Polarimetric study of birefringent turbid media with three-dimensional optic axis orientation

as-PSOCT: Volumetric microscopic imaging of human brain architecture and connectivity

Polarization sensitive optical coherence tomography (PSOCT) with serial sectioning has enabled the investigation of 3D structures in mouse and human brain tissue samples. By using intrinsic optical properties of back-scattering and birefringence, PSOCT reliably images cytoarchitecture, myeloarchitecture and fiber orientations. In this study, we developed a fully automatic serial sectioning polarization sensitive optical coherence tomography (as-PSOCT) system to enable volumetric reconstruction of human brain samples with unprecedented sample size and resolution. The 3.5 μm in-plane resolution and 50 μm through-plane voxel size allow inspection of cortical layers that are a single-cell in width, as well as small crossing fibers. We show the abilities of as-PSOCT in quantifying layer thicknesses of the cerebellar cortex and creating microscopic tractography of intricate fiber networks in the subcortical nuclei and internal capsule regions, all based on volumetric reconstructions. as-PSOCT provides a viable tool for studying quantitative cytoarchitecture and myeloarchitecture and mapping connectivity with microscopic resolution in the human brain.

Multiple scattering of polarized light in uniaxial turbid media with arbitrarily oriented linear birefringence

The effective scattering Mueller matrices obtained by the simulation were simplified to the reduced matrices and factorized using the Lu–Chipman polar decomposition, which afforded the polarization parameters in two dimensions. In general, the scalar retardance around the illumination point of a pencil beam shows a broad azimuthal dependence with an offset. Photons may behave quite differently under the birefringence according to their polarization state. In contrast, when the birefringence is oriented along the y -axis in the plane parallel to the surface ( x ? y ) plane, for example, the azimuthal dependence of the scalar retardance shows clear maxima along the x - and y -axes and sharp valleys between the maxima. Photons propagating in the medium probably experience the retardance in nearly the same way when they are polarized linearly and circularly. Moreover, the polarization parameters generally become nonsymmetric with respect to the plane perpendicular to both the x - y plane and the plane containing the birefringence axis, which suggests that the pathway of the lateral propagation of photons from the illumination point to the surrounding is slightly oblique upward relative to the x - y plane. These results were also compared with the case in which the birefringence axis is perpendicular to the x - y plane.

Quantifying three-dimensional optic axis using polarization-sensitive optical coherence tomography

The optic axis of birefringent samples indicates the direction of optical anisotropy, which should be described in three-dimensional (3-D) space. We present a method to quantify the complete 3-D optic axis orientation calculated from in-plane optic axis measurements from a polarization-sensitive optical coherence tomography system. The in-plane axis orientations with different illumination angles allow the calculation of the necessary polar angle. The method then provides the information to produce the actual birefringence. The method and results from a biological sample are presented.

Retardance of bilayer anisotropic samples consisting of well-aligned cylindrical scatterers and birefringent media

Both cylindrical scatterers and birefringent media may contribute to the anisotropy of tissue, where anisotropy can be characterized using polarization techniques. Our previous studies have shown that a layer of well-aligned cylindrical scatterers displays anisotropic properties similar to those of a piece of birefringent media, whose equivalent extraordinary axis is along the axial direction of the cylinders. We focused on a sample consisting of two layers of anisotropic media, with each layer having a different orientation; the characteristics of this sample were representative of the properties of multilayer fibrous tissues. Using a Mueller matrix decomposition method, we examined in detail how the total retardance and the equivalent extraordinary axis of the bilayered sample varied with changes in the retardance of the two layers and the direction of the extraordinary axis. The results of this study showed that, in such bilayer samples, a layer of well-aligned cylindrical scatterers generated a retardance that behaved exactly like the retardance generated by a piece of birefringent media. The simulated results were also confirmed by the results of experiments using aligned glass fibers.

Generalized Jones matrix method for homogeneous biaxial samples

The generalized Jones matrix (GJM) is a recently introduced tool to describe linear transformations of three-dimensional light fields. Based on this framework, a specific method for obtaining the GJM of uniaxial anisotropic media was recently presented. However, the GJM of biaxial media had not been tackled so far, as the previous method made use of a simplified rotation matrix that lacks a degree of freedom in the three-dimensional rotation, thus being not suitable for calculating the GJM of biaxial media. In this work we propose a general method to derive the GJM of arbitrarily-oriented homogeneous biaxial media. It is based on the differential generalized Jones matrix (dGJM), which is the three-dimensional counterpart of the conventional differential Jones matrix. We show that the dGJM provides a simple and elegant way to describe uniaxial and biaxial media, with the capacity to model multiple simultaneous optical effects. The practical usefulness of this method is illustrated by the GJM modeling of the polarimetric properties of a negative uniaxial KDP crystal and a biaxial KTP crystal for any three-dimensional sample orientation. The results show that this method constitutes an advantageous and straightforward way to model biaxial media, which show a growing relevance for many interesting applications.

Physically meaningful depolarization metric based on the differential Mueller matrix

We present a novel depolarization metric for Mueller matrices based on the differential Mueller formalism. The proposed metric relies on the statistical interpretation of the differential Mueller matrix. We show that the differential depolarization index successfully quantifies depolarization even when applied to specific types of Mueller matrices for which some widely used depolarization metrics yield erroneous results. Moreover, the fact that the presented metric is directly linked to the variances and covariances of the elementary anisotropic properties of the sample makes it a valuable tool to quantify depolarization on a physically meaningful basis.