Abstract

Holograms of colloidal dispersions encode comprehensive information about individual particles’ three-dimensional positions, sizes and optical properties. Extracting that information typically is computationally intensive, and thus slow. Here, we demonstrate that machine-learning techniques based on support vector machines (SVMs) can analyze holographic video microscopy data in real time on low-power computers. The resulting stream of precise particle-resolved tracking and characterization data provides unparalleled insights into the composition and dynamics of colloidal dispersions and enables applications ranging from basic research to process control and quality assurance.

© 2014 Optical Society of America

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References

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  1. J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. A. Bourquard, N. Pavillon, E. Bostan, C. Depeursinge, and M. Unser, “A practical inverse-problem approach to digital holographic reconstruction,” Opt. Express 21, 3417–3433 (2013).
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  9. H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  13. B. J. Krishnatreya and D. G. Grier, “Fast feature identification for holographic tracking: The orientation alignment transform,” Opt. Express 22, 12773–12778 (2014).
    [Crossref] [PubMed]
  14. See, for example, http://physics.nyu.edu/grierlab/software.html for holographic microscopy software written in the IDL programming language that was used in the present study. A comparable implementation in the python programming language is available at http://manoharan.seas.harvard.edu/holopy/ .
  15. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).
  16. C.-C. Chang and C.-J. Lin, “LIBSVM: A library for support vector machines,” ACM Trans. Intel. Sys. Tech. 2, 27 (2011).
  17. C.-C. Chang and C.-J. Lin, “Training ν-Support Vector Regression: Theory and Algorithms,” Neural Comput. 14, 1959–1977 (2002).
    [Crossref] [PubMed]
  18. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011).
    [Crossref] [PubMed]

2014 (2)

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

B. J. Krishnatreya and D. G. Grier, “Fast feature identification for holographic tracking: The orientation alignment transform,” Opt. Express 22, 12773–12778 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
[Crossref]

2011 (3)

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

C.-C. Chang and C.-J. Lin, “LIBSVM: A library for support vector machines,” ACM Trans. Intel. Sys. Tech. 2, 27 (2011).

L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2007 (2)

2006 (1)

2004 (1)

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14, 199–222 (2004).
[Crossref]

2002 (1)

C.-C. Chang and C.-J. Lin, “Training ν-Support Vector Regression: Theory and Algorithms,” Neural Comput. 14, 1959–1977 (2002).
[Crossref] [PubMed]

Amato-Grill, J.

Bell, B. A.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Blondel, M.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Bostan, E.

Bourquard, A.

Brucher, M.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Chang, C.-C.

C.-C. Chang and C.-J. Lin, “LIBSVM: A library for support vector machines,” ACM Trans. Intel. Sys. Tech. 2, 27 (2011).

C.-C. Chang and C.-J. Lin, “Training ν-Support Vector Regression: Theory and Algorithms,” Neural Comput. 14, 1959–1977 (2002).
[Crossref] [PubMed]

Cheong, F. C.

Colen-Landy, A.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Cournapeau, D.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Denis, L.

Depeursinge, C.

Dixon, L.

Dreyfus, R.

Dubourg, V.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Duchesnay, E.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Fournier, C.

Fung, J.

J. Fung and V. N. Manoharan, “Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters,” Phys. Rev. E 88, 020302 (2013).
[Crossref]

Gramfort, A.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Grier, D. G.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

B. J. Krishnatreya and D. G. Grier, “Fast feature identification for holographic tracking: The orientation alignment transform,” Opt. Express 22, 12773–12778 (2014).
[Crossref] [PubMed]

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
[Crossref]

L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011).
[Crossref] [PubMed]

F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
[Crossref] [PubMed]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17, 13071–13079 (2009).
[Crossref] [PubMed]

S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007).
[Crossref] [PubMed]

S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007).
[Crossref] [PubMed]

Grisel, O.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Hasebe, P.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

Jones, J. R.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Katz, J.

Kim, S.-H.

Krishnatreya, B. J.

B. J. Krishnatreya and D. G. Grier, “Fast feature identification for holographic tracking: The orientation alignment transform,” Opt. Express 22, 12773–12778 (2014).
[Crossref] [PubMed]

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
[Crossref]

F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express 18, 13563–13573 (2010).
[Crossref] [PubMed]

Lee, S.-H.

Lin, C.-J.

C.-C. Chang and C.-J. Lin, “LIBSVM: A library for support vector machines,” ACM Trans. Intel. Sys. Tech. 2, 27 (2011).

