Jump to ContentJump to Main Navigation

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR): 0.466
Source Normalized Impact per Paper (SNIP): 1.251

Mathematical Citation Quotient 2013: 0.51



Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings

1Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 4-5, Pages 717–768, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.048, September 2011

Publication History

Published Online:


We consider the inverse elastic scattering problem of determining a three-dimensional diffraction grating profile from scattered waves measured above the structure. In general, a grating profile cannot be uniquely determined by a single incoming plane wave. We completely characterize and classify the bi-periodic polyhedral structures under the boundary conditions of the third and fourth kinds that cannot be uniquely recovered by only one incident plane wave. Thus we have global uniqueness for a polyhedral grating profile by one incident elastic plane wave if and only if the profile belongs to neither of the unidentifiable classes, which can be explicitly described depending on the incident field and the type of boundary conditions. Our approach is based on the reflection principle for the Navier equation and the reflectional and rotational invariance of the total field.

Keywords.: Inverse scattering; uniqueness; three-dimensional diffraction grating; Navier equation; boundary conditions of the third (fourth) kind

Comments (0)

Please log in or register to comment.