Abstract

Micrometer sized particles can be accurately characterized using holographic video microscopy and Lorenz-Mie fitting. In this work, we explore some of the limitations in holographic microscopy and introduce methods for increasing the accuracy of this technique with the use of multiple wavelengths of laser illumination. Large high index particle holograms have near degenerate solutions that can confuse standard fitting algorithms. Using a model based on diffraction from a phase disk, we explain the source of these degeneracies. We introduce multiple color holography as an effective approach to distinguish between degenerate solutions and provide improved accuracy for the holographic analysis of sub-visible colloidal particles.

© 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. 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 (2007).
    [Crossref] [PubMed]
  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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
    [Crossref]
  3. F. C. Cheong, B. S. 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]
  4. H. W. Moyses, B. J. Krishnatreya, and D. G. Grier, “Robustness of Lorenz-Mie microscopy against defects in illumination,” Opt. Express 21, 5968 (2013).
    [Crossref] [PubMed]
  5. C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
    [Crossref] [PubMed]
  6. C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
    [Crossref] [PubMed]
  7. R. Kurita, D. B. Ruffner, and E. R. Weeks, “Measuring the size of individual particles from three-dimensional imaging experiments,” Nat. Commun. 3, 1127 (2012).
    [Crossref] [PubMed]
  8. L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
    [Crossref] [PubMed]
  9. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
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    [Crossref] [PubMed]
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  12. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
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    [Crossref]
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    [Crossref]
  17. Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
    [Crossref]
  18. J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
    [Crossref]
  19. D. Allan, T. Caswell, N. Keim, and C. van der Wel, “Trackpy v0.3.2,” (2016).
  20. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
    [Crossref]
  21. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. for Ind. Appl. Math. 11, 431–441 (1963).
    [Crossref]
  22. F. Cheong, K. Xiao, and D. Grier, “Technical note: characterizing individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
    [Crossref]
  23. M. Hannel, C. Middleton, and D. G. Grier, “Holographic characterization of imperfect colloidal spheres,” Appl. Phys. Lett. 107, 141905 (2015).
    [Crossref]
  24. J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.
  25. A. Perot and C. Fabry, “On the application of interference phenomena to the solution of various problems of spectroscopy and metrology,” Astrophys. J. 9, 87 (1899).
    [Crossref]
  26. Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
    [Crossref]
  27. A. V. Maslov and V. N. Astratov, “Microspherical photonics: sorting resonant photonic atoms by using light,” Appl. Phys. Lett. 105, 121113 (2014).
    [Crossref]
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    [Crossref] [PubMed]
  29. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997), 6th ed.

2017 (2)

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

2016 (2)

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

2015 (1)

M. Hannel, C. Middleton, and D. G. Grier, “Holographic characterization of imperfect colloidal spheres,” Appl. Phys. Lett. 107, 141905 (2015).
[Crossref]

2014 (3)

A. V. Maslov and V. N. Astratov, “Microspherical photonics: sorting resonant photonic atoms by using light,” Appl. Phys. Lett. 105, 121113 (2014).
[Crossref]

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

2013 (2)

H. W. Moyses, B. J. Krishnatreya, and D. G. Grier, “Robustness of Lorenz-Mie microscopy against defects in illumination,” Opt. Express 21, 5968 (2013).
[Crossref] [PubMed]

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

2012 (1)

R. Kurita, D. B. Ruffner, and E. R. Weeks, “Measuring the size of individual particles from three-dimensional imaging experiments,” Nat. Commun. 3, 1127 (2012).
[Crossref] [PubMed]

2010 (1)

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref] [PubMed]

2009 (2)

F. Cheong, K. Xiao, and D. Grier, “Technical note: characterizing individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[Crossref]

F. C. Cheong, B. S. 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]

2007 (2)

1996 (1)

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

1994 (1)

1993 (1)

N. G. Khlebtsov, “Optics of fractal clusters in the anomalous diffraction approximation,” J. Mod. Opt. 40, 2221–2235 (1993).
[Crossref]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. for Ind. Appl. Math. 11, 431–441 (1963).
[Crossref]

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
[Crossref]

1899 (1)

A. Perot and C. Fabry, “On the application of interference phenomena to the solution of various problems of spectroscopy and metrology,” Astrophys. J. 9, 87 (1899).
[Crossref]

Allan, D.

D. Allan, T. Caswell, N. Keim, and C. van der Wel, “Trackpy v0.3.2,” (2016).

Amato-Grill, J.

Ao, W.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

Astratov, V. N.

