Intensity, polarization and wavelength are intrinsic characteristics of light. Characterizing light with arbitrarily mixed information on polarization and spectrum is in high demand1–4. Despite the extensive efforts in the design of polarimeters5–18 and spectrometers19–27, concurrently yielding high-dimensional signatures of intensity, polarization and spectrum of the light fields is challenging and typically requires complicated integration of polarization- and/or wavelength-sensitive elements in the space or time domains. Here we demonstrate that simple thin-film interfaces with spatial and frequency dispersion can project and tailor polarization and spectrum responses in the wavevector domain. By this means, high-dimensional light information can be encoded into single-shot imaging and deciphered with the assistance of a deep residual network. To the best of our knowledge, our work not only enables full characterization of light with arbitrarily mixed full-Stokes polarization states across a broadband spectrum with a single device and a single measurement but also presents comparable, if not better, performance than state-of-the-art single-purpose miniaturized polarimeters or spectrometers. Our approach can be readily used as an alignment-free retrofit for the existing imaging platforms, opening up new paths to ultra-compact and high-dimensional photodetection and imaging.
