Abstract

Rayleigh-Sommerfeld back-propagation can be used to reconstruct the three-dimensional light field responsible for the recorded intensity in an in-line hologram. Deconvolving the volumetric reconstruction with an optimal kernel derived from the Rayleigh-Sommerfeld propagator itself emphasizes the objects responsible for the scattering pattern while suppressing both the propagating light and also such artifacts as the twin image. Bright features in the deconvolved volume may be identified with such objects as colloidal spheres and nanorods. Tracking their thermally-driven Brownian motion through multiple holographic video images provides estimates of the tracking resolution, which approaches 1 nm in all three dimensions.

© 2011 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011

2010

2009

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (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]

2007

2006

2005

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13, 9361–9373 (2005).
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (McGraw-Hill, 2005).

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005).
[CrossRef]

T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005).
[CrossRef]

2002

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

1999

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, 1999).

1996

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

1986

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

1967

Alsayed, A. M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Amato-Grill, J.

Cheong, F. C.

Chin, K. C.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Cotte, Y.

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]

Cuche, E.

Depeursinge, C.

Dixon, L.

Doi, M.

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

Doyle, P. S.

T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005).
[CrossRef]

T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005).
[CrossRef]

Dreyfus, R.

Edwards, S. F.

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

Emery, Y.

Fink, H.-W.

T. Latychevskaia, F. Gehri, and H.-W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 21, 22527–22544 (2010).
[CrossRef]

Gantimahapatruni, A.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Gehri, F.

T. Latychevskaia, F. Gehri, and H.-W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 21, 22527–22544 (2010).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (McGraw-Hill, 2005).

Grier, D. G.

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]

K. Xiao and D. G. Grier, “Multidimensional optical fractionation with holographic verification,” Phys. Rev. Lett. 104, 028302 (2010).
[CrossRef] [PubMed]

F. C. Cheong and D. G. Grier, “Rotational and translational diffusion of copper oxide nanorods measured with holographic video microscopy,” Opt. Express 18, 6555–6562 (2010).
[CrossRef] [PubMed]

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (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]

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]

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

Han, Y.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Hernandez, C. J.

C. J. Hernandez and T. G. Mason, “Colloidal alphabet soup: Monodisperse dispersions of shape-designed LithoParticles,” J. Phys. Chem. 111, 4477–4480 (2007).

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, S.-H.

Krishnatreya, B. J.

Latychevskaia, T.

T. Latychevskaia, F. Gehri, and H.-W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 21, 22527–22544 (2010).
[CrossRef]

Lee, S.-H.

Lim, C. T.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Lubensky, T. C.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Magistretti, P. J.

Malkiel, E.

Marquet, P.

Mason, T. G.

C. J. Hernandez and T. G. Mason, “Colloidal alphabet soup: Monodisperse dispersions of shape-designed LithoParticles,” J. Phys. Chem. 111, 4477–4480 (2007).

Nobili, M.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Nye, J. F.

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, 1999).

Pavillon, N.

Rappaz, B.

Roichman, Y.

Savin, T.

T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005).
[CrossRef]

T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005).
[CrossRef]

Schnars, U.

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

Shen, Z. X.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Sheng, J.

Sherman, G. C.

Sow, C. H.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Sun, B.

Thong, J. T. L.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Toy, M. F.

van Blaaderen, A.

van Oostrum, P.

Wee, A. T. S.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Xiao, K.

K. Xiao and D. G. Grier, “Multidimensional optical fractionation with holographic verification,” Phys. Rev. Lett. 104, 028302 (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, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[CrossRef]

Xu, X. J.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Yang, S.-M.

Yi, G.-R.

Yodh, A. G.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Yu, T.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Zhang, J.

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Zhu, Y. W.

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Appl. Opt.

Biophys. J.

T. Savin and P. S. Doyle, “Static and dynamic errors in particle tracking microrheology,” Biophys. J. 88, 623–638 (2005).
[CrossRef]

J. Colloid Interface Sci.

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

J. Dairy Sci.

F. C. Cheong, K. Xiao, and D. G. Grier, “Characterization of individual milk fat globules with holographic video microscopy,” J. Dairy Sci. 92, 95–99 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem.

C. J. Hernandez and T. G. Mason, “Colloidal alphabet soup: Monodisperse dispersions of shape-designed LithoParticles,” J. Phys. Chem. 111, 4477–4480 (2007).

Meas. Sci. Technol.