A. V. Maslov and V. N. Astratov, “Microspherical photonics: sorting resonant photonic atoms by using light,” Appl. Phys. Lett. 105, 121113 (2014).
[Crossref]

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

Barker, P. F.

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref] [PubMed]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Blusewicz, J. M.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

Bohren, C. F.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997), 6th ed.

Brunel, M.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

Carnegie, D.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

Caswell, T.

D. Allan, T. Caswell, N. Keim, and C. van der Wel, “Trackpy v0.3.2,” (2016).

Chen, J.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

Cheong, F.

F. Cheong, K. Xiao, and D. Grier, “Technical note: characterizing individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[Crossref]

Cheong, F. C.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

F. C. Cheong, B. S. 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]

Coetmellec, S.

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Crocker, J. C.

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

Dixon, L.

Draine, B. T.

B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Dreyfus, B. S. R.

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

Fabry, C.

A. Perot and C. Fabry, “On the application of interference phenomena to the solution of various problems of spectroscopy and metrology,” Astrophys. J. 9, 87 (1899).
[Crossref]

Flatau, P. J.

Gordon, H. R.

Gréhan, G.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

Grier, D.

F. Cheong, K. Xiao, and D. Grier, “Technical note: characterizing individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[Crossref]

Grier, D. G.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

M. Hannel, C. Middleton, and D. G. Grier, “Holographic characterization of imperfect colloidal spheres,” Appl. Phys. Lett. 107, 141905 (2015).
[Crossref]

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

H. W. Moyses, B. J. Krishnatreya, and D. G. Grier, “Robustness of Lorenz-Mie microscopy against defects in illumination,” Opt. Express 21, 5968 (2013).
[Crossref] [PubMed]

F. C. Cheong, B. S. 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 (2007).
[Crossref] [PubMed]

J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
[Crossref]

Hannel, M.

M. Hannel, C. Middleton, and D. G. Grier, “Holographic characterization of imperfect colloidal spheres,” Appl. Phys. Lett. 107, 141905 (2015).
[Crossref]

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 colloidal 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, 1983).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

Janssen, A. J. E. M.

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Kasimbeg, P.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

Keim, N.

D. Allan, T. Caswell, N. Keim, and C. van der Wel, “Trackpy v0.3.2,” (2016).

Khlebtsov, N. G.

N. G. Khlebtsov, “Optics of fractal clusters in the anomalous diffraction approximation,” J. Mod. Opt. 40, 2221–2235 (1993).
[Crossref]

Kim, S.-H.

Krishnatreya, B. J.

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

H. W. Moyses, B. J. Krishnatreya, and D. G. Grier, “Robustness of Lorenz-Mie microscopy against defects in illumination,” Opt. Express 21, 5968 (2013).
[Crossref] [PubMed]

Kurita, R.

R. Kurita, D. B. Ruffner, and E. R. Weeks, “Measuring the size of individual particles from three-dimensional imaging experiments,” Nat. Commun. 3, 1127 (2012).
[Crossref] [PubMed]

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

Lan, L.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

Lebrun, D.

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

Lee, S.-H.

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
[Crossref]

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

Li, R.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

Li, Y.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

Macdonald, C.

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Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. for Ind. Appl. Math. 11, 431–441 (1963).
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A. V. Maslov and V. N. Astratov, “Microspherical photonics: sorting resonant photonic atoms by using light,” Appl. Phys. Lett. 105, 121113 (2014).
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Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

McCutcheon, J. R.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

Middleton, C.

M. Hannel, C. Middleton, and D. G. Grier, “Holographic characterization of imperfect colloidal spheres,” Appl. Phys. Lett. 107, 141905 (2015).
[Crossref]

Moyses, H. W.

Perot, A.

A. Perot and C. Fabry, “On the application of interference phenomena to the solution of various problems of spectroscopy and metrology,” Astrophys. J. 9, 87 (1899).
[Crossref]

Philips, L. A.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

Rafailov, E.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

Roichman, Y.

Ruffner, D. B.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

R. Kurita, D. B. Ruffner, and E. R. Weeks, “Measuring the size of individual particles from three-dimensional imaging experiments,” Nat. Commun. 3, 1127 (2012).
[Crossref] [PubMed]

Stutt, A.

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Svitelskiy, O. V.

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

van Blaaderen, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981), corrected ed.

van der Wel, C.

D. Allan, T. Caswell, N. Keim, and C. van der Wel, “Trackpy v0.3.2,” (2016).

van Oostrum, P.

Van Stryland, E.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

Waisi, B.

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

Wang, C.

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

Ward, M. D.

