Abstract

We present measurements of the scalar-field light scattering of individual dimer, trimer, and tetrahedron shapes among colloidal clusters. By measuring the electric field with quantitative phase imaging at the sample plane and then numerically propagating to the far-field scattering plane, the two-dimensional light-scattering patterns from individual colloidal clusters are effectively and precisely retrieved. The measured scattering patterns are consistent with simulated patterns calculated from the generalized multiparticle Mie solution.

© 2012 Optical Society of America

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  1. F. Borghese, P. Denti, G. Toscano, and O. I. Sindoni, Appl. Opt. 18, 116 (1979).
    [CrossRef]
  2. Y. L. Xu, Appl. Opt. 34, 4573 (1995).
    [CrossRef]
  3. F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
    [CrossRef]
  4. O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
    [CrossRef]
  5. Z. J. Li, Z. S. Wu, and H. Y. Li, J. Opt. Soc. Am. A 28, 118 (2011).
    [CrossRef]
  6. Y. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
    [CrossRef]
  7. G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).
  8. H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
    [CrossRef]
  9. H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, Opt. Lett. 34, 1372 (2009).
    [CrossRef]
  10. Y. K. Park, C. A. Best-Popescu, R. R. Dasari, and G. Popescu, J. Biomed. Opt. 16, 011013 (2011).
    [CrossRef]
  11. Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
    [CrossRef]
  12. H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
    [CrossRef]
  13. Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
    [CrossRef]
  14. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, Opt. Lett. 31, 775 (2006).
    [CrossRef]
  15. Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Express 14, 8263 (2006).
    [CrossRef]
  16. S. K. Debnath and Y. Park, Opt. Lett. 36, 4677 (2011).
    [CrossRef]
  17. V. N. Manoharan, M. T. Elsesser, and D. J. Pine, Science 301, 483 (2003).
    [CrossRef]
  18. I. D. Nikolov and C. D. Ivanov, Appl. Opt. 39, 2067 (2000).
    [CrossRef]
  19. J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, and V. N. Manoharan, Opt. Express 19, 8051 (2011).
    [CrossRef]

2012 (1)

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

2011 (4)

2010 (2)

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

2009 (1)

2008 (1)

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

2006 (2)

2003 (1)

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, Science 301, 483 (2003).
[CrossRef]

2000 (1)

1998 (1)

Y. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

1995 (1)

1984 (2)

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

1979 (1)

Badizadegan, K.

Barman, I.

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

Berl, E.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

Best-Popescu, C. A.

Y. K. Park, C. A. Best-Popescu, R. R. Dasari, and G. Popescu, J. Biomed. Opt. 16, 011013 (2011).
[CrossRef]

Boppart, M.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

Boppart, S. A.

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, Opt. Lett. 34, 1372 (2009).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

Borghese, F.

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, and O. I. Sindoni, Appl. Opt. 18, 116 (1979).
[CrossRef]

Choi, W.

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

Dasari, R. R.

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

Y. K. Park, C. A. Best-Popescu, R. R. Dasari, and G. Popescu, J. Biomed. Opt. 16, 011013 (2011).
[CrossRef]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, Opt. Lett. 31, 775 (2006).
[CrossRef]

Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Express 14, 8263 (2006).
[CrossRef]

Debnath, S. K.

Denti, P.

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, and O. I. Sindoni, Appl. Opt. 18, 116 (1979).
[CrossRef]

Diez-Silva, M.

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

Ding, H.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, Opt. Lett. 34, 1372 (2009).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

Elsesser, M. T.

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, Science 301, 483 (2003).
[CrossRef]

Feld, M. S.

Fu, D.

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

Fung, J.

Gillette, M. U.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

Higgins, J. M.

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

Ikeda, T.

Ivanov, C. D.

Kaz, D. M.

Kim, Y.

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

Li, H. Y.

Li, Z. J.

Liu, J.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

Manoharan, V. N.

Martin, K. E.

McGorty, R.

Millet, L. J.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

Nguyen, F.

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, Opt. Lett. 34, 1372 (2009).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

Nikolov, I. D.

Park, Y.

Park, Y. K.

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

Y. K. Park, C. A. Best-Popescu, R. R. Dasari, and G. Popescu, J. Biomed. Opt. 16, 011013 (2011).
[CrossRef]

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Express 14, 8263 (2006).
[CrossRef]

Perry, R. W.

Pine, D. J.

