Mueller Tensor Nonlinear Optical Polarization Analysis in Turbid Media

A mathematical framework to treat partial polarization in second harmonic generation imaging of nonlinear optical susceptibility is described and applied to imaging tissue sections 5, 40, and 70 mu m thick, sufficient to introduce significant depolarization of the incident field. Polarization analysis becomes complicated in turbid media, in which scattering can result in degradation of polarization purity. The simplest framework for describing the polarization of purely polarized light is the Jones framework, which has been applied to great effect in the polarization analysis of second harmonic generation. However, the Jones framework lacks the necessary generality to describe a partially polarized electric field, (i.e., ones positioned within the volume of the Poincare sphere rather than on the surface). Recent work connecting the Jones framework to the Mueller-Stokes framework has enabled interpretation of results with the more intuitive Jones framework while maintaining generality of the Mueller-Stokes method. The magnitude and nature of linear interactions of the tissue with the incident infrared field are discussed. Despite substantial depolarization, the nonlinear optical susceptibility tensor elements of collagen was recoverable at each pixel images of thick tissue utilizing the described framework. For thick and thin tissues, values of the tensor element ratio rho were recovered in good agreement with previous studies. Both hyperpolarizing and depolarizing effects of SHG were observed, and the mechanism of hyperpolarization was determined to rest upon the interplay of orientation and relative contribution of polarized and depolarized incident light to elicit SHG.