Imaging the Nonlinear Susceptibility Tensor of Collagen by Nonlinear Optical Stokes Ellipsometry

Abstract

Nonlinear optical Stokes ellipsometric (NOSE) microscopy was demonstrated for the analysis of collagen-rich biological tissues. NOSE is based on polarization-dependent second harmonic generation imaging. NOSE was used to access the molecular-level distribution of collagen fibril orientation relative to the local fiber axis at every position within the field of view. Fibril tilt-angle distribution was investigated by combining the NOSE measurements with ab initio calculations of the predicted molecular nonlinear optical response of a single collagen triple helix. The results were compared with results obtained previously by scanning electron microscopy, nuclear magnetic resonance imaging, and electron tomography. These results were enabled by first measuring the laboratory-frame Jones nonlinear susceptibility tensor, then extending to the local-frame tensor through pixel-by-pixel corrections based on local orientation.

Second Harmonic Generation of Unpolarized Light

“…The modal value of ρ = 1.69 [Fig. 4(c)] is consistent with several other previous reports [4,24] for mouse tail and other collagenous assemblies such as chicken wing and human dermis. Deviations between polarization analysis and image analysis may arise from the implicit assumption that the fibers exhibit polar tilt angles of π /2, such that the fibers are assumed to lie flat within the FOV.…”

“…The polarization dependence of SHG provides rich information on orientation and arrangement of local structures, as demonstrated for characterization of biostructures [1–4], protein crystals [5], and active pharmaceutical ingredients [5,6]. However, structural information is routinely lost in measurements designed to take advantage of the increased penetration depth of nonlinear optical interactions.…”

“…Several studies have considered the effects of partial depolarization in polarization-dependent NLO imaging via the cumulative effects of scattering, birefringence, and linear or circular dichroism [3,4,10]. Optical clearing mitigates the effects of scattering by refractive index matching [11].…”

“…Optical clearing mitigates the effects of scattering by refractive index matching [11]. Careful bookkeeping of polarization-state changes has been used to remove bias in recovered tensor elements from polarization resolved SHG microscopy at tissue depths of 100 µm [3,4,10]. However, such methods do not account for the influence of depolarization arising from heterogeneity within the sample during propagation to the object plane.…”

“…For the specific case of collagen (or any uniaxial assembly), the nonzero elements within the local frame are χ z ′ z ′ z ′ , χ z ′ x ′ x ′ = χ z ′ y ′ y ′ , χ x ′ x ′ z ′ = χ x ′ z ′ x ′ and χ x ′ y ′ z ′ = χ x ′ z ′ y ′ = − χ y ′ x ′ z ′ = − χ y ′ z ′ x ′ , with the z ′ axis defined as the unique fiber axis. From quantum chemical calculations, the chiral terms are predicted to be relatively weak in collagen performed far from resonance, and disappear by symmetry for fibers aligned within the field of view (FOV) [4,20]. …”