uPTI: uniaxial permittivity tensor imaging of intrinsic density and anisotropy

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][1] implementation of the image formation model and reconstruction algorithms. ### Competing Interest Statement A patent filed by the Chan Zuckerberg Biohub with S.B.M, L.H, and I.E.I as inventors is pending and describes the uPTI method reported in this paper. B.R.C. is a founder of Tenaya Therapeutics (https://www.tenayatherapeutics.com/), a company focused on finding treatments for heart failure, including genetic cardiomyopathies. Other authors declare no competing interests. [1]: https://github.com/mehta-lab/waveorder