uPTI: uniaxial permittivity tensor imaging of intrinsic density and anisotropy

Yeh, Li-Hao; Ivanov, Ivan E.; Byrum, Janie R.; Chhun, Bryant B.; Guo, Syuan-Ming; Foltz, Cameron; Hashemi, Ezzat; Pérez-Bermejo, Juan A.; Wang, Huijun; Yu, Yanhao; Kazansky, Peter G.; Conklin, Bruce R.; Han, May H.; Mehta, Shalin B.

Biological architecture is intrinsically tensorial. The permittivity tensor (PT) of biological material reports the density, angular anisotropy, symmetry, and 3D orientation of biomolecules. High-resolution measurement of PT can enable quantitative and label-free analysis of organelle, cell, and tissue architecture, but remains challenging. We report uniaxial permittivity tensor imaging (uPTI), a label-free computational imaging method for volumetric measurement of PT with diffraction-limited resolution. uPTI encodes the components of PT into intensity modulations using oblique illumination and polarization-resolved imaging. The high-dimensional data is decoded with a vectorial image formation model and a multi-channel convex optimization, assuming that the molecular distribution in each voxel has uniaxial symmetry. We describe a modular implementation of uPTI that can be multiplexed with complementary imaging modalities. We report volumes of uPT in mouse brain tissue, SARS-CoV-2 infected cardiomyocytes, RSV infected A549 cells, H&E stained tissue sections, isotropic beads, and anisotropic glass targets. uPTI enabled volumetric imaging of the 3D orientation and symmetry of organelles, cells, and tissue components with higher spatio-angular resolution than current vectorial tomography, ptychography, and light-field microscopy methods. We provide an open source implementation of the image formation model and reconstruction algorithms.