Abstract

The problem of computing the internal electromagnetic field of a homogeneous sphere from the observation of its scattered light field is explored. Using empirical observations it shown that, to good approximation for low contrast objects, there is a simple Fourier relationship between a component of the internal E-field and the scattered light in a preferred plane. Based on this relationship an empirical algorithm is proposed to construct a spherically symmetric particle of approximately the same diameter as the original, homogeneous, one. The size parameter (ka) of this particle is then estimated and shown to be nearly identical to that of the original particle. The size parameter can then be combined with the integrated power of the scatter in the preferred plane to estimate refractive index. The estimated values are shown to be accurate in the presence of moderate noise for a class of size parameters.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Seventh Edition, 2003).
  2. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles, (Academic Press, 2000).
  3. P. J. Wyatt, “Differential Light Scattering: a Physical Method for Identifying Living Bacterial Cells,” Appl. Opt. 7, 1879–1896 (1968).
    [Crossref] [PubMed]
  4. D. Carlton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, (Springer-Verlag, Berlin, 1998).
  5. P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub wavelength optical imaging using the coupled dipole method,” Phys. Rev. B,  69 (245405): 1–7 (2004).
    [Crossref]
  6. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, (Society of Industrial and Applied Mathematics, 2001).
    [Crossref]
  7. V. V. Berdnik and V. A. Loiko, “Particle sizing by multiangle light-scattering data using the high-order neural networks,” J. Quant. Spectrosc. Radiat. Transfer 100, 55–63 (2006).
    [Crossref]
  8. J. Everitt and I. K. Ludlow, “Particle sizing using methods of discrete Legendre analysis,” Biochem Soc. Trans. 19, 504–5 (1991).
    [PubMed]
  9. K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110–5115 (2004).
    [Crossref] [PubMed]
  10. P. H. Faye, “Spatial light-scattering analysis as a means of characterizing and classifying non-spherical particles,” Meas. Sci. Technol. 9, 141–149 (1998).
    [Crossref]
  11. Y. L. Pan, K. B. Aptowicz, R. K. Chang, M. Hart, and J. D. Eversole, “Characterizing and monitoring aerosols by light scattering,” Opt. Lett. 28, 589–591 (2003).
    [Crossref] [PubMed]
  12. B. Shao, J. S. Jaffe, M. Chachisvilis, and S. C. Esener, “Angular resolved light scattering for discriminating among marine picoplankton: modeling and experimental measurements,” Opt. Express 14, 12473–12484 (2006).
    [Crossref] [PubMed]
  13. D. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-VCH, (1983).
  14. H. C. Van de Hulst, Light Scattering by Small Particles, (Dover, 1981).
  15. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge University Press, Cambridge, 2002).
  16. A. Taflove, Computational Electrodynamics: The Finite-difference Time-domain Method, (Artech House, Boston, MA, 1995).
  17. B. T. Draine, “The Discrete-dipole approximation and its application to the interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [Crossref]
  18. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. 11, 1491–1499 (1994).
    [Crossref]
  19. I. K. Ludlow and J. Everitt, “Inverse Mie Problem,” J. Opt. Soc. Am. A. 17, 2229–2235 (2000).
    [Crossref]
  20. T. L. Blundell and L. N. Johnson, Protein Crystallography, (Academic Press, 1976).
  21. A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Lett. 7, 111–112 (1982).
    [Crossref] [PubMed]
  22. A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
    [Crossref]
  23. P. L. D. Roberts and J. S. Jaffe, “Multiple angle acoustic classification of zooplankton,” J. Acous Soc. Am. 121, 2060–2070 (2007).
    [Crossref]
  24. H. R. Gordon, “Rayeigh-Gans scattering approximation: surprisingly useful for understanding backscatter from disk-like particles,” Opt. Express 15, 5572–5588 (2007).
    [Crossref] [PubMed]
  25. A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
    [Crossref]
  26. A. Lompado, “Light Scattering by a Spherical Particle,” http://diogenes.iwt.unibremen. de/vt/laser/wriedt/Mie_Type_Codes/body_mie_type_codes.html
  27. C. C. Dobson and J. W. L. Lewis, “Survey of the Mie Problem Source Function,” J. Opt. Soc. Am. A 6, 463–466 (1989).
    [Crossref]
  28. Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 9, 1354–1361 (2001).
    [Crossref]
  29. A. V. Oppenheim, R. W. Schaefer, and J. R. BuckA. V. Oppenheim, Discrete-Time Signal Processing ed., (Prentice Hall Signal Processing Series, 1999) 2nd Edition.
  30. C. Matzler, “Matlab codes for Mie Scattering and Absorption,” http://diogenes.iwt.unibremen. de/vt/laser/wriedt/Mie_Type_Codes/body_mie_type_codes.html
  31. W. Rysakov and M. Ston, “Light scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 69, 651–665 (2001).
    [Crossref]
  32. V. M. Rysakov, “light scattering by “soft” particles of arbitrary shape and size: II-Arbitrary orientation of particles in the space,” J. Quant. Spectrosc. Radiat. Transfer 98, 85–100 (2006).
    [Crossref]
  33. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [Crossref] [PubMed]
  34. L. M. Shulman, “Analysis of polarimetric data by solving the inverse scattering problem,” Quant. Spectrosc. Radiat. Transfer 88, 243–256 (2004).
    [Crossref]

