Swami M K, Manhas S, Buddhiwant P, Ghosh N, Uppal A, Gupta P K
Opt Express. 2006 Oct 2;14(20):9324-37. doi: 10.1364/oe.14.009324.
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.
任何介质的偏振特性完全由一个十六元穆勒矩阵描述，该矩阵将入射到介质上的光的偏振参数与从介质出射的光的偏振参数联系起来。测量矩阵的所有元素至少需要十六次测量，涉及线偏振光和圆偏振光。然而，对于许多诊断应用而言，如果仅通过线偏振测量就能量化偏振参数将很有用。在本文中，我们提出了一种基于穆勒矩阵极分解的方法，用于使用仅需线偏振测量的九元（3×3）穆勒矩阵来量化散射介质的偏振参数。3×3穆勒矩阵的分解方法基于先前为十六元（4×4）穆勒矩阵开发的分解过程，但假设由于散射导致的线偏振光的退偏与入射线偏振矢量的取向角无关。对各种散射样本进行的研究表明，对于像生物组织这样的混浊介质，该假设是有效的，在生物组织中，线偏振光的退偏主要是由于多次散射导致场矢量方向随机化。对于这种介质，3×3穆勒矩阵的极分解可用于以合理的精度量化四个独立的偏振参数，即线性延迟（δ）、圆延迟（ψ）、线性退偏系数（Δ）和线性衰减（d）。由于这种方法仅需要使用线性偏振器进行测量，它大大简化了测量过程，并且在使用检索到的偏振参数进行组织诊断中可能会找到有用的应用。
