Abstract

Theory of weak scattering of random optical fields from deterministic collections of particles with soft ellipsoidal scattering potentials of arbitrary shapes and orientations is developed. Far-field intensity distribution produced on scattering is shown to be influenced by source correlation properties as well as by a number, shapes and orientations of scatterers. The theory extends previous results on scattering from collections of spheres with soft Gaussian potentials and is applicable to analysis of a wide range of media including blood cells.

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References

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2011

2009

2008

S. Sahin and O. Korotkova, “Scattering of scalar light fields from collections of particles,” Phys. Rev. A78(6), 063815 (2008).
[CrossRef]

2007

O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056609 (2007).
[CrossRef] [PubMed]

D. Zhao, O. Korotkova, and E. Wolf, “Application of correlation-induced spectral changes to inverse scattering,” Opt. Lett.32(24), 3483–3485 (2007).
[CrossRef] [PubMed]

2005

1998

1994

1993

1990

1989

Behrend, M. R.

Brock, R. S.

Cai, Y.

Dogariu, A.

Eyyuboglu, H. T.

Fischer, D. G.

Foley, J. T.

Gbur, G.

Gori, F.

Heethaar, R. M.

Hegg, M. C.

Hoekstra, A. G.

Horning, M. P.

Hu, X. H.

Korotkova, O.

Lu, J.

Lu, X.

Nijhof, E. J.

Sahin, S.

Streekstra, G. J.

Tong, Z.

Z. Tong and O. Korotkova, “Method for tracing the position of an alien object embedded in a random particulate medium,” J. Opt. Soc. Am. A28(8), 1595–1599 (2011).
[CrossRef] [PubMed]

Z. Tong and O. Korotkova, “Pair-structure matrix of random collections of particles: Implications for light scattering,” Opt. Commun.284(24), 5598–5600 (2011).
[CrossRef]

Wilson, B. K.

Wolf, E.

Yang, P.

Zhao, C.

Zhao, D.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

Z. Tong and O. Korotkova, “Pair-structure matrix of random collections of particles: Implications for light scattering,” Opt. Commun.284(24), 5598–5600 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Sahin and O. Korotkova, “Scattering of scalar light fields from collections of particles,” Phys. Rev. A78(6), 063815 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

O. Korotkova and E. Wolf, “Scattering matrix theory for stochastic scalar fields,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.75(5), 056609 (2007).
[CrossRef] [PubMed]

Other

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, 2007).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).

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Figures (11)

Fig. 1
Fig. 1

Illustrating the notation relating to a single ellipsoid

Fig. 2
Fig. 2

Illustrating three basic rotations defining the orientation of the particle frame [ξ, η, ζ] relative to the laboratory frame [x, y, z].

Fig. 3
Fig. 3

Notation relating to scattering of two correlated plane waves by a collection of ellipsoids with different shapes and orientations.

Fig. 4
Fig. 4

Notation of the position of the ellipsoid particles, R=2 k 1 .

Fig. 5
Fig. 5

Contours of the spectral density of the far field, produced by scattering of two correlated plane waves on different number of ellipsoid particles with Gaussian potential. The parameters were taken as: α=β=γ=π/4 , k σ x =k σ y =1 , k σ z =1.5 (a) one ellipsoid particle; (b) three ellipsoid particles; (c) five ellipsoid particles; (d) nine ellipsoid particles.

Fig. 7
Fig. 7

Contours of the spectral density of the far field, produced by scattering of two correlated plane waves on five identical ellipsoid particles for different orientation (position shown in Fig. 4c). The parameters were taken as: k σ x =1 , k σ y =1 , k σ z =1.5 , β=γ=0 , (a) α=0 ; (b) α=π/6 ; (c) α=π/4 ; (d) α=π/3 .

Fig. 6
Fig. 6

Contours of the spectral density of the far field, produced by scattering of two correlated plane waves on five identical ellipsoid particles with different parameter k σ z (position shown in Fig. 4c). The parameters were taken as: α=β=γ=π/4 , k σ x =k σ y =1 , (a) k σ z =k σ y ; (b) k σ z =1.3k σ y ; (c) k σ z =1.6k σ y ; (d) k σ z =1.9k σ y .

