Imaging-system-aware color routers optimized for imaging information
Conventional nanophotonic color routers are typically optimized under idealized, normal plane waves. However, this standard assumption fails in real-world imaging-system environments, where structures are illuminated by converging light cones and field-dependent chief-ray angles. Here, we present an imaging-system-aware, end-to-end inverse-design framework that directly maximizes the mutual imaging information $\Iimg$ preserved by a single-layer silicon nitride color router under realistic pupil illumination. By analytically embedding the optimal reconstruction decoder directly inside the gradient loop, we co-design the optical nanostructures and the digital recovery pipeline. To scale this approach across a full sensor, we exploit the $D_4$ symmetry of the square pixel lattice, tiling $48$ distinct sensor-field regions using only six unique lithographic masks. Our optimized router is predicted to collect $2.8\times$ more photoelectrons than a conventional color-filter array. Consequently, under low-light conditions, below a green-site signal-to-noise ratio of $13.7$~dB, the color router preserves superior image information compared to the color-filter array; evaluated from its measured routing fractions together with the modeled throughput, the fabricated device reproduces this crossover at $11.1^{+2.1}_{-2.3}$~dB. This marks the first experimental demonstration, from measured routing and a modeled throughput, of a single-layer nanophotonic color router achieving a performance crossover against the color-filter array. These results establish that next-generation flat optics must shift from isolated device efficiency toward system-level co-design optimized under physical imaging-system-pupil geometry.