Polarization light microscopes are powerful tools for probing molecular order and orientation in birefringent materials. While a multitude of polarization light microscopy techniques are often used to access steady-state properties of birefringent samples, quantitative measurements of the molecular orientation dynamics on the millisecond time scale have remained a challenge. We propose polarized shearing interference microscopy (PSIM), a single-shot quantitative polarization imaging method, for extracting the retardance and orientation angle of the laser beam transmitting through optically anisotropic specimens with complex structures. The measurement accuracy and imaging performances of PSIM are validated by imaging a rotating wave plate and a bovine tendon specimen. We demonstrate that PSIM can quantify the dynamics of a flowing lyotropic chromonic liquid crystal in a microfluidic channel at an imaging speed of 506 frames per second (only limited by the camera frame rate), with a field-of-view of up to $350times350 mu m^2$ and a diffraction-limit spatial resolution of $sim 2mu m$. We envision that PSIM will find a broad range of applications in quantitative material characterization under dynamical conditions.
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