Abstract

We extend the previously proposed concept of equiphase sphere (EPS) to analyze light-scattering properties of arbitrarily shaped particles. Our analyses based on the Wentzel-Kramers-Brillouin technique and numerical studies based on the finite-difference time-domain method demonstrate that a wide range of irregularly shaped particles can be approximated as their equivalent equiphase ellipsoids to determine their total scattering cross-section (TSCS) spectra. As a result, a simple expression given by the EPS approximation can be used to calculate the TSCS spectra of these particles. We find that the accuracy of the EPS approximation is influenced by both the magnitude and the geometric scale of the surface perturbation of the particle, and we derive validity conditions of the EPS approximation to guide the practical application of this method.

© 2004 Optical Society of America

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  1. L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
    [CrossRef]
  2. J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
    [CrossRef] [PubMed]
  3. A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
    [PubMed]
  4. Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
    [CrossRef]
  5. H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
    [CrossRef] [PubMed]
  6. J. W. Pyhtila, R. N. Graf, A. Wax, “Determining nuclear morphology using an improved angle-resolved low coherence interferometry system,” Opt. Exp. 11, 3473–3484 (2003), http://www.opticsexpress.org .
    [CrossRef]
  7. M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).
  8. P. Chylek, J. Zhan, “Interference structure of the Mie extinction cross section,” J. Opt. Soc. Am. A 6, 1846–1851 (1989).
    [CrossRef]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  10. Z. Chen, A. Taflove, V. Backman, “Concept of the equiphase sphere for light scattering by nonspherical dielectric particles,” J. Opt. Soc. Am. A 21, 88–97 (2004).
    [CrossRef]
  11. X. Li, Z. Chen, J. Gong, A. Taflove, V. Backman, “Novel analytical techniques to address forward and inverse problems of light scattering by irregularly shaped particles,” Opt. Lett. 29, 1239–1401 (2004).
    [CrossRef] [PubMed]
  12. A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).
  13. H. Nussenzveig, W. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
    [CrossRef]
  14. Z. Chen, A. Taflove, V. Backman, “Equivalent volume-averaged light scattering behavior of randomly inhomogeneous dielectric spheres in the resonant range,” Opt. Lett. 28, 765–767 (2003).
    [CrossRef] [PubMed]
  15. C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (Springer-Verlag, New York, 1999).
    [CrossRef]
  16. J. D. Klett, R. A. Sutherland, “Approximate methods for modeling the scattering properties of non-spherical particles: evaluation of the Wentzel-Kramers-Brillouin method,” Appl. Opt. 31, 373–386 (1992).
    [CrossRef] [PubMed]
  17. K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000).
    [CrossRef]
  18. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  19. K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
    [CrossRef]
  20. A. Taflove, K. R. Umashankar, “Radar cross-section of general three-dimensional structures,” IEEE Trans. Electromagn. Compat. 25, 433–440 (1983).
    [CrossRef]
  21. K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
    [CrossRef]
  22. K. Muinonen, T. Nousiainen, G-sphere, 2002. Available under the GNU General Public License, http://www.meteo.helsinki.fi/∼tpnousia/gsphere/index.html .

2004 (3)

2003 (4)

J. W. Pyhtila, R. N. Graf, A. Wax, “Determining nuclear morphology using an improved angle-resolved low coherence interferometry system,” Opt. Exp. 11, 3473–3484 (2003), http://www.opticsexpress.org .
[CrossRef]

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Z. Chen, A. Taflove, V. Backman, “Equivalent volume-averaged light scattering behavior of randomly inhomogeneous dielectric spheres in the resonant range,” Opt. Lett. 28, 765–767 (2003).
[CrossRef] [PubMed]

2002 (1)

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

1998 (1)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

1996 (1)

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1992 (1)

1989 (1)

1983 (1)

A. Taflove, K. R. Umashankar, “Radar cross-section of general three-dimensional structures,” IEEE Trans. Electromagn. Compat. 25, 433–440 (1983).
[CrossRef]

1982 (1)

K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

1980 (1)

H. Nussenzveig, W. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

Aida, T.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

Backman, V.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

X. Li, Z. Chen, J. Gong, A. Taflove, V. Backman, “Novel analytical techniques to address forward and inverse problems of light scattering by irregularly shaped particles,” Opt. Lett. 29, 1239–1401 (2004).
[CrossRef] [PubMed]

Z. Chen, A. Taflove, V. Backman, “Concept of the equiphase sphere for light scattering by nonspherical dielectric particles,” J. Opt. Soc. Am. A 21, 88–97 (2004).
[CrossRef]

Z. Chen, A. Taflove, V. Backman, “Equivalent volume-averaged light scattering behavior of randomly inhomogeneous dielectric spheres in the resonant range,” Opt. Lett. 28, 765–767 (2003).
[CrossRef] [PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Bender, C. M.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (Springer-Verlag, New York, 1999).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Boone, C. W.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Carpenter, S.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

Chen, K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Chen, Z.

