An inverse problem in diffractive optics: conditional stability

Authors: Bruckner G.¹; Cheng J.²; Yamamoto M.³

Source: Inverse Problems, Volume 18, Number 2, 2002 , pp. 415-433(19)

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Abstract:

In this paper, we prove conditional stability for the inverse problem in diffractive optics of determining a periodic curve in the case of perfect reflection. Introducing a time-periodic solution, we formulate the problem in terms of the Helmholtz equation. Taking a plane wave as an incident wave, we observe the total field along a segment which is remote from the unknown curve. Our proof is based on a Carleman estimate for the Laplace operator.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Weierstrass Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, Berlin D-10117, Germany 2: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China 3: Department of Mathematical Sciences, The University of Tokyo, Komaba 3-8-1 Meguro, Tokyo 153-8914, Japan

Publication date: 2002-01-01