Optical metasurfaces composed of precisely engineered nanostructures have gained significant attention for their ability to manipulate light and implement distinct functionalities based on the properties of the incident field. Computational imaging systems have started harnessing this capability to produce sets of coded measurements that benefit certain tasks when paired with digital post-processing. Inspired by these works, we introduce a new system that uses a birefringent metasurface with a polarizer-mosaicked photosensor to capture four optically-coded measurements in a single exposure. We apply this system to the task of incoherent opto-electronic filtering, where digital spatial-filtering operations are replaced by simpler, per-pixel sums across the four polarization channels, independent of the spatial filter size. In contrast to previous work on incoherent opto-electronic filtering that can realize only one spatial filter, our approach can realize a continuous family of filters from a single capture, with filters being selected from the family by adjusting the post-capture digital summation weights. To find a metasurface that can realize a set of user-specified spatial filters, we introduce a form of gradient descent with a novel regularizer that encourages light efficiency and a high signal-to-noise ratio. We demonstrate several examples in simulation and with fabricated prototypes, including some with spatial filters that have prescribed variations with respect to depth and wavelength. Visit the Project Page at https://deanhazineh.github.io/publications/Multi_Image_Synthesis/MIS_Home.html

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