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

Weeks, E. R.

R. Kurita, D. B. Ruffner, and E. R. Weeks, “Measuring the size of individual particles from three-dimensional imaging experiments,” Nat. Commun. 3, 1127 (2012).
[Crossref] [PubMed]

Wichitwong, W.

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997), 6th ed.

Wu, X.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

Wu, Y.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

Xiao, K.

F. Cheong, K. Xiao, and D. Grier, “Technical note: characterizing individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[Crossref]

F. C. Cheong, B. S. 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).
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Yang, S.-M.

Yi, G.-R.

Zhong, X.

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

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 colloidal sphere,” Am. J. Phys. 82, 23–31 (2014).
[Crossref]

Appl. Phys. Lett. (2)

M. Hannel, C. Middleton, and D. G. Grier, “Holographic characterization of imperfect colloidal spheres,” Appl. Phys. Lett. 107, 141905 (2015).
[Crossref]

A. V. Maslov and V. N. Astratov, “Microspherical photonics: sorting resonant photonic atoms by using light,” Appl. Phys. Lett. 105, 121113 (2014).
[Crossref]

Astrophys. J. (2)

A. Perot and C. Fabry, “On the application of interference phenomena to the solution of various problems of spectroscopy and metrology,” Astrophys. J. 9, 87 (1899).
[Crossref]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

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J. C. Crocker and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298–310 (1996).
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J. Dairy Sci. (1)

F. Cheong, K. Xiao, and D. Grier, “Technical note: characterizing individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[Crossref]

J. Eur. Opt. Soc. (1)

S. Coetmellec, W. Wichitwong, G. Gréhan, D. Lebrun, M. Brunel, and A. J. E. M. Janssen, “Digital in-line holography assessment for general phase and opaque particle,” J. Eur. Opt. Soc. 9, 14021 (2014).
[Crossref]

J. Mod. Opt. (1)

N. G. Khlebtsov, “Optics of fractal clusters in the anomalous diffraction approximation,” J. Mod. Opt. 40, 2221–2235 (1993).
[Crossref]

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

J. Pharm. Sci. (1)

C. Wang, X. Zhong, D. B. Ruffner, A. Stutt, L. A. Philips, M. D. Ward, and D. G. Grier, “Holographic characterization of protein aggregates,” J. Pharm. Sci. 105, 1074–1085 (2016).
[Crossref] [PubMed]

J. Quant. Spectrosc. Radiat. Transf. (1)

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transf. 199, 26–35 (2017).
[Crossref]

J. Soc. for Ind. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. for Ind. Appl. Math. 11, 431–441 (1963).
[Crossref]

Light Sci. Appl. (1)

Y. Li, O. V. Svitelskiy, A. V. Maslov, D. Carnegie, E. Rafailov, and V. N. Astratov, “Giant resonant light forces in microspherical photonics,” Light Sci. Appl. 2, e64 (2013).
[Crossref]

Nat. Commun. (1)

R. Kurita, D. B. Ruffner, and E. R. Weeks, “Measuring the size of individual particles from three-dimensional imaging experiments,” Nat. Commun. 3, 1127 (2012).
[Crossref] [PubMed]

Opt. Express (4)

Phys. Rev. Lett. (1)

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref] [PubMed]

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K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
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Soft Matter (1)

C. Wang, F. C. Cheong, D. B. Ruffner, X. Zhong, M. D. Ward, and D. G. Grier, “Holographic characterization of colloidal fractal aggregates,” Soft Matter 12, 8774–8780 (2016).
[Crossref] [PubMed]

Water Res. (1)

L. A. Philips, D. B. Ruffner, F. C. Cheong, J. M. Blusewicz, P. Kasimbeg, B. Waisi, J. R. McCutcheon, and D. G. Grier, “Holographic characterization of contaminants in water: differentiation of suspended particles in heterogeneous dispersions,” Water Res. 122, 431–439 (2017).
[Crossref] [PubMed]

Other (6)

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

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), 3rd ed.

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1981), corrected ed.

D. Allan, T. Caswell, N. Keim, and C. van der Wel, “Trackpy v0.3.2,” (2016).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999), 3rd ed.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1997), 6th ed.

