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.

© 2013 OSA

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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. Express15, 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. Express15, 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,” Optik123, 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. E7, 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. Fluids39, 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. Acta48, 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. Express17, 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. Express18, 13563–13573 (2010).
    [CrossRef] [PubMed]
  16. L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express19, 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 Matter7, 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. E80, 010401(R) (2009).
    [CrossRef]

2012

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

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik123, 1469–1473 (2012).
[CrossRef]

2011

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter7, 6816–6819 (2011).
[CrossRef]

L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express19, 4393–4398 (2011).
[CrossRef] [PubMed]

2010

2009

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

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta48, 109–115 (2009).
[CrossRef]

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E80, 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. Express17, 13071–13079 (2009).
[CrossRef] [PubMed]

2008

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

2006

2005

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. Fluids39, 1–9 (2005).
[CrossRef]

2004

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

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

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E7, 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,” Optik123, 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. Fluids39, 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,” Optik123, 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. Fluids39, 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. E80, 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. Acta48, 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]

L. Dixon, F. C. Cheong, and D. G. Grier, “Holographic particle-streak velocimetry,” Opt. Express19, 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 Matter7, 6816–6819 (2011).
[CrossRef]

F. C. Cheong, B. J. Krishnatreya, and D. G. Grier, “Strategies for three-dimensional particle tracking with holographic video microscopy,” Opt. Express18, 13563–13573 (2010).
[CrossRef] [PubMed]

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E80, 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. Express17, 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. Acta48, 109–115 (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. Express15, 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. Express15, 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. E80, 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,” Optik123, 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. Fluids39, 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. E80, 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. Fluids39, 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. Fluids39, 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 Matter7, 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. Fluids39, 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. Express15, 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.

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. Express17, 13071–13079 (2009).
[CrossRef] [PubMed]

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E80, 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]

Thompson, B. J.

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E7, 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 Matter7, 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. Express17, 13071–13079 (2009).
[CrossRef] [PubMed]

Xu, W.

Yang, S.-M.

Yi, G.-R.

Appl. Opt.

Appl. Phys. Lett.

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

Exp. Fluids

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. Fluids39, 1–9 (2005).
[CrossRef]

J. Phys. E

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E7, 781–788 (1974).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf.

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.

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

Opt. Commun.

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

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]

Opt. Express

Optik

D. G. Abdelsalam, B. J. Baek, and D. Kim, “Influence of the collimation of the reference wave in off-axis digital holography,” Optik123, 1469–1473 (2012).
[CrossRef]

Phys. Rev. E

B. Sun, J. Lin, E. Darby, A. Y. Grosberg, and D. G. Grier, “Brownian vortexes,” Phys. Rev. E80, 010401(R) (2009).
[CrossRef]

Phys. Rev. Lett.

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

F. C. Cheong, S. Duarte, S.-H. Lee, and D. G. Grier, “Holographic microrheology of polysaccharides from Streptococcus mutans biofilms,” Rheol. Acta48, 109–115 (2009).
[CrossRef]

Soft Matter

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter7, 6816–6819 (2011).
[CrossRef]

Other

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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