Abstract

A method to extract the complex refractive index of spherical particles from a polydisperse suspension at concentrations where multiple light-scattering effects are significant is presented. The optical constants are estimated from total diffuse reflectance and transmittance measurements and inverting the measurements using the radiative transfer equation (RTE) and the Mie theory for scattering by polydisperse spherical particles. The method is tested by applying it to three different polydisperse polystyrene suspensions and extracting the optical constants of polystyrene particles in the wavelength range of 450-1200 nm. The effect of particle size, concentration, and polydispersity on the estimated values of the optical constants is also discussed.

© 2007 Optical Society of America

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  1. D. M. Scott, "Characterizing particle characterization," Part. Part. Syst. Charact. 20, 305-310 (2003).
  2. M. A. Bartlett and H. Jiang, "Effect of refractive index on the measurement of optical properties in turbid media," Appl. Opt. 40, 1735-1741 (2001).
  3. X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).
  4. S. A. Prahl, "The adding doubling method," in Optical Thermal Response of Laser Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 101-129.
  5. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 25 of IEEE/OUP Series on Electromagnetic Wave Theory (IEEE, 1997), p. 574.
  7. V. d. Hulst, Light Scattering by Small Particles, 1st ed., in Structure of Matter Series (Wiley, 1964), p. 470.
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  10. W. J. Wiscombe, "The Delta-M method:rapid yet accurate radiative flux calculations for strongly asymmetric phase functions," J. Atmos. Sci. 34, 1408-1422 (1977).
  11. I. D. Nikolov and C. D. Ivanov, "Optical plastic refractive measurements in the visible and the near-infrared regions," Appl. Opt. 2000 39, 2067-2070 (2000).
  12. P. Salgi and R. Rajagopalan, "Polydispersity in colloids: implications to static structure and scattering," Adv. Colloid Interface Sci. 43, 169-288 (1993).
  13. D. Qiu, T. Cosgrove, and A., Howe, "Small-angle neutron scattering of concentrated colloidal dispersions: electrostatic/steric composite interactions between colloidal particles, Langmuir 22, 6060-6067 (2006).
  14. G. L. Frontini and B. E. M. Fernandez, "Inversion of elastic light scattering measurements to determine refractive index and particle size distribution of polymeric emulsions," Inverse Probl. Eng. 11, 329-340 (2003).

2006 (1)

D. Qiu, T. Cosgrove, and A., Howe, "Small-angle neutron scattering of concentrated colloidal dispersions: electrostatic/steric composite interactions between colloidal particles, Langmuir 22, 6060-6067 (2006).

2003 (3)

G. L. Frontini and B. E. M. Fernandez, "Inversion of elastic light scattering measurements to determine refractive index and particle size distribution of polymeric emulsions," Inverse Probl. Eng. 11, 329-340 (2003).

D. M. Scott, "Characterizing particle characterization," Part. Part. Syst. Charact. 20, 305-310 (2003).

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

2001 (1)

2000 (1)

I. D. Nikolov and C. D. Ivanov, "Optical plastic refractive measurements in the visible and the near-infrared regions," Appl. Opt. 2000 39, 2067-2070 (2000).

1993 (1)

P. Salgi and R. Rajagopalan, "Polydispersity in colloids: implications to static structure and scattering," Adv. Colloid Interface Sci. 43, 169-288 (1993).

1977 (1)

W. J. Wiscombe, "The Delta-M method:rapid yet accurate radiative flux calculations for strongly asymmetric phase functions," J. Atmos. Sci. 34, 1408-1422 (1977).

1972 (1)

Bartlett, M. A.

Bohren, C. F.

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

Brewster, M. Q.

M. Q. Brewster, Thermal Radiative Transfer and Properties (Wiley, 1992), p. 322.

Brock, S. R.

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Cosgrove, T.

D. Qiu, T. Cosgrove, and A., Howe, "Small-angle neutron scattering of concentrated colloidal dispersions: electrostatic/steric composite interactions between colloidal particles, Langmuir 22, 6060-6067 (2006).

Fernandez, B. E. M.

G. L. Frontini and B. E. M. Fernandez, "Inversion of elastic light scattering measurements to determine refractive index and particle size distribution of polymeric emulsions," Inverse Probl. Eng. 11, 329-340 (2003).

Frontini, G. L.

G. L. Frontini and B. E. M. Fernandez, "Inversion of elastic light scattering measurements to determine refractive index and particle size distribution of polymeric emulsions," Inverse Probl. Eng. 11, 329-340 (2003).

