Abstract

Lorenz-Mie analysis of colloidal spheres’ holograms has been reported to achieve remarkable resolution not only for the spheres’ three-dimensional positions, but also for their sizes and refractive indexes. Here we apply numerical modeling to establish limits on the instrumental resolution for tracking and characterizing individual colloidal spheres with Lorenz-Mie microscopy.

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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, 3893–3901 (2006).
    [Crossref] [PubMed]
  2. S.-H. Lee and D. G. Grier, “Holographic microscopy of holographically trapped three-dimensional structures,” Opt. Express 15, 1505–1512 (2007).
    [Crossref] [PubMed]
  3. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).
  4. 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]
  5. T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to speciment shape compensation,” Appl. Opt. 45, 851–863 (2006).
    [Crossref] [PubMed]
  6. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836–850 (2006).
    [Crossref] [PubMed]
  7. D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik 123, 1469–1473 (2012).
    [Crossref]
  8. U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
    [Crossref]
  9. J. H. Milgram and W. C. Li, “Computational reconstruction of images from holograms,” Appl. Opt. 41, 853–864 (2002).
    [Crossref] [PubMed]
  10. B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
    [Crossref]
  11. S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. 240, 253–260 (2004).
    [Crossref]
  12. S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
    [Crossref]
  13. F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009).
    [Crossref]
  14. 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]
  15. 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]
  16. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express 19, 4393–4398 (2011).
    [Crossref] [PubMed]
  17. F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
    [Crossref]
  18. H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101, 091102 (2012).
    [Crossref]
  19. J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110, 800–807 (2009).
    [Crossref]
  20. G. Gouesbet, “T-matrix fomulationand generalized Lorenz-Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
    [Crossref]
  21. Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
    [Crossref] [PubMed]
  22. B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
    [Crossref]

2012 (2)

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik 123, 1469–1473 (2012).
[Crossref]

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

2011 (2)

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

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[Crossref]

2010 (2)

2009 (4)

J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110, 800–807 (2009).
[Crossref]

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009).
[Crossref]

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]

2008 (1)

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (3)

2005 (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

2004 (1)

S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. 240, 253–260 (2004).
[Crossref]

2002 (2)

U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

J. H. Milgram and W. C. Li, “Computational reconstruction of images from holograms,” Appl. Opt. 41, 853–864 (2002).
[Crossref] [PubMed]

1974 (1)

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
[Crossref]

Abdelsalam, D. G.

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik 123, 1469–1473 (2012).
[Crossref]

Allano, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

Amato-Grill, J.

Asakura, T.

S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. 240, 253–260 (2004).
[Crossref]

Aspert, N.

Baek, B. J.

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik 123, 1469–1473 (2012).
[Crossref]

Bohren, C. F.

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

Cen, K. F.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

Charrière, F.

Cheong, F. C.

Colomb, T.

Cuche, E.

Darby, E.

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

Depeursinge, C.

Dixon, L.

Dreyfus, R.

Duarte, S.

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009).
[Crossref]

Garcia-Sucerquia, J.

Gouesbet, G.

G. Gouesbet, “T-matrix fomulationand generalized Lorenz-Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
[Crossref]

J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110, 800–807 (2009).
[Crossref]

Grier, D. G.

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

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[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]

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009).
[Crossref]

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[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]

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]

Grosberg, A. Y.

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

Huffman, D. R.

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

Jericho, M. H.

Jericho, S. K.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

Katz, J.

Kim, D.

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik 123, 1469–1473 (2012).
[Crossref]

Kim, S.-H.

Klages, P.

Kreuzer, H. J.

Krishnatreya, B. J.

Kühn, J.

Lebrun, D.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

Lee, S.-H.

Li, W. C.

Lin, J.

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

Lock, J. A.

J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110, 800–807 (2009).
[Crossref]

Malek, M.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

Malkiel, E.

Marquet, P.

Milgram, J. H.

Montfort, F.

Patte-Rouland, B.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

Pine, D. J.

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[Crossref]

Pu, S. L.

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

Roichman, Y.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[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]

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

Sheng, J.

Shpaisman, H.

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

Soontaranon, S.

