Reconstruction of three-dimensional refractive-index tensor of optically anisotropic objects by solving an inverse scattering problem of vectorial fields

Abstract

Active matter extracts surrounding energy and converts it into mechanical movements. Ranging from industrial active matter such as liquid crystal (LC) to living active matter including cytoskeleton dynamics, active matter and its dynamics are one of the hot topics in soft matter physics and biological sciences. Particularly, an LC droplet serves a unique platform to study molecular interactions in a confined volume. Interestingly, the materials including LC, cytoskeleton, and cell membranes exhibit birefringence, due to the regular arrangement of anisotropic molecules, proteins, or lipids. Optical diffraction tomography (ODT) techniques have been successfully demonstrated in reconstructing thethree-dimensional (3D) refractive index distribution for various research areas, including material science, biophysics, and biophotonics. However, applications of the techniques have been restricted to optically isotropic objects, due to the scalar wave assumption in the ODT principles. This assumption severely limits broader applications of the ODT techniques to optically anisotropic objects, particularly for liquid crystalline materials and filament structures in biological cells. In this thesis, we propose and experimentally demonstrate a method for the reconstruction of the 3D dielectric tensor distribution of an optically anisotropic object. Optical anisotropy causes anisotropic electric excitations depending on the direction of the external electric field, which is characterized by a dielectric tensor. Hence, an anisotropic object can be described by the 3D dielectric tensor distribution. Similar to the scalar ODT principles, the vectorial wave equation with a 3D dielectric tensor distribution is linearized under the weak scattering assumption. In consequence of solving the equation, the 3D dielectric tensor distribution can be reconstructed by mapping 3D vector fields diffracted from an anisotropic sample for various illumination angles. For the experimental demonstration, we also develop a method to retrieve the 3D vector fields from two recorded holograms with orthogonal incident polarizations by exploiting the angular spectral decomposition. The feasibility of the present theory is validated by reconstructing the 3D dielectric tensor distributions of an LC droplets and phase transition dynamics of LC droplets.