Label-free microscopy methods have been developed to measure isotropic (phase) and anisotropic components of the uniaxial permittivity tensor (uPT) separately. These methods are now broadly used to analyze biological architecture. Few methods have combined these measurements, but they do not provide complete measurement of uPT considering diffraction. Here we report a computational microscopy method, termed uniaxial permittivity tensor imaging (uPTI) for diffraction-aware measurements of uPT. The invisible uPT is converted into visible intensity variations using add-on microscopy modules for asymmetric illumination and polarization-sensitive detection. We develop a vectorial partially coherent imaging model that describes the intensities in terms of uPT. We retrieve the uPT with a multi-channel deconvolution algorithm. We demonstrate the multi-modal high-resolution imaging of biological specimens with uPTI.
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