S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. 240, 253–260 (2004).
[Crossref]

Stolarski, A.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Sun, B.

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

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]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Thompson, B. J.

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
[Crossref]

van Blaaderen, A.

van Oostrum, P.

Widjaja, J.

S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. 240, 253–260 (2004).
[Crossref]

Xiao, K.

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[Crossref]

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]

Xu, W.

Yang, S.-M.

Yi, G.-R.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

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

Exp. Fluids (1)

S. L. Pu, D. Allano, B. Patte-Rouland, M. Malek, D. Lebrun, and K. F. Cen, “Particle field characterization by digital in-line holography: 3D location and sizing,” Exp. Fluids 39, 1–9 (2005).
[Crossref]

J. Phys. E (1)

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E 7, 781–788 (1974).
[Crossref]

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

J. A. Lock and G. Gouesbet, “Generalized Lorenz-Mie theory and applications,” J. Quant. Spectrosc. Radiat. Transf. 110, 800–807 (2009).
[Crossref]

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002).
[Crossref]

Opt. Commun. (2)

S. Soontaranon, J. Widjaja, and T. Asakura, “Improved holographic particle sizing by using absolute values of the wavelet transform,” Opt. Commun. 240, 253–260 (2004).
[Crossref]

G. Gouesbet, “T-matrix fomulationand generalized Lorenz-Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521 (2010).
[Crossref]

Opt. Express (5)

Optik (1)

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik 123, 1469–1473 (2012).
[Crossref]

Phys. Rev. E (1)

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E 80, 010401(R) (2009).
[Crossref]

Phys. Rev. Lett. (1)

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, “Influence of non-conservative optical forces on the dynamics of optically trapped colloidal spheres: The fountain of probability,” Phys. Rev. Lett. 101, 128301 (2008).
[Crossref] [PubMed]

Rheol. Acta (1)

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta 48, 109–115 (2009).
[Crossref]

Soft Matter (1)

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[Crossref]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Schematic representation of image formation by in-line holography. (a) Ideal configuration, with scatterer at height zp above the imaging plane. (b) Diverging illumination. (c) Inclined illumination. Grayscale images are computed holograms illustrating the influence of illumination defects.

Fig. 2
Fig. 2

Relative errors in (a) radius ap, (b) refractive index np and (c) axial position zp as a function of the wavefront radius z0 for various values of the divergence angle Ω.

Fig. 3
Fig. 3

Relative errors in (a) radius ap, (b) refractive index np and (c) axial position zp as a function of angle of inclination of the illumination.

Equations (12)

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

I ( r ) = | E 0 ( r ) + E s ( r r p ) | 2
E s ( r ) = E 0 ( r p ) f ( k ( r r p ) ) ,
f ( k r ) = n = 1 m = n n { r m n [ M e m n ( 3 ) ( k r ) i M o m n ( 3 ) ( k r ) ] i s m n [ N e m n ( 3 ) ( k r ) i N o m n ( 3 ) ( k r ) ] } ,
r m n = i n + 3 m | m | 2 n + 1 n ( n + 1 ) ( n m ) ! ( n | m | ) ! g n , TE m β n ( k a p , n p / n m ) and
s m n = i n + 3 m | m | 2 n + 1 n ( n + 1 ) ( n m ) ! ( n | m | ) ! g n , TM m α n ( k a p , n p / n m ) ,
B ( r ) I ( r ) I 0 ( r ) | x ^ + α e i k z p f ( k ( r r p ) ) | 2 .
E 0 ( r ) = D ( z ) exp ( D ( z ) x 2 + y 2 w 0 2 ) exp ( i k [ z + z 0 ] ) x ^ , where
D ( z ) = ( 1 + 2 i z + z 0 k w 0 2 ) 1 .
i g n , TE 1 = i g n , TE 1 = g n , TM ± 1 = 1 2 exp ( D ( z p ) [ k w 0 ] 2 [ n + 1 2 ] 2 ) .
Ω = tan 1 ( 2 k w 0 ) .
E 0 ( r ) = exp ( i k r ) ε ^ .
f n ^ ( k r ) = R n ^ ( θ ) f ( R n ^ 1 ( θ ) k r )

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