Abstract

We investigate the wave-optical light scattering properties of deformed thin circular films of constant thickness using the discrete-dipole approximation. Effects on the intensity distribution of the scattered light due to different statistical roughness models, model dependent roughness parameters, and uncorrelated, random, small-scale porosity of the inhomogeneous medium are studied. The suitability of the discrete-dipole approximation for rough-surface scattering problems is evaluated by considering thin films as computationally feasible rough-surface analogs. The effects due to small-scale inhomogeneity of the scattering medium are compared with the analytic approximation by Maxwell Garnett, and the results are found to agree with the approximation.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  2. B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  3. E. L. Wright, "Fractal dust grains around R Coronae Borealis stars," Astrophys. J. Lett. 346, L89-L91 (1989).
    [CrossRef]
  4. K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
    [CrossRef]
  5. M. A. Yurkin and A. G. Hoekstra, "User manual for the discrete dipole approximation code 'amsterdam dda'," http://www.science.uva.nl/research/scs/Software/adda/index.html.
  6. B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti--Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
    [CrossRef]
  7. J. J. Goodman, B. T. Draine, and P. J. Flatau, "Application of fast-Fourier-transform techniques to the discrete-dipole approximation," Opt. Lett. 16, 1198-1200 (1991).
    [CrossRef] [PubMed]
  8. R. J. Adler, The Geometry of Random Fields (Wiley, 1981).
  9. C. Preston, Random Fields (Springer-Verlag, 1976).
  10. I. A. Ibragimov and Y. A. Rozanov, Gaussian Random Processes (Springer-Verlag, 1970).
  11. G. A. Fenton, "Simulation and analysis of random fields," Ph.D. thesis (Princeton University, 1990).
  12. H. P. Parviainen, "Ray tracing model for light scattering from self-affine random rough surfaces," M.S. thesis (University of Helsinki, 2006).
  13. T. Dieker, "Simulation of fractional Brownian motion," M.S. thesis (University of Twente, 2002).
  14. H. P. Parviainen and K. Muinonen, "Rough-surface shadowing of self-affine random rough surfaces," J. Quant. Spectrosc. Radiat. Transf. 106, 398-416 (2007).
    [CrossRef]
  15. C. A. Guérin and A. Sentenac, "Separation of surface and volume effects in scattering from heterogeneous rough surfaces: derivation of a splitting rule," J. Opt. Soc. Am. A 24, 385-390 (2007).
    [CrossRef]
  16. C. F. Bohren and D. R. Huffman, Absorbtion and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  17. J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 358-420 (1904).
  18. B. T. Draine and P. J. Flatau, "User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0," http://arxiv.org/abs/astro-ph/0309069.
  19. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
  20. M. J. Collinge and B. T. Draine, "Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry," J. Opt. Soc. Am. A 21, 2023-2028 (2004).
    [CrossRef]
  21. T. M. Elfouhaily and C. A. Guérin, "Topical review: A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).
    [CrossRef]

2007 (2)

H. P. Parviainen and K. Muinonen, "Rough-surface shadowing of self-affine random rough surfaces," J. Quant. Spectrosc. Radiat. Transf. 106, 398-416 (2007).
[CrossRef]

C. A. Guérin and A. Sentenac, "Separation of surface and volume effects in scattering from heterogeneous rough surfaces: derivation of a splitting rule," J. Opt. Soc. Am. A 24, 385-390 (2007).
[CrossRef]

2006 (1)

H. P. Parviainen, "Ray tracing model for light scattering from self-affine random rough surfaces," M.S. thesis (University of Helsinki, 2006).

2004 (2)

T. M. Elfouhaily and C. A. Guérin, "Topical review: A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).
[CrossRef]

M. J. Collinge and B. T. Draine, "Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry," J. Opt. Soc. Am. A 21, 2023-2028 (2004).
[CrossRef]

2002 (1)

T. Dieker, "Simulation of fractional Brownian motion," M.S. thesis (University of Twente, 2002).

1998 (1)

C. F. Bohren and D. R. Huffman, Absorbtion and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

1994 (2)

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

1993 (1)

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti--Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

1991 (1)

1990 (1)

G. A. Fenton, "Simulation and analysis of random fields," Ph.D. thesis (Princeton University, 1990).

1989 (1)

E. L. Wright, "Fractal dust grains around R Coronae Borealis stars," Astrophys. J. Lett. 346, L89-L91 (1989).
[CrossRef]

1988 (1)

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1981 (1)

R. J. Adler, The Geometry of Random Fields (Wiley, 1981).

1976 (1)

C. Preston, Random Fields (Springer-Verlag, 1976).

1973 (1)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

1970 (1)

I. A. Ibragimov and Y. A. Rozanov, Gaussian Random Processes (Springer-Verlag, 1970).

1904 (1)

J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 358-420 (1904).

