, J. M.

Egelhaaf, S. U.

M. C. Jenkins and S. U. Egelhaaf, “Colloidal suspensions in modulated light fields,” J. Phys. Condens. Matter 20(40), 404220 (2008).
[Crossref]

Elgeti, J.

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers-single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78(5), 056601 (2015).
[Crossref] [PubMed]

Florin, E. L.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
[Crossref]

Frey, E.

E. Frey and K. Kroy, “Brownian motion: a paradigm of soft matter and biological physics,” Ann. Phys. 14(1–3), 20–50 (2005).
[Crossref]

Giavazzi, F.

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

Golding, I.

I. Golding and E. C. Cox, “Physical nature of bacterial cytoplasm,” Phys. Rev. Lett. 96(9), 098102 (2006).
[Crossref] [PubMed]

Gompper, G.

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers-single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78(5), 056601 (2015).
[Crossref] [PubMed]

Gong, Z.

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

Guo, C. S.

C. S. Guo, Y. N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Guo, J.

Gupta, P. K.

Hänggi, P.

M. Campisi, P. Talkner, and P. Hänggi, “Influence of measurements on the statistics of work performed on a quantum system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041114 (2011).
[Crossref] [PubMed]

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys. 81(1), 387–442 (2009).
[Crossref]

He, K.

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Hong, Z.

C. S. Guo, Y. N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Hörber, J. K. H.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
[Crossref]

Horowitz, A. M.

A. M. Horowitz, “The second order Langevin equation and numerical simulations,” Nucl. Phys. B 280, 510–522 (1987).
[Crossref]

Hu, S.

Jenkins, M. C.

M. C. Jenkins and S. U. Egelhaaf, “Colloidal suspensions in modulated light fields,” J. Phys. Condens. Matter 20(40), 404220 (2008).
[Crossref]

Joanny, J. F.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Karniadakis, G. E.

X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9(1), 28–37 (2013).
[Crossref] [PubMed]

Krishnamoorti, R.

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Kroy, K.

E. Frey and K. Kroy, “Brownian motion: a paradigm of soft matter and biological physics,” Ann. Phys. 14(1–3), 20–50 (2005).
[Crossref]

Langevin, P.

P. Langevin, “Sur la théorie du mouvement brownien,” Acad. Sci. 146, 530–533 (1908).

Li, X.

X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9(1), 28–37 (2013).
[Crossref] [PubMed]

Li, Y. M.

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

Liverpool, T. B.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Lou, L.

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Marchesoni, F.

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys. 81(1), 387–442 (2009).
[Crossref]

Marchetti, M. C.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Martinez, V. A.

M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
[Crossref] [PubMed]

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Mason, T. G.

T. M. Squires and T. G. Mason, “Fluid Mechanics of Microrheology,” Annu. Rev. Fluid Mech. 42(1), 413–438 (2010).
[Crossref]

McGorty, R.

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Palacci, J.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Pine, D. J.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Poling-Skutvik, R.

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

Poon, W. C.

M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
[Crossref] [PubMed]

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Pralle, A.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
[Crossref]

Prost, J.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Pusey, P. N.

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Qi, X.

Qiu, J.

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

Ramaswamy, S.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Rao, M.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Regan, K. E.

Retterer, S. T.

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Reufer, M.

M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
[Crossref] [PubMed]

Robertson-Anderson, R. M.

Rubinsztein-Dunlop, H.

Sacanna, S.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Safari, M. S.

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

Schurtenberger, P.

M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
[Crossref] [PubMed]

Schwarz-Linek, J.

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Simha, R. A.

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Squires, T. M.

T. M. Squires and T. G. Mason, “Fluid Mechanics of Microrheology,” Annu. Rev. Fluid Mech. 42(1), 413–438 (2010).
[Crossref]

Steinberg, A. P.

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Stelzer, E. H. K.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
[Crossref]

Tailleur, J.

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Talkner, P.

M. Campisi, P. Talkner, and P. Hänggi, “Influence of measurements on the statistics of work performed on a quantum system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041114 (2011).
[Crossref] [PubMed]

Thomas, D. K.

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Trappe, V.

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

R. Cerbino and V. Trappe, “Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope,” Phys. Rev. Lett. 100(18), 188102 (2008).
[Crossref] [PubMed]

Vekilov, P. G.

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

Vlahovska, P. M.

X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9(1), 28–37 (2013).
[Crossref] [PubMed]

von Smoluchowski, M.

M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
[Crossref]

Vorontsova, M. A.

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

Wilson, L. G.

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

Winkler, R. G.

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers-single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78(5), 056601 (2015).
[Crossref] [PubMed]

Wulstein, D. M.

Yu, Y. N.

C. S. Guo, Y. N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Yuan, Z.

Acad. Sci. (1)

P. Langevin, “Sur la théorie du mouvement brownien,” Acad. Sci. 146, 530–533 (1908).

ACS Nano (1)

K. He, F. Babaye Khorasani, S. T. Retterer, D. K. Thomas, J. C. Conrad, and R. Krishnamoorti, “Diffusive dynamics of nanoparticles in arrays of nanoposts,” ACS Nano 7(6), 5122–5130 (2013).
[Crossref] [PubMed]

Ann. Phys. (2)

E. Frey and K. Kroy, “Brownian motion: a paradigm of soft matter and biological physics,” Ann. Phys. 14(1–3), 20–50 (2005).
[Crossref]

M. von Smoluchowski, “Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen,” Ann. Phys. 326(14), 756–780 (1906).
[Crossref]

Annu. Rev. Biochem. (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent Advances in Optical Tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Annu. Rev. Fluid Mech. (1)

T. M. Squires and T. G. Mason, “Fluid Mechanics of Microrheology,” Annu. Rev. Fluid Mech. 42(1), 413–438 (2010).
[Crossref]

Appl. Opt. (1)

Appl. Phys., A Mater. Sci. Process. (1)

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Hörber, “Photonic force microscope calibration by thermal noise analysis,” Appl. Phys., A Mater. Sci. Process. 66(7), S75–S78 (1998).
[Crossref]

Biomed. Opt. Express (1)

Chin. J. Lasers (1)

H. Chen, Y. M. Li, L. Lou, Z. Gong, and J. Qiu, “Experimental conditions dependence of trap stiffness in optical tweezers,” Chin. J. Lasers 31(11), 1361–1366 (2004).

