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We report Tensorial tomographic Fourier Ptychography (ToFu), a newnon-scanning label-free tomographic microscopy method for simultaneous imagingof quantitative phase and anisotropic specimen information in 3D. Built uponFourier Ptychography, a quantitative phase imaging technique, ToFu additionallyhighlights the vectorial nature of light. The imaging setup consists of astandard microscope equipped with an LED matrix, a polarization generator, anda polarization-sensitive camera. Permittivity tensors of anisotropic samplesare computationally recovered from polarized intensity measurements acrossthree dimensions. We demonstrate ToFu's efficiency through volumetricreconstructions of refractive index, birefringence, and orientation for variousvalidation samples, as well as tissue samples from muscle fibers and diseasedheart tissue. Our reconstructions of muscle fibers resolve their 3Dfine-filament structure and yield consistent morphological measurementscompared to gold-standard second harmonic generation scanning confocalmicroscope images found in the literature. Additionally, we demonstratereconstructions of a heart tissue sample that carries important polarizationinformation for detecting cardiac amyloidosis.

Tensorial tomographic Fourier Ptychography with applications to muscle tissue imaging