Periodic surface identification with phase or phaseless near-field data. (English) Zbl 1516.35547
Summary: We investigate the inverse diffraction grating problem which is to reconstruct the periodic surface from the diffracted field. The surface is assumed to be a sufficiently smooth and small perturbation of the flat surface. A novel computational method is developed to solve the inverse problem with super-resolution by using phase or phaseless near-field data. The method utilizes Rayleigh’s coefficients of the near field data and updates iteratively the approximated surface function by solving a truncated linearized system. Monotonicity of the error estimate is proved under the small perturbation assumption of the surface. Numerical examples are shown to verify the theoretical findings and illustrate the effectiveness of the proposed method.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
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