Near-field reconstruction of periodic structures with superimposed illumination

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.