Chylek, P.

Crawford, J. M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Dam, J. V.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Dasari, R. R.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Fast, P.

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Feld, M. S.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Freyer, J. P.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

Goldberg, M. J.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Gong, J.

Graf, R. N.

J. W. Pyhtila, R. N. Graf, A. Wax, “Determining nuclear morphology using an improved angle-resolved low coherence interferometry system,” Opt. Exp. 11, 3473–3484 (2003), http://www.opticsexpress.org .
[CrossRef]

Guerra, A.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

Hagness, S.

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Hamano, T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

Itzkan, I.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Johnson, T. M.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

Kim, Y. L.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Klett, J. D.

Kromine, A. K.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Li, X.

Lima, C.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Liu, Y.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Lumme, K.

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Manoharan, R.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

Mourant, J. R.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

Muinonen, K.

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000).
[CrossRef]

Müller, M.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Nines, R.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Nousiainen, T.

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Nusrat, A.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Nussenzveig, H.

H. Nussenzveig, W. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

Orszag, S. A.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (Springer-Verlag, New York, 1999).
[CrossRef]

Peltoniemi, J. I.

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Perelman, L. T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Pyhtila, J. W.

J. W. Pyhtila, R. N. Graf, A. Wax, “Determining nuclear morphology using an improved angle-resolved low coherence interferometry system,” Opt. Exp. 11, 3473–3484 (2003), http://www.opticsexpress.org .
[CrossRef]

Roy, H. K.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Seiler, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Shields, S.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Steele, V. E.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Stoner, G. D.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Sutherland, R. A.

Taflove, A.

X. Li, Z. Chen, J. Gong, A. Taflove, V. Backman, “Novel analytical techniques to address forward and inverse problems of light scattering by irregularly shaped particles,” Opt. Lett. 29, 1239–1401 (2004).
[CrossRef] [PubMed]

Z. Chen, A. Taflove, V. Backman, “Concept of the equiphase sphere for light scattering by nonspherical dielectric particles,” J. Opt. Soc. Am. A 21, 88–97 (2004).
[CrossRef]

Z. Chen, A. Taflove, V. Backman, “Equivalent volume-averaged light scattering behavior of randomly inhomogeneous dielectric spheres in the resonant range,” Opt. Lett. 28, 765–767 (2003).
[CrossRef] [PubMed]

A. Taflove, K. R. Umashankar, “Radar cross-section of general three-dimensional structures,” IEEE Trans. Electromagn. Compat. 25, 433–440 (1983).
[CrossRef]

K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

Umashankar, K. R.

A. Taflove, K. R. Umashankar, “Radar cross-section of general three-dimensional structures,” IEEE Trans. Electromagn. Compat. 25, 433–440 (1983).
[CrossRef]

K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wali, R.

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

Wali, R. K.

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

Wallace, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Wax, A.

J. W. Pyhtila, R. N. Graf, A. Wax, “Determining nuclear morphology using an improved angle-resolved low coherence interferometry system,” Opt. Exp. 11, 3473–3484 (2003), http://www.opticsexpress.org .
[CrossRef]

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Wiscombe, W.

H. Nussenzveig, W. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

Yang, C.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Zhan, J.

Zonios, G.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Appl. Opt. (1)

Cancer Res. (1)

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Gastroenterology (1)

H. K. Roy, Y. Liu, R. Wali, Y. L. Kim, A. K. Kromine, M. J. Goldberg, V. Backman, “Four-dimensional elastic light-scattering fingerprints as preneoplastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126, 1071–1081 (2004).
[CrossRef] [PubMed]

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

Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromine, K. Chen, V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243–256 (2003).
[CrossRef]

IEEE Trans. Electromagn. Compat. (2)

K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

A. Taflove, K. R. Umashankar, “Radar cross-section of general three-dimensional structures,” IEEE Trans. Electromagn. Compat. 25, 433–440 (1983).
[CrossRef]

J. Biomed. Opt. (1)

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002).
[CrossRef] [PubMed]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Opt. Exp. (1)

J. W. Pyhtila, R. N. Graf, A. Wax, “Determining nuclear morphology using an improved angle-resolved low coherence interferometry system,” Opt. Exp. 11, 3473–3484 (2003), http://www.opticsexpress.org .
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

