Polarization, the path along which light’s electric field oscillates, is a key property of electromagnetic radiation. In this work, we motivate a mathematical framework—Matrix Fourier optics—that enables a simple description of light’s interaction with diffractive optics that spatially modify polarization. This formalism generalizes a large body of past work in metasurface polarization optics. We show how Matrix Fourier optics allows for the design of arbitrary polarization-analyzing metasurface gratings. These gratings can be used as the single polarization component in a compact full-Stokes polarization camera. We demonstrate practical, real-time polarization photography with this camera, which may find application in machine vision and remote sensing.
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