## 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.

© 2012 OSA

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### Equations (5)

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(1)
$${a}^{(i)}({u}^{\prime},\omega )={a}^{(i)}({{u}^{\prime}}_{1},\omega ){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{1})+{a}^{(i)}({{u}^{\prime}}_{2},\omega ){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{2}),$$
(2)
$$\begin{array}{l}{A}^{(i)}({{u}^{\prime}}_{1},{{u}^{\prime}}_{2};\omega )=a({{u}^{\prime}}_{1},{{u}^{\prime}}_{1};\omega ){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{1}){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{1})\\ +a({{u}^{\prime}}_{2},{{u}^{\prime}}_{2};\omega ){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{2}){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{2})\\ +a({{u}^{\prime}}_{1},{{u}^{\prime}}_{2};\omega ){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{1}){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{2})\\ +a({{u}^{\prime}}_{2},{{u}^{\prime}}_{1};\omega ){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{2}){\delta}^{(2)}({u}^{\prime}-{{u}^{\prime}}_{1}),\end{array}$$
(3)
$$a({{u}^{\prime}}_{p},{{u}^{\prime}}_{q};\omega )=\u3008{a}^{(i)*}({{u}^{\prime}}_{p};\omega ){a}^{(i)}({{u}^{\prime}}_{q};\omega )\u3009(p,q=1,2),$$
(4)
$$a({{u}^{\prime}}_{p},{{u}^{\prime}}_{q};\omega )={a}_{pq}{\text{e}}^{(-{k}^{2}{\Delta}^{2}/2){({{u}^{\prime}}_{p}-{{u}^{\prime}}_{q})}^{2}}(p,q=1,2),$$
(5)
$$\begin{array}{l}{S}^{(t)}(ru;\omega )=\frac{4{G}^{2}{\pi}^{5}{u}_{z}^{2}}{{k}^{2}{r}^{2}}\{{a}_{11}{\displaystyle \sum _{l1=1}^{L}{\displaystyle \sum _{l2=1}^{L}\sqrt{\frac{1}{{B}_{l1}^{(1)}{C}_{l1}^{(1)}{C}_{l1}^{(3)}{B}_{l2}^{(1)}{C}_{l2}^{(1)}{C}_{l2}^{(3)}}}}}\mathrm{exp}\left[-\left(\frac{1}{4{B}_{l1}^{(1)}}+\frac{1}{4{B}_{l2}^{(1)}}\right){K}_{1X}^{2}\right]\\ \times \mathrm{exp}\left[-\left(\frac{1}{4{C}_{l1}^{(1)}}+\frac{1}{4{C}_{l2}^{(1)}}\right){K}_{1Y}^{2}\right]\mathrm{exp}\left[-\left(\frac{1}{4{C}_{l1}^{(3)}}+\frac{1}{4{C}_{l2}^{(3)}}\right){K}_{1Z}^{2}\right]{\displaystyle \sum _{n=1}^{{M}_{l1}}{\displaystyle \sum _{m=1}^{{M}_{l2}}{e}^{-i[{K}_{1}\cdot ({r}_{2m}-\cdot {r}_{1n})]}}}\\ +{a}_{22}{\displaystyle \sum _{l1=1}^{L}{\displaystyle \sum _{l2=1}^{L}\sqrt{\frac{1}{{B}_{l1}^{(1)}{C}_{l1}^{(1)}{C}_{l1}^{(3)}{B}_{l2}^{(1)}{C}_{l2}^{(1)}{C}_{l2}^{(3)}}}}}\mathrm{exp}\left[-\left(\frac{1}{4{B}_{l1}^{(1)}}+\frac{1}{4{B}_{l2}^{(1)}}\right){K}_{2X}^{2}\right]\\ \times \mathrm{exp}\left[-\left(\frac{1}{4{C}_{l1}^{(1)}}+\frac{1}{4{C}_{l2}^{(1)}}\right){K}_{2Y}^{2}\right]\mathrm{exp}\left[-\left(\frac{1}{4{C}_{l1}^{(3)}}+\frac{1}{4{C}_{l2}^{(3)}}\right){K}_{2Z}^{2}\right]{\displaystyle \sum _{n=1}^{{M}_{l1}}{\displaystyle \sum _{m=1}^{{M}_{l2}}{e}^{-i[{K}_{2}\cdot ({r}_{2m}-\cdot {r}_{1n})]}}}\\ +{\text{e}}^{-\frac{{k}^{2}{\Delta}^{2}{({{u}^{\prime}}_{2}-{{u}^{\prime}}_{1})}^{2}}{2}}\mathrm{Re}[{a}_{12}{\displaystyle \sum _{l1=1}^{L}{\displaystyle \sum _{l2=1}^{L}\sqrt{\frac{1}{{B}_{l1}^{(1)}{C}_{l1}^{(1)}{C}_{l1}^{(3)}{B}_{l2}^{(1)}{C}_{l2}^{(1)}{C}_{l2}^{(3)}}}}}\mathrm{exp}\left[-\left(\frac{{K}_{1X}^{2}}{4{B}_{l1}^{(1)}}+\frac{{K}_{2X}^{2}}{4{B}_{l2}^{(1)}}\right)\right]\\ \times \mathrm{exp}\left[-\left(\frac{{K}_{1Y}^{2}}{4{C}_{l1}^{(1)}}+\frac{{K}_{2Y}^{2}}{4{C}_{l2}^{(1)}}\right)\right]\mathrm{exp}\left[-\left(\frac{{K}_{1Z}^{2}}{4{C}_{l1}^{(3)}}+\frac{{K}_{2Z}^{2}}{4{C}_{l2}^{(3)}}\right)\right]{\displaystyle \sum _{n=1}^{{M}_{l1}}{\displaystyle \sum _{m=1}^{{M}_{l2}}{e}^{-i[{K}_{2}\cdot {r}_{2m}-{K}_{1}\cdot {r}_{1n}]}}]}\}.\end{array}$$