2007 (2)

P. L. D. Roberts and J. S. Jaffe, “Multiple angle acoustic classification of zooplankton,” J. Acous Soc. Am. 121, 2060–2070 (2007).
[Crossref]

H. R. Gordon, “Rayeigh-Gans scattering approximation: surprisingly useful for understanding backscatter from disk-like particles,” Opt. Express 15, 5572–5588 (2007).
[Crossref] [PubMed]

2006 (3)

V. V. Berdnik and V. A. Loiko, “Particle sizing by multiangle light-scattering data using the high-order neural networks,” J. Quant. Spectrosc. Radiat. Transfer 100, 55–63 (2006).
[Crossref]

B. Shao, J. S. Jaffe, M. Chachisvilis, and S. C. Esener, “Angular resolved light scattering for discriminating among marine picoplankton: modeling and experimental measurements,” Opt. Express 14, 12473–12484 (2006).
[Crossref] [PubMed]

V. M. Rysakov, “light scattering by “soft” particles of arbitrary shape and size: II-Arbitrary orientation of particles in the space,” J. Quant. Spectrosc. Radiat. Transfer 98, 85–100 (2006).
[Crossref]

2004 (3)

L. M. Shulman, “Analysis of polarimetric data by solving the inverse scattering problem,” Quant. Spectrosc. Radiat. Transfer 88, 243–256 (2004).
[Crossref]

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110–5115 (2004).
[Crossref] [PubMed]

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub wavelength optical imaging using the coupled dipole method,” Phys. Rev. B,  69 (245405): 1–7 (2004).
[Crossref]

2003 (2)

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Y. L. Pan, K. B. Aptowicz, R. K. Chang, M. Hart, and J. D. Eversole, “Characterizing and monitoring aerosols by light scattering,” Opt. Lett. 28, 589–591 (2003).
[Crossref] [PubMed]

2002 (1)

A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
[Crossref]

2001 (2)

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 9, 1354–1361 (2001).
[Crossref]

W. Rysakov and M. Ston, “Light scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 69, 651–665 (2001).
[Crossref]

2000 (1)

I. K. Ludlow and J. Everitt, “Inverse Mie Problem,” J. Opt. Soc. Am. A. 17, 2229–2235 (2000).
[Crossref]

1998 (1)

P. H. Faye, “Spatial light-scattering analysis as a means of characterizing and classifying non-spherical particles,” Meas. Sci. Technol. 9, 141–149 (1998).
[Crossref]

1994 (1)

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

1991 (1)

J. Everitt and I. K. Ludlow, “Particle sizing using methods of discrete Legendre analysis,” Biochem Soc. Trans. 19, 504–5 (1991).
[PubMed]

1989 (1)

1988 (1)

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

1982 (2)

1968 (1)

Alfano, R, R.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Alimova, A.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Aptowicz, K. B.

Belkebir, K.

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub wavelength optical imaging using the coupled dipole method,” Phys. Rev. B,  69 (245405): 1–7 (2004).
[Crossref]

Berdnik, V. V.

V. V. Berdnik and V. A. Loiko, “Particle sizing by multiangle light-scattering data using the high-order neural networks,” J. Quant. Spectrosc. Radiat. Transfer 100, 55–63 (2006).
[Crossref]

Blundell, T. L.

T. L. Blundell and L. N. Johnson, Protein Crystallography, (Academic Press, 1976).

Bohren, D. R.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Seventh Edition, 2003).

