Abstract

A superposition rule for light scattering by composite particles is presented that expresses the scattering amplitude of a composite particle as a superposition of that of the host particle and those of the shadowed inclusions. The superposition rule is derived for a soft composite particle but also provides insight into light scattering by a general composite scatterer. Favorable comparison with an exact numerical method demonstrates the usefulness of the rule in analyzing light scattering by composite particles such as biological cells.

© 2006 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  2. M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 1999).
  3. M. P. Ioannidou, I. I. Bakatsoula, and D. P. Chrissoulidis, Appl. Opt. 39, 4205 (2000).
    [CrossRef]
  4. D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
    [CrossRef] [PubMed]
  5. R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
    [CrossRef] [PubMed]
  6. G. Videen, D. Ngo, P. Chýlek, and R. G. Pinnick, J. Opt. Soc. Am. A 12, 922 (1995).
    [CrossRef]
  7. D. R. Secker, P. H. Kaye, R. S. Greenaway, E. Hirst, D. L. Bartley, and G. Videen, Appl. Opt. 39, 5023 (2000).
    [CrossRef]
  8. M. Xu, M. Lax, and R. R. Alfano, Opt. Lett. 28, 179 (2003).
    [CrossRef] [PubMed]
  9. M. Xu, Appl. Opt. 42, 6710 (2003).
    [CrossRef] [PubMed]
  10. Y. Liu, W. P. Arnott, and J. Hallett, Appl. Opt. 37, 5019 (1998).
    [CrossRef]
  11. P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
    [CrossRef]
  12. The coated sphere Mie code by C. Mätzler, is available at http://www.t-matrix.de/.
  13. W. J. Wiscombe, Appl. Opt. 19, 1505 (1980).
    [CrossRef] [PubMed]

2004 (1)

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

2003 (4)

M. Xu, M. Lax, and R. R. Alfano, Opt. Lett. 28, 179 (2003).
[CrossRef] [PubMed]

M. Xu, Appl. Opt. 42, 6710 (2003).
[CrossRef] [PubMed]

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

2000 (2)

1998 (1)

1995 (1)

1980 (1)

Alfano, R. R.

Arifler, D.

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

Arnott, W. P.

Bakatsoula, I. I.

Bartley, D. L.

Baum, B.

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

Bioko, I.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

Carraro, A.

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

Chrissoulidis, D. P.

Chýlek, P.

Collier, T.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

Drezek, R.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

Follen, M.

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

Greenaway, R. S.

Guillaud, M.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

Hallett, J.

Hirst, E.

Hu, Y.

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

Huang, H.-L.

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

Ioannidou, M. P.

Kaye, P. H.

Lax, M.

Liu, Y.

Macaulay, C.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

Malpica, A.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

Mätzler, C.

The coated sphere Mie code by C. Mätzler, is available at http://www.t-matrix.de/.

Ngo, D.

Pinnick, R. G.

Richards-Kortum, R.

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

Secker, D. R.

van de Hulst, H. C.

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

Videen, G.

Wiscombe, W. J.

Xu, M.

Yang, P.

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

Zhang, Z.

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

Appl. Opt. (5)

J. Biomed. Opt. (2)

D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 484 (2003).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Bioko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, J. Biomed. Opt. 8, 7 (2003).
[CrossRef] [PubMed]

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

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

P. Yang, Z. Zhang, B. Baum, H.-L. Huang, and Y. Hu, J. Quant. Spectrosc. Radiat. Transf. 89, 421 (2004).
[CrossRef]

Opt. Lett. (1)

Other (3)

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

M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 1999).

The coated sphere Mie code by C. Mätzler, is available at http://www.t-matrix.de/.

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Figures (3)

Fig. 1
Fig. 1

(a) Composite scatterer illuminated by an incident beam along the z axis. (b) Equivalent configuration with an outside nucleus shadowed by the host particle. The shadowed nucleus has a modified refractive index.

Fig. 2
Fig. 2

Extinction efficiencies for various concentric spheres of radius (a) a = 8 μ m and (b) a = 32 μ m . The ratio of the size of the nucleus over that of the host particle is γ = 0.5 . The relative refractive indices are m 0 = 1.02 for the host particle and m 1 = 1.08 for the nucleus. The refractive index of the environment is assumed to be 1.33. The values obtained by using the superposition rule agree well with the exact ones. The extinction efficiencies for the host particle alone are also plotted for comparison.

Fig. 3
Fig. 3

Angular light scattering by various concentric spheres of the same parameters as those in Fig. 2. The wavelength of the incident light is 500 nm . The angular spectra obtained by using the superposition rule agree well with the exact ones. The angular spectra for the host particle alone are also plotted for comparison.

Equations (7)

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S ( q ) = k 2 2 π { 1 exp [ i p ( ξ , η ) ] } e i ( ξ q ξ + η q η ) d ξ d η ,
S ( q ) = S 0 ( q ) + exp ( i r c q ) f c S n ( q ) ,
f c S n ( q ) = k 2 2 π f c ( ξ , η ) { 1 exp [ i δ p ( ξ , η ) ] } e i ( ξ q ξ + η q η ) d ξ d η ,
S ( q ) = S 0 ( q ) + exp ( i r c q i ρ ¯ ) S n ( q ) ,
S ( q ) = S 0 ( q ) + j exp ( i r c j q i ρ ¯ j ) S j ( q ) ,
S ( q ) = S 0 ( q ) + f ( q , r c ) S n ( q ) ,
f ( q ) ¯ = 3 0 π 2 exp ( i ρ max 1 ϵ 2 cos 2 τ ) J 0 ( q a ϵ cos τ ) cos τ sin 2 τ d τ ,

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