Hale, G. M.

Howe, A.

D. Qiu, T. Cosgrove, and A., Howe, "Small-angle neutron scattering of concentrated colloidal dispersions: electrostatic/steric composite interactions between colloidal particles, Langmuir 22, 6060-6067 (2006).

Hu, X.-H.

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Huffman, D. R.

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

Hulst, V. d.

V. d. Hulst, Light Scattering by Small Particles, 1st ed., in Structure of Matter Series (Wiley, 1964), p. 470.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 25 of IEEE/OUP Series on Electromagnetic Wave Theory (IEEE, 1997), p. 574.

Ivanov, C. D.

I. D. Nikolov and C. D. Ivanov, "Optical plastic refractive measurements in the visible and the near-infrared regions," Appl. Opt. 2000 39, 2067-2070 (2000).

Jacobs, K. M.

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Jiang, H.

Lu, Q. L.

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Ma, X.

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Nikolov, I. D.

I. D. Nikolov and C. D. Ivanov, "Optical plastic refractive measurements in the visible and the near-infrared regions," Appl. Opt. 2000 39, 2067-2070 (2000).

Prahl, S. A.

S. A. Prahl, "The adding doubling method," in Optical Thermal Response of Laser Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 101-129.

Qiu, D.

D. Qiu, T. Cosgrove, and A., Howe, "Small-angle neutron scattering of concentrated colloidal dispersions: electrostatic/steric composite interactions between colloidal particles, Langmuir 22, 6060-6067 (2006).

Querry, M. R.

Rajagopalan, R.

P. Salgi and R. Rajagopalan, "Polydispersity in colloids: implications to static structure and scattering," Adv. Colloid Interface Sci. 43, 169-288 (1993).

Salgi, P.

P. Salgi and R. Rajagopalan, "Polydispersity in colloids: implications to static structure and scattering," Adv. Colloid Interface Sci. 43, 169-288 (1993).

Scott, D. M.

D. M. Scott, "Characterizing particle characterization," Part. Part. Syst. Charact. 20, 305-310 (2003).

Wiscombe, W. J.

W. J. Wiscombe, "The Delta-M method:rapid yet accurate radiative flux calculations for strongly asymmetric phase functions," J. Atmos. Sci. 34, 1408-1422 (1977).

Yang, P.

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Adv. Colloid Interface Sci. (1)

P. Salgi and R. Rajagopalan, "Polydispersity in colloids: implications to static structure and scattering," Adv. Colloid Interface Sci. 43, 169-288 (1993).

Appl. Opt. (2)

Appl. Opt. 2000 (1)

I. D. Nikolov and C. D. Ivanov, "Optical plastic refractive measurements in the visible and the near-infrared regions," Appl. Opt. 2000 39, 2067-2070 (2000).

Inverse Probl. Eng. (1)

G. L. Frontini and B. E. M. Fernandez, "Inversion of elastic light scattering measurements to determine refractive index and particle size distribution of polymeric emulsions," Inverse Probl. Eng. 11, 329-340 (2003).

J. Atmos. Sci. (1)

W. J. Wiscombe, "The Delta-M method:rapid yet accurate radiative flux calculations for strongly asymmetric phase functions," J. Atmos. Sci. 34, 1408-1422 (1977).

Langmuir (1)

D. Qiu, T. Cosgrove, and A., Howe, "Small-angle neutron scattering of concentrated colloidal dispersions: electrostatic/steric composite interactions between colloidal particles, Langmuir 22, 6060-6067 (2006).

Part. Part. Syst. Charact. (1)

D. M. Scott, "Characterizing particle characterization," Part. Part. Syst. Charact. 20, 305-310 (2003).

Phys. Med. Biol. (1)

X. Ma, Q. L. Lu, S. R. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, "Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm," Phys. Med. Biol. 48, 4165-4172 (2003).

Other (5)

S. A. Prahl, "The adding doubling method," in Optical Thermal Response of Laser Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), pp. 101-129.

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

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 25 of IEEE/OUP Series on Electromagnetic Wave Theory (IEEE, 1997), p. 574.

V. d. Hulst, Light Scattering by Small Particles, 1st ed., in Structure of Matter Series (Wiley, 1964), p. 470.

M. Q. Brewster, Thermal Radiative Transfer and Properties (Wiley, 1992), p. 322.

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