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Figures (5)

Fig. 1
Fig. 1 Schematic for models of holographic microscopy. (a) Thin disk model for hologram formation where incident light, represented by green arrows, impinges on the particle represented by the orange disk. The transmitted light is delayed by the disk, and then diffracts and interferes with the incident light. This interference creates the hologram represented by the ringed pattern below the plane of the disk. The hologram shown is data collected from a sample of 1.5 µm polystyrene particles suspended in DI water and illuminated by a 532nm laser. (b) The particle as a Fabry-Perot etalon where the orange cylinder represents a particle and the green arrows represent light that reflects from or transmits through the particle.
Fig. 2
Fig. 2 Experimental evidence of degenerate solutions. Images (b–d), marked “Data”, are experimentally measured holograms of 1.5 µm diameter polystyrene spheres. Each hologram was measured with a different illumination wavelength, 450 nm, 532 nm and 635 nm respectively. Below, images (e–g), marked “Sphere”, represent the best fit using Lorenz-Mie theory to the corresponding experimental hologram, with an initial guess in diameter, dp, and refractive index, np, at the expected values of 1.5 µm in diameter and 1.6 in refractive index. In (a), additional local minima are found at slightly different size and significantly different refractive index values. The color of the points corresponds to the illumination wavelength, blue: 450 nm, green: 532 nm, and red: 635 nm. For each point in (a), we plot the radial profile, or azimuthal average, of the theoretical hologram corresponding to a sphere with such size and refractive index values in (h–j). The theoretical radial profiles are grouped and colored according to their wavelength. Each theoretical radial profile is compared to the corresponding experimental radial profile (black curve) for that wavelength.
Fig. 3
Fig. 3 Comparison of fits using Fabry-Perot disk model to experimental holograms. Images (b–d), marked “Data”, are experimentally measured holograms of 1.5 µm diameter polystyrene spheres repeated from Fig. 2. Below, images (e–g), marked “Disk”, represent the best fit using the transparent disk model to the corresponding experimental hologram, with an initial guess in size and refractive index near the expected values of 1.5 µm in size and 1.6 in refractive index. Similar to Lorenz-Mie theory, additional local minima are found at slightly different size and significantly different refractive index values. These points are shown in (a) as stars with the corresponding points from Lorenz-Mie theory replotted from Fig. 2(a). The color of the points corresponds to the illumination wavelength, blue: 450 nm, green: 532 nm, and red: 635 nm. For each point in (a), we plot the radial profile, or azimuthal average, of the theoretical hologram corresponding to a disk with such size and refractive index in (h–j). The theoretical radial profiles are grouped and colored according to their wavelength. Each theoretical radial profile is compared to the experimental radial profile, colored black, for that wavelength.
Fig. 4
Fig. 4 Comparison of errors of Lorenz-Mie theory (solid lines) and the disk model (dotted lines) as a function of refractive index for two PS spheres: 1.5 µm (left column) and 9.7 µm (right column). In each panel, the normalized sum of the squared differences between the theoretical hologram and the experimental hologram are plotted versus the refractive index while all other fit parameters are held constant. Each row corresponds to data at a specific wavelength: (a–b) 450 nm, (c–d) 532 nm, and (e–f) 635 nm.
Fig. 5
Fig. 5 Experimental distributions of particle hologram fits to Lorenz-Mie theory as a function of refractive index. Panels (a) and (b) show the fit distributions of 9.7 µm PS particles measured in 450 nm and 532 nm illumination respectively. The vertical dashed lines represent expected position of degenerate peaks. After the true peak is determined, the particles are refit using the true values as starting parameters, and the resulting narrow distributions are plotted in (c) for 450 nm and (d) for 532 nm. In panels (c) and (d), the global minimum is indicated by the vertical gray line.

Equations (12)

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

E 0 ( r ) = E 0 exp ( i k z ) x ^
E s ( r ) = E 0 exp ( i k z p ) f s ( k ( r r p ) )
b ( r ) | E s ( r ) | 2 E 0 2 = | x ^ + exp ( i k z p ) f s ( k ( r r p ) ) | 2 .
Δ ϕ = 2 π λ ( n p n m ) d c .
E ( r ) = E 0 ( r ) + E d ( r ) ( exp ( i Δ ϕ ) 1 )
E 0 ( r ) = E 0 exp ( i k z )
E d ( r ) = i k exp ( i k r ) r d c 2 4 E 0 J 1 ( k d c 2 sin θ ) k d c 2 sin θ
n N = N λ d p + n p .
R = ( E r E i ) 2 = ( n p n m n p + n m ) 2
t c = E t E i = ( 1 R ) exp ( i Δ ϕ ) 1 R exp ( i 2 Δ ϕ ) .
E ( r ) = E 0 ( r ) + E d ( r ) ( t c 1 ) .
Norm Sq . Diff . = i ( I ( r i ) I model ( r i ) ) 2 i | I ( r i ) 1 | .

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