  We report Tensorial tomographic Fourier Ptychography (ToFu), a new
non-scanning label-free tomographic microscopy method for simultaneous imaging
of quantitative phase and anisotropic specimen information in 3D. Built upon
Fourier Ptychography, a quantitative phase imaging technique, ToFu additionally
highlights the vectorial nature of light. The imaging setup consists of a
standard microscope equipped with an LED matrix, a polarization generator, and
a polarization-sensitive camera. Permittivity tensors of anisotropic samples
are computationally recovered from polarized intensity measurements across
three dimensions. We demonstrate ToFu's efficiency through volumetric
reconstructions of refractive index, birefringence, and orientation for various
validation samples, as well as tissue samples from muscle fibers and diseased
heart tissue. Our reconstructions of muscle fibers resolve their 3D
fine-filament structure and yield consistent morphological measurements
compared to gold-standard second harmonic generation scanning confocal
microscope images found in the literature. Additionally, we demonstrate
reconstructions of a heart tissue sample that carries important polarization
information for detecting cardiac amyloidosis.