Buck, J. R.

A. V. Oppenheim, R. W. Schaefer, and J. R. BuckA. V. Oppenheim, Discrete-Time Signal Processing ed., (Prentice Hall Signal Processing Series, 1999) 2nd Edition.

Carlton, D.

D. Carlton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, (Springer-Verlag, Berlin, 1998).

Chachisvilis, M.

Chang, R. K.

Chaumet, P. C.

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub wavelength optical imaging using the coupled dipole method,” Phys. Rev. B,  69 (245405): 1–7 (2004).
[Crossref]

Chernyshev, A. V.

Chu, D. Z

A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
[Crossref]

Devaney, A. J.

Dobson, C. C.

Draine, B. T.

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

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

Esener, S. C.

Everitt, J.

I. K. Ludlow and J. Everitt, “Inverse Mie Problem,” J. Opt. Soc. Am. A. 17, 2229–2235 (2000).
[Crossref]

J. Everitt and I. K. Ludlow, “Particle sizing using methods of discrete Legendre analysis,” Biochem Soc. Trans. 19, 504–5 (1991).
[PubMed]

Eversole, J. D.

Faye, P. H.

P. H. Faye, “Spatial light-scattering analysis as a means of characterizing and classifying non-spherical particles,” Meas. Sci. Technol. 9, 141–149 (1998).
[Crossref]

Fienup, J. R.

Flatau, P. J.

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

Fu, Q.

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 9, 1354–1361 (2001).
[Crossref]

Gordon, H. R.

Hart, M.

Hoekstra, A. G.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles, (Academic Press, 2000).

Huffman, D. R.

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

Jaffe, J. S.

Johnson, L. N.

T. L. Blundell and L. N. Johnson, Protein Crystallography, (Academic Press, 1976).

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, (Society of Industrial and Applied Mathematics, 2001).
[Crossref]

Katz, A.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Kress, R.

D. Carlton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, (Springer-Verlag, Berlin, 1998).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge University Press, Cambridge, 2002).

Lavery, A. C.

A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
[Crossref]

Lewis, J. W. L.

Loiko, V. A.

V. V. Berdnik and V. A. Loiko, “Particle sizing by multiangle light-scattering data using the high-order neural networks,” J. Quant. Spectrosc. Radiat. Transfer 100, 55–63 (2006).
[Crossref]

Lompado, A.

A. Lompado, “Light Scattering by a Spherical Particle,” http://diogenes.iwt.unibremen. de/vt/laser/wriedt/Mie_Type_Codes/body_mie_type_codes.html

Ludlow, I. K.

I. K. Ludlow and J. Everitt, “Inverse Mie Problem,” J. Opt. Soc. Am. A. 17, 2229–2235 (2000).
[Crossref]

J. Everitt and I. K. Ludlow, “Particle sizing using methods of discrete Legendre analysis,” Biochem Soc. Trans. 19, 504–5 (1991).
[PubMed]

Maltsev, V. P.

Matzler, C.

C. Matzler, “Matlab codes for Mie Scattering and Absorption,” http://diogenes.iwt.unibremen. de/vt/laser/wriedt/Mie_Type_Codes/body_mie_type_codes.html

McCormick, S. A.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

McGehee, D. E.

A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles, (Academic Press, 2000).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge University Press, Cambridge, 2002).

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schaefer, and J. R. BuckA. V. Oppenheim, Discrete-Time Signal Processing ed., (Prentice Hall Signal Processing Series, 1999) 2nd Edition.

Pan, Y. L.

Roberts, P. L. D.

P. L. D. Roberts and J. S. Jaffe, “Multiple angle acoustic classification of zooplankton,” J. Acous Soc. Am. 121, 2060–2070 (2007).
[Crossref]

Rosen, R. B.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Rudolph, E.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Rysakov, V. M.

V. M. Rysakov, “light scattering by “soft” particles of arbitrary shape and size: II-Arbitrary orientation of particles in the space,” J. Quant. Spectrosc. Radiat. Transfer 98, 85–100 (2006).
[Crossref]

Rysakov, W.

W. Rysakov and M. Ston, “Light scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 69, 651–665 (2001).
[Crossref]

Savage, H. E.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Schaefer, R. W.