Fig. 8
Fig. 8

Contours of the spectral density of the far field, produced by scattering of two correlated plane waves on five different orientating ellipsoid particles shown as Fig. 10. The parameters were taken as: k σ x =1 , k σ y =1 , k σ z =1.5 .

Fig. 9
Fig. 9

Contours of the spectral density of the far field, produced by scattering of two correlated plane waves on three layers different orientating ellipsoid particles shown as Fig. 11. The parameters were taken as: k σ x =1 , k σ y =1 , k σ z =1.5 .

Fig. 10
Fig. 10

Illustrating the collection of different orientating ellipsoid particles, (a) Five particles in the same orientation α=β=γ=0 ; (b) the rotation angle α=π/3 of a particle at the center; (c) the rotation angle α=π/3 of three particles in the x-direction; (d) the rotation angle α=π/3 of all five particles.

Fig. 11
Fig. 11

Illustrating the collection of three layers different orientating ellipsoid particles, (a) all particles in the same orientation α=β=γ=0 ; (b) the rotation angle α=π/3 of a layer of particles at z=d+R ; (c) the rotation angle α=π/3 of two layers of particles at z=d+R and z=d ; (d) the rotation angle α=π/3 of all particles.

Equations (5)

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a (i) ( u ,ω)= a (i) ( u 1 ,ω) δ (2) ( u u 1 )+ a (i) ( u 2 ,ω) δ (2) ( u u 2 ),
A (i) ( u 1 , u 2 ;ω)=a( u 1 , u 1 ;ω) δ (2) ( u u 1 ) δ (2) ( u u 1 ) +a( u 2 , u 2 ;ω) δ (2) ( u u 2 ) δ (2) ( u u 2 ) +a( u 1 , u 2 ;ω) δ (2) ( u u 1 ) δ (2) ( u u 2 ) +a( u 2 , u 1 ;ω) δ (2) ( u u 2 ) δ (2) ( u u 1 ),
a( u p , u q ;ω)= a (i)* ( u p ;ω) a (i) ( u q ;ω) (p,q=1,2),
a( u p , u q ;ω)= a pq e ( k 2 Δ 2 /2) ( u p u q ) 2 (p,q=1,2),
S (t) (ru;ω)= 4 G 2 π 5 u z 2 k 2 r 2 { a 11 l1=1 L l2=1 L 1 B l1 (1) C l1 (1) C l1 (3) B l2 (1) C l2 (1) C l2 (3) exp[ ( 1 4 B l1 (1) + 1 4 B l2 (1) ) K 1X 2 ] ×exp[ ( 1 4 C l1 (1) + 1 4 C l2 (1) ) K 1Y 2 ]exp[ ( 1 4 C l1 (3) + 1 4 C l2 (3) ) K 1Z 2 ] n=1 M l1 m=1 M l2 e i[ K 1 ( r 2m r 1n )] + a 22 l1=1 L l2=1 L 1 B l1 (1) C l1 (1) C l1 (3) B l2 (1) C l2 (1) C l2 (3) exp[ ( 1 4 B l1 (1) + 1 4 B l2 (1) ) K 2X 2 ] ×exp[ ( 1 4 C l1 (1) + 1 4 C l2 (1) ) K 2Y 2 ]exp[ ( 1 4 C l1 (3) + 1 4 C l2 (3) ) K 2Z 2 ] n=1 M l1 m=1 M l2 e i[ K 2 ( r 2m r 1n )] + e k 2 Δ 2 ( u 2 u 1 ) 2 2 Re[ a 12 l1=1 L l2=1 L 1 B l1 (1) C l1 (1) C l1 (3) B l2 (1) C l2 (1) C l2 (3) exp[ ( K 1X 2 4 B l1 (1) + K 2X 2 4 B l2 (1) ) ] ×exp[ ( K 1Y 2 4 C l1 (1) + K 2Y 2 4 C l2 (1) ) ]exp[ ( K 1Z 2 4 C l1 (3) + K 2Z 2 4 C l2 (3) ) ] n=1 M l1 m=1 M l2 e i[ K 2 r 2m K 1 r 1n ] ] }.

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