Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem
- 1 March 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 29 (2), 232-238
- https://doi.org/10.1109/tap.1981.1142588
Abstract
An efficient algorithm is presented to compute the shape of perfectly conducting cylinders via knowledge of scattering cross sections. This choice of scattering data avoids the difficulties linked with the phase measurements or reconstructions. The mathematical analysis is performed in terms of operator and functions, and the fundamental instability of the problem is demonstrated. Then the stability is restored by means of a Tikhonov-Miller regularization. The efficiency of the method is outlined by numerical examples. References are given which show that the same algorithm applies to other electromagnetic inverse problems, especially to gratings.Keywords
This publication has 12 references indexed in Scilit:
- Inverse scattering method in electromagnetic optics: Application to diffraction gratingsJournal of the Optical Society of America, 1980
- Grating profile optimizations by inverse scattering methodsOptics Communications, 1980
- Electromagnetic Theory of GratingsTopics in Current Physics, 1980
- The Perfectly Conducting Grating from the Point of View of Inverse DiffractionOptica Acta: International Journal of Optics, 1979
- Restoration of optical objects using regularizationOptics Letters, 1978
- On a problem of inverse scattering in optics: the dielectric inhomogeneous mediumJournal of Optics, 1978
- On the inverse problem for a hyperbolic dispersive partial differential equationJournal of Mathematical Physics, 1972
- Least Squares Methods for Ill-Posed Problems with a Prescribed BoundSIAM Journal on Mathematical Analysis, 1970
- The Scattering and Diffraction of WavesPublished by Harvard University Press ,1959
- On the characteristic values of linear integral equationsActa Mathematica, 1931