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, Science 301, 483 (2003).
[CrossRef]

Popescu, G.

Y. K. Park, C. A. Best-Popescu, R. R. Dasari, and G. Popescu, J. Biomed. Opt. 16, 011013 (2011).
[CrossRef]

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

H. Ding, F. Nguyen, S. A. Boppart, and G. Popescu, Opt. Lett. 34, 1372 (2009).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, Opt. Express 14, 8263 (2006).
[CrossRef]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, Opt. Lett. 31, 775 (2006).
[CrossRef]

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

Saija, R.

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

Sindoni, O. I.

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, and O. I. Sindoni, Appl. Opt. 18, 116 (1979).
[CrossRef]

Suresh, S.

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

Toscano, G.

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

F. Borghese, P. Denti, G. Toscano, and O. I. Sindoni, Appl. Opt. 18, 116 (1979).
[CrossRef]

Wang, R. T.

Y. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

Wang, Z.

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

Wu, Z. S.

Xu, Y.

Y. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

Xu, Y. L.

Aerosol Sci. Technol. (2)

F. Borghese, P. Denti, R. Saija, G. Toscano, and O. I. Sindoni, Aerosol Sci. Technol. 3, 227 (1984).
[CrossRef]

O. I. Sindoni, F. Borghese, P. Denti, R. Saija, and G. Toscano, Aerosol Sci. Technol. 3, 237 (1984).
[CrossRef]

Appl. Opt. (3)

IEEE J. Sel. Top. Quantum Electron. (1)

H. Ding, E. Berl, Z. Wang, L. J. Millet, M. U. Gillette, J. Liu, M. Boppart, and G. Popescu, IEEE J. Sel. Top. Quantum Electron. 16, 909 (2010).
[CrossRef]

J. Biomed. Opt. (3)

Y. Kim, J. M. Higgins, R. R. Dasari, S. Suresh, and Y. K. Park, J. Biomed. Opt. 17, 040501 (2012).
[CrossRef]

Y. K. Park, C. A. Best-Popescu, R. R. Dasari, and G. Popescu, J. Biomed. Opt. 16, 011013 (2011).
[CrossRef]

Y. K. Park, M. Diez-Silva, D. Fu, G. Popescu, W. Choi, I. Barman, S. Suresh, and M. S. Feld, J. Biomed. Opt. 15, 020506 (2010).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (1)

Y. Xu and R. T. Wang, Phys. Rev. E 58, 3931 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

H. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, Phys. Rev. Lett. 101, 238102 (2008).
[CrossRef]

Science (1)

V. N. Manoharan, M. T. Elsesser, and D. J. Pine, Science 301, 483 (2003).
[CrossRef]

Other (1)

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw-Hill, 2011).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Diffraction phase microscopy setup, (b) amplitude, (c) phase maps of a PMMA dimer, and (d) 2D light-scattering pattern obtained from the dimer.

Fig. 2.
Fig. 2.

Two-dimensional scattering patterns of the (a),(d) dimer, (b),(e), trimer, and (c),(f) tetrahedron in the experiment (top) and simulation (bottom). Insets show the respective orientations. Solid and dashed lines in (d)–(f) represent principal and auxiliary axes, respectively.

Fig. 3.
Fig. 3.

Coordinate system for light-scattering intensity. A plane wave propagates along the z direction. The scattering plane is determined by the azimuthal angle ϕ. The intensity map is calculated along θ for each azimuthal angle corresponding to the primary and auxiliary axes. The dimer, trimer, and tetrahedron are aligned as shown in (a)–(c), respectively.

Fig. 4.
Fig. 4.

Light-scattering intensity from individual (a),(b) dimers, (c),(d) trimers, and (e),(f) tetrahedrons along the principal and auxiliary axes. The light solid blue lines indicate the experimental data for the individual clusters, and the dark solid blue lines are the averaged experimental data over 10 samples per group. The red error bars indicate the polydispersity in the simulation, taking into account the size variation of single PMMA spheres. Insets show the orientation of each cluster and scattering plane.

Equations (3)

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

I(kx,ky)=12π|A(x,y)exp[i(kxx+kyy)]dxdy|2.
(E||,sE,s)=exp[ik(rz)]ikr(S2S3S4S1)(E||,iE,i),
Iϕ(θ)=|S2(θ)+S3(θ)|ϕ2+|S4(θ)+S1(θ)|ϕ2.

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