J. Phys. Condens. Matter (1)

M. C. Jenkins and S. U. Egelhaaf, “Colloidal suspensions in modulated light fields,” J. Phys. Condens. Matter 20(40), 404220 (2008).
[Crossref]

Langmuir (1)

M. Reufer, V. A. Martinez, P. Schurtenberger, and W. C. Poon, “Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics,” Langmuir 28(10), 4618–4624 (2012).
[Crossref] [PubMed]

Nature (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Nucl. Phys. B (1)

A. M. Horowitz, “The second order Langevin equation and numerical simulations,” Nucl. Phys. B 280, 510–522 (1987).
[Crossref]

Opt. Commun. (1)

C. S. Guo, Y. N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, “Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 031403 (2009).
[Crossref] [PubMed]

M. S. Safari, M. A. Vorontsova, R. Poling-Skutvik, P. G. Vekilov, and J. C. Conrad, “Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92(4), 042712 (2015).
[Crossref] [PubMed]

M. Campisi, P. Talkner, and P. Hänggi, “Influence of measurements on the statistics of work performed on a quantum system,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(4), 041114 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

I. Golding and E. C. Cox, “Physical nature of bacterial cytoplasm,” Phys. Rev. Lett. 96(9), 098102 (2006).
[Crossref] [PubMed]

L. G. Wilson, V. A. Martinez, J. Schwarz-Linek, J. Tailleur, G. Bryant, P. N. Pusey, and W. C. Poon, “Differential dynamic microscopy of bacterial motility,” Phys. Rev. Lett. 106(1), 018101 (2011).
[Crossref] [PubMed]

R. Cerbino and V. Trappe, “Differential Dynamic Microscopy: Probing Wave Vector Dependent Dynamics with a Microscope,” Phys. Rev. Lett. 100(18), 188102 (2008).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

J. Elgeti, R. G. Winkler, and G. Gompper, “Physics of microswimmers-single particle motion and collective behavior: a review,” Rep. Prog. Phys. 78(5), 056601 (2015).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys. 81(1), 387–442 (2009).
[Crossref]

M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85(3), 1143–1189 (2013).
[Crossref]

Science (1)

J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339(6122), 936–940 (2013).
[Crossref] [PubMed]

Soft Matter (2)

P. Cicuta and A. M. Donald, “Microrheology: a review of the method and applications,” Soft Matter 3(12), 1449–1455 (2007).
[Crossref]

X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9(1), 28–37 (2013).
[Crossref] [PubMed]

Other (5)

J. Perrin, Brownian movements and molecular reality (New York: Courier Dover. Publications, 2005).

R. Brown, The miscellaneous botanical works of Robert Brown (The Ray Society, 1866).

A. Einstein, Investigations on the Theory of Brownian movement (New York: Dover Publications, 1956).

C. Gardiner and P. Zoller, Quantum Noise, a Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer-Verlag, 2000).

H. Risken, The Fokker–Planck equation: Methods of Solution and Applications (Springer-Verlag, 1984).

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of experimental setup. A laser beam with a wavelength of 635 nm combined with illuminating light that is collimated using convex lens L1 passes through the dichroic mirror (DM) at an angle of 45°, and the light beams are subsequently coaxially incident into the aperture of objective lens L2 and the sample cell. Brownian particles suspended in water under the optical field formed by the laser are observed via objective lens L3 and detected using a CCD camera. An additional optical filter (L4) is added to eliminate the laser light safely for real-space image analysis. (b) Experimental setup. A chopper or other appropriate equipment can be added to modulate the amplitude, polarization and phase of the optical field between the laser and the DM.
Fig. 2
Fig. 2 (a) Weak Gaussian optical fields. (b), (c) Microscopy images of a colloidal dispersion of 800 nm particles at laser powers of 0 mW and 19.32 mW, respectively.
Fig. 3
Fig. 3 Characteristic delay time τ(q) versus wave vector q obtained from fitting of Eq. (3) to the experimental data for laser powers ranging from 0 to 19.32 mW. (a) Comparison between D me and D mt obtained by data fitting without the optical field. Black squares denote experimental data that are fitted to the red line. (b) Three groups of data fitted under different external optical field intensities.
Fig. 4
Fig. 4 Experimental (black squares, D me ) and simulated (red dots, D mt ) diffusion values under different laser powers.

Tables (1)

Tables Icon

Table 1 The experiment result. Nine groups of experimental data are presented to show values of the diffusion coefficient D me and the variations under different external optical field intensities regulated using different laser powers.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

σ 2 (Δt)= | F D ( u x , u y ;Δt) | 2 d u x d u y
D m = K B T/ 3πηd
| F D ( q;Δt ) | 2 =A(q)[ 1exp( Δt/ τ(q) ) ]+B(q)
γ x ˙ = V( x(t) ) x +ξ(t)
P(x,t) t = x [ 1 γ V(x) x P(x,t) ]+ K B T γ 2 P(x,t) x 2
x i (t+Δt)= x i (t)+f(x)Δt+ 2 K B TΔt w

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