Double Stokes polarimetric microscopy for chiral fibrillar aggregates

Second harmonic generation (SHG) microscopy is a powerful tool for imaging collagen and other noncentrosymmetric fibrillar structures in biological tissue. Polarimetric SHG measurements provide ultrastructural information about the fibrillar organization in a focal volume (voxel). We present a reduced nonlinear polarimetry method named double Stokes polarimetry (DSP) for quick characterization of chiral $C_6$ symmetry fibers without data fitting that simplifies and speeds up the polarimetric analysis. The method is based on double Stokes-Mueller polarimetry and uses linear and circular incident and outgoing polarization states. The analytical expressions of DSP polarimetric parameters are defined in terms of conventional SHG Stokes vector components. A complex chiral susceptibility (CCS) model is assumed to derive expressions of ultrastructural parameters consisting of the magnitude and phase of molecular complex-valued chiral susceptibility ratio, real-valued achiral ratio, and fiber orientation in a voxel. The ultrastructural parameters are expressed in terms of directly measurable DSP polarimetric parameters. DSP is validated with rat tail tendons sectioned at different orientations. DSP can be applied to investigate the origin of chiral complex-valued susceptibility of collagen, to study modifications of collagen in cancerous tissue, and to map ultrastructural parameters of large areas for whole-slide histopathology.