  This paper presents a microscopic imaging technique that uses variable-angle
illumination to recover the complex polarimetric properties of a specimen at
high resolution and over a large field-of-view. The approach extends Fourier
ptychography, which is a synthetic aperture-based imaging approach to improve
resolution with phaseless measurements, to additionally account for the
vectorial nature of light. After images are acquired using a standard
microscope outfitted with an LED illumination array and two polarizers, our
vectorial Fourier Ptychography (vFP) algorithm solves for the complex 2x2 Jones
matrix of the anisotropic specimen of interest at each resolved spatial
location. We introduce a new sequential Gauss-Newton-based solver that
additionally jointly estimates and removes polarization-dependent imaging
system aberrations. We demonstrate effective vFP performance by generating
large-area (29 mm$^2$), high-resolution (1.24 $\mu$m full-pitch)
reconstructions of sample absorption, phase, orientation, diattenuation, and
retardance for a variety of calibration samples and biological specimens.
