  This paper addresses the reconstruction of periodic structures using phase or
phaseless near-field measurements. We introduce a novel illumination strategy
based on the quasi-periodic condition. Employing the Dirichlet-to-Neumann (DtN)
map, we reformulate the scattering problem into a uniquely solvable boundary
value problem. Our theoretical analysis shows the advantages of employing a
fixed wavenumber superposition illumination strategy and proves that a specific
wavenumber interval and fixed direction uniquely determine the grating
structure. Numerical results confirm the efficacy of this illumination strategy
and reconstruction algorithm, enabling super-resolution imaging from both phase
and phaseless near-field measurements.