A. V. Oppenheim, R. W. Schaefer, and J. R. BuckA. V. Oppenheim, Discrete-Time Signal Processing ed., (Prentice Hall Signal Processing Series, 1999) 2nd Edition.

Semyanov, K. A.

Sentenac, A.

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub wavelength optical imaging using the coupled dipole method,” Phys. Rev. B,  69 (245405): 1–7 (2004).
[Crossref]

Shah, M. K.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Shao, B.

Shulman, L. M.

L. M. Shulman, “Analysis of polarimetric data by solving the inverse scattering problem,” Quant. Spectrosc. Radiat. Transfer 88, 243–256 (2004).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, (Society of Industrial and Applied Mathematics, 2001).
[Crossref]

Stanton, T. K.

A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
[Crossref]

Ston, M.

W. Rysakov and M. Ston, “Light scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 69, 651–665 (2001).
[Crossref]

Sun, W.

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 9, 1354–1361 (2001).
[Crossref]

Taflove, A.

A. Taflove, Computational Electrodynamics: The Finite-difference Time-domain Method, (Artech House, Boston, MA, 1995).

Tarasov, P. A.

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles, (Academic Press, 2000).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge University Press, Cambridge, 2002).

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles, (Dover, 1981).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Seventh Edition, 2003).

Wyatt, P. J.

Xu, M.

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

Zharinov, A. E.

Appl. Opt. (4)

Astrophys. J. (1)

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

Biochem Soc. Trans. (1)

J. Everitt and I. K. Ludlow, “Particle sizing using methods of discrete Legendre analysis,” Biochem Soc. Trans. 19, 504–5 (1991).
[PubMed]

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

A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R, R. Alfano, “Bacteria Size Determination by Elastic Light Scattering,” IEEE J. Sel. Top. Quantum Electron. 9, 277–287 (2003).
[Crossref]

J. Acous Soc. Am. (1)

P. L. D. Roberts and J. S. Jaffe, “Multiple angle acoustic classification of zooplankton,” J. Acous Soc. Am. 121, 2060–2070 (2007).
[Crossref]

J. Acous. Soc. Am (1)

A. C. Lavery, T. K. Stanton, D. E. McGehee, and D. Z Chu, “Three-dimensional modeling of acoustic backscattering from fluid-like zooplankton,”  111, J. Acous. Soc. Am1197–1210 (2002).
[Crossref]

J. Opt. Soc. Am. (1)

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

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

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

I. K. Ludlow and J. Everitt, “Inverse Mie Problem,” J. Opt. Soc. Am. A. 17, 2229–2235 (2000).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (3)

V. V. Berdnik and V. A. Loiko, “Particle sizing by multiangle light-scattering data using the high-order neural networks,” J. Quant. Spectrosc. Radiat. Transfer 100, 55–63 (2006).
[Crossref]

W. Rysakov and M. Ston, “Light scattering by spheroids,” J. Quant. Spectrosc. Radiat. Transfer 69, 651–665 (2001).
[Crossref]

V. M. Rysakov, “light scattering by “soft” particles of arbitrary shape and size: II-Arbitrary orientation of particles in the space,” J. Quant. Spectrosc. Radiat. Transfer 98, 85–100 (2006).
[Crossref]

Meas. Sci. Technol. (1)

P. H. Faye, “Spatial light-scattering analysis as a means of characterizing and classifying non-spherical particles,” Meas. Sci. Technol. 9, 141–149 (1998).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (1)

P. C. Chaumet, K. Belkebir, and A. Sentenac, “Three-dimensional sub wavelength optical imaging using the coupled dipole method,” Phys. Rev. B,  69 (245405): 1–7 (2004).
[Crossref]

Quant. Spectrosc. Radiat. Transfer (1)

L. M. Shulman, “Analysis of polarimetric data by solving the inverse scattering problem,” Quant. Spectrosc. Radiat. Transfer 88, 243–256 (2004).
[Crossref]

Other (12)

A. V. Oppenheim, R. W. Schaefer, and J. R. BuckA. V. Oppenheim, Discrete-Time Signal Processing ed., (Prentice Hall Signal Processing Series, 1999) 2nd Edition.

