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 μm
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 Poincaré 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 ρ 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.