Mueller matrix approach for determination of optical rotation in chiral turbid media in backscattering geometry

Abstract

For in vivo determination of optically active (chiral) substances in turbid media, like for example glucose in human tissue, the backscattering geometry is particularly convenient. However, recent polarimetric measurements performed in the backscattering geometry have shown that, in this geometry, the relatively small rotation of the polarization vector arising due to the optical activity of the medium is totally swamped by the much larger changes in the orientation angle of the polarization vector due to scattering. We show that the change in the orientation angle of the polarization vector arises due to the combined effect of linear diattenuation and linear retardance of light scattered at large angles and can be decoupled from the pure optical rotation component using polar decomposition of Mueller matrix. For this purpose, the method developed earlier for polar decomposition of Mueller matrix was extended to incorporate optical rotation in the medium. The validity of this approach for accurate determination of the degree of optical rotation using the Mueller matrix measured from the medium in both forward and backscattering geometry was tested by conducting studies on chiral turbid samples prepared using known concentration of scatterers and glucose molecules.

Physical model of differential Mueller matrix for depolarizing uniform media

“…The scattering-induced diattenuation is due mainly to the weakly scattered photons [17]. This effect is even more important in the backscattering geometry as compared to forward scattering geometry.…”

Q(M) and the depolarization index scalar metrics

“…Note that all the metrics describe the Mueller matrix as associated with a partial depolarizing system, as was reported by the authors of Ref. [15]. Figures 1(a) and 1(b) represent the DoPðM; SÞ and the gain, respectively, when all the incident Stokes vectors are taken from the Poincarè sphere [10].…”

Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle

“…Theoretically, there are multiple possible decomposition families [19]. In this study, we applied the original method introduced by Lu and Chipman [8] and used by others [9][10][11] for tissue characterizations. The specific procedures applied in this study are described below.…”

“…According to the method described in [10,11], the linear retardance can be further derived by representing the retardance matrix M R as a combination of optical rotation (R C ) and linear retardance (R L ). The linear retardance R L can be obtained from the retardance submatrix m R as [11] R L ¼ cos …”

“…Swami et al [9] explored a simplified decomposition algorithm for use in a subset (3 × 3) of the Mueller matrix measured with only linearly polarized light. Manhas et al [10] and Ghosh et al [11] recently extended Lu and Chipman's original method by further decomposing the total retardance into linear retardance and optical rotation.…”