C.-C. Chang and C.-J. Lin, “Training ν-Support Vector Regression: Theory and Algorithms,” Neural Comput. 14, 1959–1977 (2002).
[Crossref] [PubMed]

Malkiel, E.

Manoharan, V. N.

J. Fung and V. N. Manoharan, “Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters,” Phys. Rev. E 88, 020302 (2013).
[Crossref]

Michel, V.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Passos, A.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Pavillon, N.

Pedregosa, F.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Perrot, M.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Prettenhofer, P.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Roichman, Y.

Schölkopf, B.

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14, 199–222 (2004).
[Crossref]

Seifi, M.

Sheng, J.

Shpaisman, H.

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
[Crossref]

Smola, A. J.

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14, 199–222 (2004).
[Crossref]

Sun, B.

Sunda-Meya, A.

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Thirion, B.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Unser, M.

van Blaaderen, A.

van Oostrum, P.

Vanderplas, J.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Varoquaux, G.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Weiss, R.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Xiao, K.

Yang, S.-M.

Yi, G.-R.

ACM Trans. Intel. Sys. Tech. (1)

C.-C. Chang and C.-J. Lin, “LIBSVM: A library for support vector machines,” ACM Trans. Intel. Sys. Tech. 2, 27 (2011).

Am. J. Phys. (1)

B. J. Krishnatreya, A. Colen-Landy, P. Hasebe, B. A. Bell, J. R. Jones, A. Sunda-Meya, and D. G. Grier, “Measuring Boltzmann’s constant through holographic video microscopy of a single sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
[Crossref]

J. Mach. Learn. Res. (1)

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

J. Opt. Soc. Am. A (1)

Neural Comput. (1)

C.-C. Chang and C.-J. Lin, “Training ν-Support Vector Regression: Theory and Algorithms,” Neural Comput. 14, 1959–1977 (2002).
[Crossref] [PubMed]

Opt. Express (7)

Phys. Rev. E (1)

J. Fung and V. N. Manoharan, “Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters,” Phys. Rev. E 88, 020302 (2013).
[Crossref]

Stat. Comput. (1)

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14, 199–222 (2004).
[Crossref]

Other (2)

See, for example, http://physics.nyu.edu/grierlab/software.html for holographic microscopy software written in the IDL programming language that was used in the present study. A comparable implementation in the python programming language is available at http://manoharan.seas.harvard.edu/holopy/ .

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).

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Figures (2)

Fig. 1
Fig. 1

Colloidal characterization by holographic microscopy and machine learning. Colloidal spheres flowing down a microfluidic sample scatter light from a collimated laser beam to form an in-line hologram. Features in the beam are identified, and their radial profiles presented to support vector machines (SVMs) that compare them with a library of training data to estimate each spheres’ radius ap and refractive index np. The scatter plot shows results for 2,500 spheres drawn at random from a mixture of four different types of spheres. Each point is colored by the local density of data points, ρ(ap, np).

Fig. 2
Fig. 2

Tracking and characterizing a single colloidal sphere. (a) The estimated axial position zp(t) relative to the focal plane of the microscope of a single polystyrene sphere sedimenting through water as it diffuses. The line is a least-squares fit. Insets show the sphere’s hologram at the beginning and end of the trajectory. (b) The radius ap and refractive index np estimated from each hologram in the same sequence, colored by time. Each dot corresponds to values obtained from a single hologram. (c) The mean-squared displacement, Δ z p 2 ( τ ) as a function of lag time τ computed from the data in (a), including statistical error bars. The superimposed line is a fit to Eq. (7).

Equations (7)

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

E 0 ( r ) = u 0 ( r ) e i φ 0 ( r ) e i k z x ^ ,
E s ( r ) = E 0 ( r p ) f s ( k ( r r p ) | a p , n p ) ) ,
I ( r ) = | E 0 ( r ) + E s ( r ) | 2 .
b ( r ) = I ( r ) I 0 ( r ) | x ^ + e i k z p f s ( k ( r r p ) | a p , n p ) | 2 ,
k n ( b ) = exp ( γ | b n ( r ) b ( r ) | 2 d r ) ,
s ˜ ( b ) = n ω n k n ( b ) + s 0 ,
Δ z p 2 ( τ ) [ z p ( t + τ ) z p ( t ) ] 2 t = 2 D τ + v p 2 τ 2 + 2 ε z 2 ,

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