H. Nussenzveig, W. Wiscombe, “Efficiency factors in Mie scattering,” Phys. Rev. Lett. 45, 1490–1494 (1980).
[CrossRef]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. V. Dam, J. M. Crawford, M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[CrossRef]

Other (6)

M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements and Applications (Academic, San Diego, Calif., 2000).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

K. Muinonen, “Light scattering by stochastically shaped particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000).
[CrossRef]

K. Muinonen, T. Nousiainen, G-sphere, 2002. Available under the GNU General Public License, http://www.meteo.helsinki.fi/∼tpnousia/gsphere/index.html .

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (Springer-Verlag, New York, 1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

TSCS spectra calculated with FDTD simulations and EPS approximations for ellipsoids with different aspect ratios. is the wave vector of the incident light in the legends illustrating the geometry and orientation of the particles. (a) 2a = 4.5 μm, 2b = 3.0 μm, 2c = 3.5 μm, β = 0.18; (b) 2a = 4.0 μm, 2b = 3.0 μm, 2c = 3.5 μm, β = 0.18; (c) 2a = 3.5 μm, 2b = 3.0 μm, 2c = 3.5 μm, β = 0.18; (d) 2a = 2.5 μm, 2b = 3.0 μm, 2c = 3.5 μm, β = 0.5; (e) 2a = 2.0 μm, 2b = 3.0 μm, 2c = 3.5 μm, β = 1.1; (f) 2a = 1.5 μm, 2b = 3.0 μm, 2c = 3.5 μm, β = 2.1.

Fig. 2
Fig. 2

Representative Gaussian sphere geometries. (a)–(c) Gaussian spheres with increasing Δ (γ g is fixed at 70°). (d)–(f) Gaussian spheres with decreasing γ g (Δ is fixed at 0.1).

Fig. 3
Fig. 3

TSCS spectra calculated by FDTD simulations and EPS approximations for a variety of Gaussian spheres. The geometries of the Gaussian sphere and its corresponding best-fitting ellipsoid are illustrated on the left two panels for each example. The incident light propagates in the direction. (a) Δ = 0.1, γ g = 70°; (b) Δ = 0.1, γ g = 10°; (c) Δ = 0.2, γ g = 70°; (d) Δ = 0.2, γ g = 15°; (e) Δ = 0.2, γ g = 40°; (f) Δ = 0.6, γ g = 70°.

Fig. 4
Fig. 4

Accuracy measurements of the EPS approximation as functions of the validity condition of parameter β2. The labeled data points correspond to the cases illustrated in Figs. 3(a)3(f). FDTD simulation results are used as the benchmark data. (a) rms error (%) versus β2, (b) correlation coefficient versus β2.

Equations (25)

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σsλ= 12 πd21-2 sin ρ/ρ+4 sin2ρ/2/ρ2,
ρ= 2πλ dn-1.
d= 1n-1λ1λ2λ2-λ1,
σsλ=σssλ+σsvλ.
σssλ2S 2π3V/4π1/3/λ-2/3,
σsv=2 ReS1-expiξ rd2r,
σsvλ=2S1-2n sin ρ/ρ+4n sin2ρ/2/ρ2,
ρ1, n<2,
ρδL rmax<π/2,
β4n-1bδL/λ 16π2n-12n2aλb/a-b2/a21+a2/b2<1.
β4n-1aδL/λ 16π2n-12n2aλa/b-11+b2/a2<1.
S=πab,
ρ=4πλ cn-1.
β4n-1bδL/λ 16π2n-12n2cλ|c/mina, b-1|1+mina2, b2/c2<1.
σsλ=2S2π 3V/4π1/3/λ-2/3+2S 1-2n sin ρ/ρ+4n sin2ρ/2/ρ2,
argc, ηT, ϕ0|minδLr2.
β1 2πλn-1δLr  1.
12πRe  expiδξdφ-1<1, 12π  expiδξdφ<1,
σ12π  δξdφ< π2.
σ12π  δξdφ n-1λ σi=1N δLiδφi n-1λ δφσδLrN,
β2 22λπn-1ΓσδLr<1.
rϑ, φ= R1+Δ2expsϑ, φ,
sϑ, φ=l=0m=-ll slmYlmϑ, φ.
CsΩ=exp- sin2Ω/22 sin2γg/2,
rci=1NTSCSFDTDλi-TSCSFDTDλTSCSEPSλi-TSCSEPSλNσTSCSFDTDλσTSCSEPSλ,

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