Adler, R. J.

R. J. Adler, The Geometry of Random Fields (Wiley, 1981).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorbtion and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Collinge, M. J.

Dieker, T.

T. Dieker, "Simulation of fractional Brownian motion," M.S. thesis (University of Twente, 2002).

Draine, B. T.

M. J. Collinge and B. T. Draine, "Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry," J. Opt. Soc. Am. A 21, 2023-2028 (2004).
[CrossRef]

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti--Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

J. J. Goodman, B. T. Draine, and P. J. Flatau, "Application of fast-Fourier-transform techniques to the discrete-dipole approximation," Opt. Lett. 16, 1198-1200 (1991).
[CrossRef] [PubMed]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

B. T. Draine and P. J. Flatau, "User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0," http://arxiv.org/abs/astro-ph/0309069.

Elfouhaily, T. M.

T. M. Elfouhaily and C. A. Guérin, "Topical review: A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).
[CrossRef]

Fenton, G. A.

G. A. Fenton, "Simulation and analysis of random fields," Ph.D. thesis (Princeton University, 1990).

Flatau, P. J.

Goodman, J.

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti--Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

Goodman, J. J.

Guérin, C. A.

C. A. Guérin and A. Sentenac, "Separation of surface and volume effects in scattering from heterogeneous rough surfaces: derivation of a splitting rule," J. Opt. Soc. Am. A 24, 385-390 (2007).
[CrossRef]

T. M. Elfouhaily and C. A. Guérin, "Topical review: A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).
[CrossRef]

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, "User manual for the discrete dipole approximation code 'amsterdam dda'," http://www.science.uva.nl/research/scs/Software/adda/index.html.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorbtion and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Ibragimov, I. A.

I. A. Ibragimov and Y. A. Rozanov, Gaussian Random Processes (Springer-Verlag, 1970).

Lumme, K.

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 358-420 (1904).

Muinonen, K.

H. P. Parviainen and K. Muinonen, "Rough-surface shadowing of self-affine random rough surfaces," J. Quant. Spectrosc. Radiat. Transf. 106, 398-416 (2007).
[CrossRef]

Parviainen, H. P.

H. P. Parviainen and K. Muinonen, "Rough-surface shadowing of self-affine random rough surfaces," J. Quant. Spectrosc. Radiat. Transf. 106, 398-416 (2007).
[CrossRef]

H. P. Parviainen, "Ray tracing model for light scattering from self-affine random rough surfaces," M.S. thesis (University of Helsinki, 2006).

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Preston, C.

C. Preston, Random Fields (Springer-Verlag, 1976).

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Rahola, J.

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

Rozanov, Y. A.

I. A. Ibragimov and Y. A. Rozanov, Gaussian Random Processes (Springer-Verlag, 1970).

Sentenac, A.

Wright, E. L.

E. L. Wright, "Fractal dust grains around R Coronae Borealis stars," Astrophys. J. Lett. 346, L89-L91 (1989).
[CrossRef]

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, "User manual for the discrete dipole approximation code 'amsterdam dda'," http://www.science.uva.nl/research/scs/Software/adda/index.html.

Astrophys. J. (4)

E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994).
[CrossRef]

B. T. Draine and J. Goodman, "Beyond Clausius-Mossotti--Wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993).
[CrossRef]

Astrophys. J. Lett. (1)

E. L. Wright, "Fractal dust grains around R Coronae Borealis stars," Astrophys. J. Lett. 346, L89-L91 (1989).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

H. P. Parviainen and K. Muinonen, "Rough-surface shadowing of self-affine random rough surfaces," J. Quant. Spectrosc. Radiat. Transf. 106, 398-416 (2007).
[CrossRef]

Opt. Lett. (1)

Philos. Trans. R. Soc. London, Ser. A (1)

J. C. Maxwell Garnett, "Colours in metal glasses and in metallic films," Philos. Trans. R. Soc. London, Ser. A 203, 358-420 (1904).

Waves Random Media (1)

T. M. Elfouhaily and C. A. Guérin, "Topical review: A critical survey of approximate scattering wave theories from random rough surfaces," Waves Random Media 14, R1-R40 (2004).
[CrossRef]

Other (9)

B. T. Draine and P. J. Flatau, "User Guide for the Discrete Dipole Approximation Code DDSCAT.6.0," http://arxiv.org/abs/astro-ph/0309069.

