  Sampling is a pivotal element in the design of metasurfaces, enabling a broad
spectrum of applications. Despite its flexibility, sampling can result in
reduced efficiency and unintended diffractions, which are more pronounced at
high numerical aperture or shorter wavelengths, e.g. ultraviolet spectrum.
Prevailing metasurface research has often relied on the conventional Nyquist
sampling theorem to assess sampling appropriateness, however, our findings
reveal that the Nyquist criterion is insufficient for preventing the
diffractive distortion. Specifically, we find that the performance of a
metasurface is significantly correlated to the geometric relationship between
the spectrum morphology and sampling lattice. Based on lattice-based
diffraction analysis, we demonstrate several anti-aliasing strategies from
visible to ultraviolet regimes. These approaches significantly reduce aliasing
phenomena occurring in high numerical aperture metasurfaces.
