Ranging from material science to soft matter physics, liquid-crystal displays, and tissue biology, three-dimensional (3D) optically anisotropic structures have been investigated for versatile purposes in various research areas. However, conventional methods indirectly access information of 3D anisotropic structure, due to the lack of direct imaging modality for 3D anisotropy.

 

Optical diffraction tomography (ODT) techniques have been successfully demonstrated in reconstructing 3D refractive index (RI) distribution for various research areas. 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.

 

Here, we present dielectric tensor tomography as a label-free modality for reconstructing 3D dielectric tensors of anisotropic structures. Dielectric tensor, a physical descriptor for vectorial light-matter interaction, serves intrinsic information of optical anisotropy including principal refractive indices and optic axes. By measuring diffracted electric fields and inversely solving a vectorial wave equation, the present method offers 3D distributions of dielectric tensors, principal RIs, and optic axes of anisotropic structures. The feasibility of the present method is validated by numerical simulations and experimental results. We demonstrate quantitative tomographic measurements of various nematic liquid-crystal structures and their fast 3D nonequilibrium dynamics.