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Microscopic imaging of anisotropic samples has many important applications in cytopathology. The endogenous contrast from the polarization properties of a specimen, such as its birefringence, provides valuable diagnostic information for several deadly diseases, including cardiac amyloidosis and squamous cell carcinoma, for example. In the past, polarized light microscopy (PLM) has been widely used as a diagnostic tool during the clinical review. However, in analogy with the standard microscope, the PLM typically has a restricted spatial-bandwidth product (SBP). As a consequence, one can either image a large area with low resolution or see the details of a very small area of the sample at the resolutions required for accurate analysis. To address the SBP issue of the PLM, we propose a computational microscopy method, termed vectorial Fourier ptychography, to illuminate the specimen with polarized light from different angles and detects different polarization states of the diffracted light. By illuminating a specimen with plane waves from different angles, our vectorial Fourier ptychography method effectively modulates the high-spatial-frequency components of the specimen into lower frequencies that can be detected by the optical system. With a Jones calculus-based forward model and a second-order phase retrieval method, we can reconstruct high-resolution, wide field-of-view(FOV) amplitude, phase, birefringence, retardance, and diattenuation of the specimen. To assess the reconstruction accuracy of our method, we imaged polystyrene beads submerged in immersion oils of different refractive index, as well as monosodium urate crystals. Further, To validate the diattenuation reconstruction accuracy, we reconstruct a USAF resolution test chart with a half blocked by a linear polarizer. These experiments confirm quantitatively accurate reconstruction results with a 1.25 um full-pitch resolution over a FOV of 6.6 x 4.4 mm^2, which is 5 times higher than the native (brightfield) resolution of the non-computational optical system. Finally, we demonstrate our technique by producing high SBP polarization images of several anisotropic biologic samples, includes collagen tissue, congo red stained cardiac tissue, and a bean root sample.
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