Periodic surface identification with phase or phaseless near-field data. (9th October 2017)

• Record Type: Journal Article
• Authors: Zheng, Jinchang; Cheng, Jin; Li, Peijun; Lu, Shuai
• Is Part Of: Inverse problems. Volume 33:Number 11(2017:Nov.)
• Publication Date: 2017-10-09
• Subjects: inverse diffraction grating problem -- the Helmholtz equation -- near-field imaging; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa8cb3
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.