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

Nanotechnology

T. Yu, C. H. Sow, A. Gantimahapatruni, F. C. Cheong, Y. W. Zhu, K. C. Chin, X. J. Xu, C. T. Lim, Z. X. Shen, J. T. L. Thong, and A. T. S. Wee, “Patterning and fusion of CuO nanorods with a focused laser beam,” Nanotechnology 16, 1238–1244 (2005).
[CrossRef]

Opt. Express

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, “Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,” Opt. Express 13, 9361–9373 (2005).
[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 and D. G. Grier, “Rotational and translational diffusion of copper oxide nanorods measured with holographic video microscopy,” Opt. Express 18, 6555–6562 (2010).
[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]

Y. Cotte, M. F. Toy, N. Pavillon, and C. Depeursinge, “Microscopy image resolution improvement by deconvolution of complex fields,” Opt. Express 18, 19462–19478 (2010).
[CrossRef] [PubMed]

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

T. Latychevskaia, F. Gehri, and H.-W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 21, 22527–22544 (2010).
[CrossRef]

Phys. Rev. E

T. Savin and P. S. Doyle, “Role of finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 041106 (2005).
[CrossRef]

Phys. Rev. Lett.

K. Xiao and D. G. Grier, “Multidimensional optical fractionation with holographic verification,” Phys. Rev. Lett. 104, 028302 (2010).
[CrossRef] [PubMed]

Science

Y. Han, A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2009).
[CrossRef]

Other

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, 1986).

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, 1999).

F. C. Cheong, K. Xiao, D. J. Pine, and D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter (to be published), DOI: .
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics , 3rd ed. (McGraw-Hill, 2005).

Supplementary Material (2)

» Media 1: MPG (1904 KB)     
» Media 2: MPG (1992 KB)     

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Figures (2)

Fig. 1
Fig. 1

(a) Normalized holographic video image of a three-dimensional arrangement of nine colloidal silica spheres in water together with the volumetric reconstruction obtained with Eq. (13). (b) Hologram and reconstruction of a copper-oxide nanorod diffusing freely in water. (c) Deconvolved reconstruction of the hologram in (a), obtained with Eq. (14). (d) (Media 1) Deconvolved reconstruction of the nanorod in (b). The same color and opacity table is used to visualize all four reconstructions.

Fig. 2
Fig. 2

(a) Mean-square displacement of a colloidal silica sphere obtained with holographic deconvolution tracking, together with a least-squares fit to Eq. (15). The inset shows the particle’s measured trajectory over 3 minutes. (b) Mean-squared displacement of the orientational unit vector of the diffusing copper-oxide nanorod from Fig. 1, together with a least-squares fit to Eq. (16). The inset shows the positions visited by ŝ(t) on the unit sphere, and are colored by time according to the rainbow color table. (c) Mean-squared displacement of the nanorod’s center of mass along (||) and transverse (⊥) to its instantaneous orientation, together with the predicted Einstein-Smoluchowski dependence on lag time τ. The inset (Media 2) shows 3 minutes of the nanorod’s diffusion as a ribbon tracing out r(t) and oriented along ŝ(t). Colors track orientation. (d) Hologram and deconvolved reconstruction of a lithographically patterned colloid in the form of the letter “X”. Inset: Conventional bright-field image of a similar particle lying flat in the focal plane.

Equations (22)

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

E 0 ( r , z ) = E 0 ( r ) e i k z ɛ ^ 0 ,
E S ( r , z ) = E S ( r , z ) ɛ ^ ( r , z )
I ( r ) = | E 0 ( r , 0 ) + E S ( r , 0 ) | 2
= E 0 2 ( r ) + 2 R e { E 0 ( r ) E S ( r , 0 ) ɛ ^ 0 * ɛ ^ ( r , 0 ) } + | E S ( r , 0 ) | 2 .
b ( r ) I ( r ) I 0 ( r ) 1 2 R e { E R ( r , 0 ) } ,
E R ( r , z ) = E R ( r , 0 ) h ( r , z )
h ( r , z ) = 1 2 π z e i k R R ,
E ˜ R ( q , z ) = E ˜ R ( q , 0 ) H ( q , z ) ,
E ˜ R ( q , z ) = E R ( r , z ) e i q r d 2 r
H ( q , z ) = e i z ( k 2 q 2 ) 1 2
B ( q ) E ˜ R ( q , 0 ) + E ˜ R * ( q , 0 ) .
B ( q ) H ( q , z ) = E ˜ R ( q , z ) + E ˜ R * ( q , z )
E R ( r , z ) e i k z 4 π 2 B ( q ) H ( q , z ) e i q r d 2 q .
I ˜ D ( ρ ) = I ˜ R ( ρ ) K ˜ ( ρ ) + χ ,
Δ r j 2 ( τ ) = [ r j ( t + τ ) r j ( t ) ] 2 t = 2 D j τ + 2 ɛ j 2
Δ s 2 ( τ ) = | s ^ ( t + τ ) s ^ ( t ) | 2 t
Δ s 2 ( τ ) = 2 [ 1 ( 1 ɛ s 2 ) exp ( 2 D r τ ) ]
Δ r | | 2 ( τ ) = 2 D | | τ + 2 ɛ | | 2      and
Δ r 2 ( τ ) = 4 D τ + 4 ɛ 2 ,
D r = 3 k B T π η L 3 [ ln ( L σ ) γ ] ,
D | | = k B T 2 π η L [ ln ( L σ ) γ ] and
D = k B T 4 π η L [ ln ( L σ ) + γ ] ,

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