摘要： One-shot optical polarimetry using ultra-thin nanostructured metagratings opens up new opportunities for diverse applications, facilitating the measurement of both classical and quantum polarization states. Despite the significant progress, there appeared fundamental limitations associated with a need to interleave multiple metagratings on a metasurface in order to split several distinct pairs of polarization components, which limited diffraction efficiency and negatively affected the beam quality. A recent study demonstrated polarimetry with a single metagrating, however it required an additional linear polarizer with the associated detrimental effects of attenuating the detected optical power, reducing the device compactness, and increasing the setup complexity. We formulate a new conceptual approach for polarization measurements with a single metagrating, which allows us to overcome the limitations that were inherent to the previous schemes. We find that those limitations occurred due to the attempts of replicating traditional polarimetry based on close-to-perfect polarizers, where each measurement characterizes a definite polarization component. Yet in general, metasurfaces can behave like sets of imperfect (partial) polarizers, and it is our key finding that full Stokes polarization reconstruction is possible in this regime. Specifically, we develop a rigorous polarimetry approach based on the positive operator-valued measure (POVM) formalism originating from quantum mechanics. This fundamentally lifts the restrictions on metasurface design and enables robust operation even under significant fabrication inaccuracies.