# American Institute of Mathematical Sciences

November  2013, 7(4): 1393-1407. doi: 10.3934/ipi.2013.7.1393

## Reconstruction of penetrable grating profiles

 1 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 2 LSEC and Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, China

Received  September 2012 Revised  June 2013 Published  November 2013

This paper is concerned with the inverse problem of recovering a penetrable grating profile in the TM-polarization case from the scattered field measured only above the structure, corresponding to a countably infinite number of incident quasi-periodic waves. A sampling method is proposed to reconstruct the penetrable grating profile based on a near field linear operator equation in $l^2$. The mathematical justification of the sampling method is established and numerical results are presented to show the validity of the inversion algorithm.
Citation: Jiaqing Yang, Bo Zhang, Ruming Zhang. Reconstruction of penetrable grating profiles. Inverse Problems & Imaging, 2013, 7 (4) : 1393-1407. doi: 10.3934/ipi.2013.7.1393
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