## Abstract

The concentration determination of optically active species in moderately turbid suspensions is studied both experimentally and with a validated three-dimensional polarization-sensitive Monte Carlo model. It is shown that the orientation of the polarization of the scattered light exhibits a strong dependence on exit position in the side or backscattered directions, but not in the forward direction. In addition, it is shown that the increased path length of photons due to multiple scattering in a 1 cm cuvette filled with forward-peaked scatterers (anisotropy around 0.93) increases the optical rotation by up to 15%, but only for scattering coefficients under 30 cm^{-1}, after which it decreases again. It is concluded that in order to avoid systematic errors in concentration determination of optically-active molecular species in turbid samples, the scattered light in the forward direction should be used.

©2005 Optical Society of America

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### Equations (33)

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(1)
$$C=\frac{\alpha}{{\left[\alpha \right]}_{\lambda}^{T}\u3008L\u3009},$$
(2)
$$\mathrm{tan}2\gamma =\frac{U}{Q},$$
(3)
$$\alpha =\frac{1}{2}{\mathrm{tan}}^{-1}\left(-\frac{{Q}_{2{f}_{p}}\u2044{Q}_{{f}_{c}}}{\pi {J}_{2}\left({\delta}_{\u25cb}\right)\mathcal{F}\left(2{f}_{p}\right)\u2044\mathcal{F}\left({f}_{c}\right)-{Q}_{2{f}_{p}}\u2044{Q}_{{f}_{c}}}\right),$$
(4)
$$\mathbf{S}=\left(\begin{array}{c}I\\ Q\\ U\\ V\end{array}\right),$$
(5)
$$I\equiv {E}_{\parallel}{E}_{\parallel}^{*}+{E}_{\perp}{E}_{\perp}^{*},$$
(6)
$$Q\equiv {E}_{\parallel}{E}_{\parallel}^{*}-{E}_{\perp}{E}_{\perp}^{*},$$
(7)
$$U\equiv {E}_{\parallel}{E}_{\perp}^{*}+{E}_{\parallel}^{*}{E}_{\perp},$$
(8)
$$V\equiv i\left({E}_{\parallel}{E}_{\perp}^{*}-{E}_{\parallel}^{*}{E}_{\perp}\right),$$
(9)
$${\mathbf{I}}^{\u2020}=\left(\begin{array}{cccc}1& 0& 0& 0\end{array}\right),$$
(10)
$${\mathbf{Q}}^{\u2020}=\left(\begin{array}{cccc}0& 1& 0& 0\end{array}\right),$$
(11)
$${\mathbf{U}}^{\u2020}=\left(\begin{array}{cccc}0& 0& 1& 0\end{array}\right).$$
(12)
$${\hat{e}\prime}_{\perp}={\mathit{BR}}_{3}\left(\varphi \right){\left(\begin{array}{ccc}1& 0& 0\end{array}\right)}^{T},$$
(13)
$${\hat{e}\prime}_{\parallel}={\mathit{BR}}_{3}\left(\varphi \right){\left(\begin{array}{ccc}0& 1& 0\end{array}\right)}^{T},$$
(14)
$$\mathbf{S}\prime ={R}_{S}\left(\varphi \right)\mathbf{S}.$$
(15)
$${R}_{3}\left(\varphi \right)=\left(\begin{array}{ccc}\mathrm{cos}\varphi & -\mathrm{sin}\varphi & 0\\ \mathrm{sin}\varphi & \mathrm{cos}\varphi & 0\\ 0& 0& 1\end{array}\right),$$
(16)
$${R}_{S}\left(\varphi \right)=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& \mathrm{cos}2\varphi & \mathrm{sin}2\varphi & 0\\ 0& -\mathrm{sin}2\varphi & \mathrm{cos}2\varphi & 0\\ 0& 0& 0& 1\end{array}\right),$$
(17)
$$B=\left(\begin{array}{ccc}{\hat{e}}_{\perp}\xb7\hat{x}& {\hat{e}}_{\parallel}\xb7\hat{x}& {\hat{e}}_{3}\xb7\hat{x}\\ {\hat{e}}_{\perp}\xb7\hat{y}& {\hat{e}}_{\parallel}\xb7\hat{y}& {\hat{e}}_{3}\xb7\hat{y}\\ {\hat{e}}_{\perp}\xb7\hat{z}& {\hat{e}}_{\parallel}\xb7\hat{z}& {\hat{e}}_{3}\xb7\hat{z}\end{array}\right).$$
(18)
$${\hat{e}\prime}_{\parallel}={\mathit{BR}}_{\perp}\left(\theta \right){\left(\begin{array}{ccc}0& 1& 0\end{array}\right)}^{T},$$
(19)
$${\hat{e}\prime}_{3}={\mathit{BR}}_{\perp}\left(\theta \right){\left(\begin{array}{ccc}0& 0& 1\end{array}\right)}^{T},$$
(20)
$$\mathbf{S}\prime ={M}_{S}\left(\theta \right)\mathbf{S}.$$
(21)
$${R}_{\perp}\left(\theta \right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& \mathrm{cos}\theta & -\mathrm{sin}\theta \\ 0& \mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right),$$
(22)
$$S+t\mathbf{d}=C,$$
(23)
$$\overline{\mathit{OC}}\xb7\hat{n}=0,$$
(24)
$$t=\frac{-\overline{\mathit{OS}}\xb7\hat{n}}{\mathbf{d}\xb7\hat{n}}.$$
(25)
$$u=\overline{\mathit{OC}}\xb7\mathbf{a}\u2044\mid \mathbf{a}\mid ,$$
(26)
$$u=\overline{\mathit{OC}}\xb7\mathbf{b}\u2044\mid \mathbf{b}\mid .$$
(27)
$${\hat{e\prime}}_{\parallel}={\mathit{BR}}_{\perp}\left({\theta}_{i}-{\theta}_{t}\right){\left(\begin{array}{ccc}0& 1& 0\end{array}\right)}^{T},$$
(28)
$${\hat{e\prime}}_{3}={\mathit{BR}}_{\perp}\left({\theta}_{i}-{\theta}_{t}\right){\left(\begin{array}{ccc}0& 1& 0\end{array}\right)}^{T},$$
(29)
$$\mathbf{S}\prime =\U0001d4e3\left(\text{}{\theta}_{i}\right)\mathbf{S},$$
(30)
$$\U0001d4e3\left({\theta}_{i}\right)=\frac{1}{2}\left(\begin{array}{cccc}{t}_{p}^{2}+{t}_{s}^{2}& {t}_{p}^{2}-{t}_{s}^{2}& 0& 0\\ {t}_{p}^{2}-{t}_{s}^{2}& {t}_{p}^{2}+{t}_{s}^{2}& 0& 0\\ 0& 0& 2{t}_{p}{t}_{s}& 0\\ 0& 0& 0& 2{t}_{p}{t}_{s}\end{array}\right),$$
(31)
$${\hat{e\prime}}_{\parallel}={\mathit{BR}}_{\perp}\left({2\theta}_{i}-\pi \right){\left(\begin{array}{ccc}0& 1& 0\end{array}\right)}^{T},$$
(32)
$${\hat{e\prime}}_{3}={\mathit{BR}}_{\perp}\left({2\theta}_{i}-\pi \right){\left(\begin{array}{ccc}0& 0& 1\end{array}\right)}^{T},$$
(33)
$$\mathbf{S}\prime =\Re \left({\theta}_{i}\right)\mathbf{S},$$