Spatial-Spectral Trade-offs in Metasurface-Based Snapshot Hyperspectral Imaging

Abstract: Snapshot hyperspectral imaging maps a spatial--spectral datacube onto a two-dimensional detector, with recoverability depending on the datacube sampling regime, the scene prior, and the optical encoding. We study this co-dependence with algorithmic recovery and optical design optimization in a differentiable metasurface model by varying the spatial--spectral ratio and comparing average-coherence, mutual-information, and end-to-end objectives. For compressed imaging with three bands, optimization of single-parameter dielectric pillars produces lens-like designs with overlapping wavelength-dependent point-spread functions across the objectives tested. End-to-end reconstruction can mask this collapse on restricted training distributions, showing that reconstruction fidelity depends jointly on the optical encoding and scene prior. For simple nano-pillar meta-atom geometries, the optimized singular-value spectrum deteriorates as the datacube becomes more spectrally dominated, whereas a relaxed model with independent complex transmission at each wavelength reduces this dependence. These results identify restricted wavelength-dependent transmission control in the pillar library as an important contributor to the observed spectral collapse. This motivates an illustrative local super-pixel spectrometer model in which spectral encoding is studied separately from global image formation under a plane-wave illumination approximation.