Advances in Differential Equations and Control Processes
Volume 17, Issue 2, Pages 99 - 115
(May 2016) http://dx.doi.org/10.17654/DE017020099 |
|
ANALYSIS OF THE INVERSE PROBLEM OF DETERMINING THE DEFECT ON OPTICAL SURFACES
J. Oliveros, M. MorÃn, J. Escamilla, J. Serrano and H. RamÃrez
|
Abstract: This work addresses the problem of determining the defect on optical surfaces from the transversal aberration and the Malacara formula for the case of symmetry around the optical axis. This can be considered as an inverse problem which is ill-posed in the Hadamard sense. This is due to the non-uniqueness of the solution of the inverse problem, that is, there are different configurations of the defect surface that produce the same transversal aberration. We give conditions for guaranteeing the uniqueness of the solution of the problem. Furthermore, we prove the numerical stability regarding the errors on the transversal aberration and the parameter of the problem. These results are illustrated through numerical examples. |
Keywords and phrases: transversal aberration, Malacara formula, Ronchi ruling, uniqueness theorem, integration methods. |
|
Number of Downloads: 346 | Number of Views: 1159 |
|