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.

The polarization properties of any medium are completely described by the sixteen element Mueller matrix that relates the polarization parameters of the light incident on the medium to that emerging from it. Measurement of all the elements of the matrix requires a minimum of sixteen measurements involving both linear and circularly polarized light. However, for many diagnostic applications, it would be useful if the polarization parameters can be quantified with linear polarization measurements alone. In this paper, we present a method based on polar decomposition of Mueller matrix for quantification of the polarization parameters of a scattering medium using the nine element (3 x 3) Mueller matrix that requires linear polarization measurements only. The methodology for decomposition of the 3 x 3 Mueller matrix is based on the previously developed decomposition process for sixteen element (4 x 4) Mueller matrix but with an assumption that the depolarization of linearly polarized light due to scattering is independent of the orientation angle of the incident linear polarization vector. Studies conducted on various scattering samples demonstrated that this assumption is valid for a turbid medium like biological tissue where the depolarization of linearly polarized light primarily arises due to the randomization of the field vector's direction as a result of multiple scattering. For such medium, polar decomposition of 3 x 3 Mueller matrix can be used to quantify the four independent polarization parameters namely, the linear retardance (delta ), the circular retardance (psi), the linear depolarization coefficient (Delta) and the linear diattenuation (d) with reasonable accuracy. Since this approach requires measurements using linear polarizers only, it considerably simplifies measurement procedure and might find useful applications in tissue diagnosis using the retrieved polarization parameters.

We present a fast and accurate approach for simultaneous determination of both the mean diameter and refractive index of a collection of red blood cells (RBCs). The approach uses the peak frequency of the power spectrum and the corresponding phase angle obtained by performing Fourier transform on the measured angular distribution of scattered light to determine these parameters. Results on the measurement of two important clinical parameters, the mean cell volume and mean cell hemoglobin concentration of a collection of RBCs, are presented.

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