## Abstract

Phase-modulated Mueller ellipsometry (PMME) is used to probe
scattering by suspensions of polystyrene latex spheres, with particle
diameters ranging from 400 nm to 3 µm. PMME allows
simultaneous measurement of the 16 coefficients of the Mueller
matrix. Furthermore PMME measurements can easily be carried out
owing to a calibration procedure implemented in a scattering
configuration. The measurements performed on low concentrations
show good agreement with Mie theory. Moreover size distribution
could be obtained with a least-squares method based on a genetic fit
algorithm. Experimental evidence of multiple scattering on PMME
measurements is also presented.

© 2000 Optical Society of America

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### Equations (6)

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(1)
$${\mathbf{S}}_{\mathrm{out}}=\mathbf{M}\xb7{\mathbf{S}}_{\mathrm{in}}$$
(2)
$${M}_{\mathit{ij}}*={M}_{11}\mathrm{if}i=1\mathrm{and}j=1,{M}_{\mathit{ij}}*={M}_{\mathit{ij}}/{M}_{11}\mathrm{otherwise}.$$
(3)
$$\left[\begin{array}{c}{i}_{1}\left(t\right)\\ {i}_{2}\left(t\right)\\ {i}_{3}\left(t\right)\\ {i}_{4}\left(t\right)\end{array}\right]=\mathbf{A}\mathbf{M}\mathbf{W}\left(\begin{array}{l}sin\mathrm{\omega}t\\ cos2\mathrm{\omega}t\\ sin3\mathrm{\omega}t\\ cos4\mathrm{\omega}t\end{array}\right)+\text{higher orders}.$$
(4)
$${\mathbf{M}}_{\mathrm{sphere}}={M}_{11}\left(\begin{array}{llll}1& {M}_{12}*& 0& 0\\ {M}_{12}*& 1& 0& 0\\ 0& 0& {M}_{33}*& {M}_{34}*\\ 0& 0& -{M}_{34}*& {M}_{33}*\end{array}\right)\times \mathrm{with}{M}_{12}{*}^{2}+{M}_{33}{*}^{2}+{M}_{34}{*}^{2}=1.$$
(5)
$${\mathbf{M}}_{\mathrm{suspension}}=\sum _{\mathrm{sphere}i}{\mathbf{M}}_{\mathrm{sphere}}\left(i\right)=\mathrm{\tau}\left(\begin{array}{cccc}1& a& 0& 0\\ a& 1& 0& 0\\ 0& 0& b& c\\ 0& 0& -c& b\end{array}\right)\mathrm{with}{a}^{2}+{b}^{2}+{c}^{2}\le 1,$$
(6)
$${\mathbf{M}}_{\mathrm{sca}}{\left({\mathrm{\theta}}_{1}\right)}^{-1}{\mathbf{M}}_{\mathrm{sca}}\left({\mathrm{\theta}}_{2}\right)\text{close to}\left(\begin{array}{cccc}1& \pm 0.5& 0& 0\\ \pm 0.5& 1& 0& 0\\ 0& 0& 0& \pm 0.5\\ 0& 0& \mp 0.5& 0\end{array}\right).$$