C. F. Bohren and D. R. Huffman, Absorbtion and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, "User manual for the discrete dipole approximation code 'amsterdam dda'," http://www.science.uva.nl/research/scs/Software/adda/index.html.

R. J. Adler, The Geometry of Random Fields (Wiley, 1981).

C. Preston, Random Fields (Springer-Verlag, 1976).

I. A. Ibragimov and Y. A. Rozanov, Gaussian Random Processes (Springer-Verlag, 1970).

G. A. Fenton, "Simulation and analysis of random fields," Ph.D. thesis (Princeton University, 1990).

H. P. Parviainen, "Ray tracing model for light scattering from self-affine random rough surfaces," M.S. thesis (University of Helsinki, 2006).

T. Dieker, "Simulation of fractional Brownian motion," M.S. thesis (University of Twente, 2002).

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 (10)

Fig. 1
Fig. 1

Realizations of the film geometry with fBm and Gc roughness models and horizontal roughness parameter τ varying from small-scale to large-scale roughness. In the upper row we show the fBm model, in the lower the Gc model. Horizontal roughness parameter changes from left to right as H = 0.25 , 0.5, 0.9 and l L = 0.215 , 0.5, 0.75.

Fig. 2
Fig. 2

Realizations of the film geometry with different porosities and void sizes for fBm roughness model with H = 0.5 . The upper row has void size of one dipole and ρ = 1.0 , 0.5, and 0.3 starting from left. The lower row has ρ = 0.5 and void sizes of 2, 4, and 8 dipoles. It can be seen that even the most porous geometry with ρ = 0.3 still preserves most of its wavelength-scale ( 22 dipoles) structure.

Fig. 3
Fig. 3

Simulation geometry. θ i is the angle between the incident radiation and the normal of the film; θ e , between the emergent radiation and the normal of the film, and ϕ i and ϕ e are the azimuth angles computed from the x axis.

Fig. 4
Fig. 4

Distribution of the scattered intensity M 11 as a function of angle of emergence θ e computed for the films with fBm roughness (upper row) and Gc roughness (lower row) and normal incident radiation. The angle of emergence shown ranges from the backscattering and specular direction θ e = 0 ° to θ e = 90 ° , and the diffraction-dominated forward-scattering direction is omitted.

Fig. 5
Fig. 5

Same as Fig. 4 but for θ e ( 0 ° , 20 ° ) .

Fig. 6
Fig. 6

Same Fig. 4 but for θ i = 15 ° , θ e = ( 90 ° 90 ° ) , H ( 0.5 , 0.625 ) , and l ( 3.0 , 5.0 ) . The limits for the angle of emergence are different since the distribution is no longer symmetric around θ e = 0 ° . The shapes of the scattering distributions follow the shapes for normal incident radiation, with clear distinction between the fBm and Gc roughness models.

Fig. 7
Fig. 7

Distribution of scattered intensity shown for fBm films with H ( 0.5 , 0.625 ) , normal incident radiation, and three values for the imaginary part of the refractive index [ k ( 0.01 , 0.1 , 1.0 ) ] .

Fig. 8
Fig. 8

Distribution of scattered intensity for inhomogeneous films with ρ = ( 0.5 , 0.3 ) and solid films with effective index of refraction. Here we show the results for normal incident radiation and θ e = ( 0 ° 360 ° ) (we include the diffraction-dominated forward-scattering direction for clarity).

Fig. 9
Fig. 9

Distribution of the scattered intensity from inhomogeneous films as a function of emergent angle θ e for normal incident radiation and four values of the void size. Shown are the results for films with ρ = 0.5 and fBm roughness of H = 0.5 . The results for void size of one dipole correspond to the results shown in Fig. 4b.

Fig. 10
Fig. 10

Same Fig. 9 but for θ i = 15 ° .

Equations (4)

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

E inc , j = E 0 exp ( i k r j i ω t )
E self , j = k j A j k P k .
A j k P k = exp ( i k r j k ) r j k 3 { k 2 r j k × ( r j k × P k ) + 1 i k r j k r j k 2 [ r j k 2 P k 3 r j k ( r j k P k ) ] } ( j k ) ,
ϵ eff = ϵ m [ 1 + 3 f ( ϵ i ϵ m ϵ i + 2 ϵ m ) 1 f ( ϵ i ϵ m ϵ i + 2 ϵ m ) ] ,

Metrics