Recovering the Grating Profile from Limited-Aperture Observation: Data Retrieval and Shape Reconstruction*

This paper proposes a two-stage framework to address the inverse diffraction grating problem with limited-aperture data. The first stage introduces a deep learning network for data retrieval, fea turing a dual-branch, cross-attention architecture. Motivated by an information-theoretic analysis, this design is tailored to separate and adaptively fuse the diffracted field's low-and high-frequency components, effectively handling their distinct noise sensitivities. The second stage employs a com putationally efficient Newton-type algorithm for shape reconstruction, which avoids the need for a forward solver at each iteration. Numerical experiments show that our framework provides accurate and robust reconstructions.