C. Matzler, “Matlab codes for Mie Scattering and Absorption,” http://diogenes.iwt.unibremen. de/vt/laser/wriedt/Mie_Type_Codes/body_mie_type_codes.html

A. Lompado, “Light Scattering by a Spherical Particle,” http://diogenes.iwt.unibremen. de/vt/laser/wriedt/Mie_Type_Codes/body_mie_type_codes.html

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, (Society of Industrial and Applied Mathematics, 2001).
[Crossref]

D. Carlton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, (Springer-Verlag, Berlin, 1998).

M. Born and E. Wolf, Principles of Optics, (Cambridge University Press, Seventh Edition, 2003).

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles, (Academic Press, 2000).

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

H. C. Van de Hulst, Light Scattering by Small Particles, (Dover, 1981).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge University Press, Cambridge, 2002).

A. Taflove, Computational Electrodynamics: The Finite-difference Time-domain Method, (Artech House, Boston, MA, 1995).

T. L. Blundell and L. N. Johnson, Protein Crystallography, (Academic Press, 1976).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1.
Fig. 1.

The observed complex angular light scattered data can be viewed as the coefficients of the Fourier Transform of the structure: ��(k struc ) on the Ewald sphere [20] that is centered - k inc at a radius of |k|=2π/λ.

Fig. 2.
Fig. 2.

Two graphs of the phase of the internal Ex field along the z-axis for the cases where (a,m)=(1 µm, 1.05) (a) or (1 µm, 1.58) (b). The graph depicts a superposition of the z-dependent phase along with the standard deviation of those phases at a given z location. Graphs were produced via the implementation of Mie theory to compute the interior electric field for a spherical particle embedded inside a cubic lattice of dimensions (21)3.

Tables (2)

Tables Icon

Table 1. Averages and standard deviations of retrieved values for the size index when m=1.035+0.00i. The data was obtained by performing 100 repeated tomographic inversions after 10% multiplicative noise was added to the real and imaginary parts of the simulated complex angular scatter.

Tables Icon

Table 2. Averages and standard deviations of retrieved values of the refractive index for the case m=1.035+0.00i. The data was obtained by performing 100 repeated tomographic inversions when 10% multiplicative noise was added to the real and imaginary parts of the simulated complex angular scatter.

Equations (16)

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

E i = ( E 0    e ^ 0 + E 0 e ^ i ) exp ( ik in c    z  i ω t ) .
E s = E | | s e ^ | | s + E s e ^ s where e ^ | | s = e ^ θ ,        e ^ s =    e ^ ϕ ,        e ^ s × e ^ | | s = e ^ r .
( E s E s ) = exp i k ( r z ) ikr ( S 2 S 3 S 4 S 1 ) ( E i E i )
E i = E 0 n = 1 i n 2 n + 1 n ( n + 1 ) ( M o ln ( 1 ) i N e ln ( 1 ) )
E int = E 0 n = 1 i n 2 n + 1 n ( n + 1 ) ( c n M o ln ( 1 ) i d n N e ln ( 1 ) ) ,
E s = E 0 n = 1 i n 2 n + 1 n ( n + 1 ) ( i b n N o ln ( 3 ) a n M e ln ( 3 ) ) ,
( E s E s ) = exp i k ( r z ) ikr ( S 2 0 0 S 1 ) ( E i E i ) .
E s ( d ) = k 2 exp ( i k d ) d j = 1 N exp ( i k d ̂ · r j ) ( d ̂ d ̂ l 3 ) P j .
E s ( k ̂ obs d ) = k 2 exp ( ik d ) d j = 1 N exp ( i k k ̂ obs · r j ) ( k ̂ obs k ̂ obs l 3 ) P j .
E sx ( k ̂ obs ) = k 2 exp ( i k d ) d j = 1 N exp ( i k obs · r j ) ( P jx ) .
E sx ( k obs ) = k 2 exp ( ik d ) d α j = 1 N E x int ( r j ) exp ( i k obs · r j ) .
a n = 1 2 n ( n + 1 ) 0 π [ S ( θ ) τ n ( θ ) + S ( θ ) π n ( θ ) ] sin θ d θ .
b n = 1 2 n ( n + 1 ) 0 π [ S ( θ ) π n ( θ ) + S ( θ ) τ n ( θ ) ] sin θ d θ .
f scat = k 2 4 π V N ( r v ) e i ( k scat k inc ) 2 i · r v d V .
E x int = E x ( r j ) exp ( i k inc · r j ) .
E xs ( k obs ) = k 2 exp ( ik d ) d α j = 1 N E x int ( r j ) exp ( i ( k obs k inc ) int ) · r j

Metrics