Inverse Problems in Optics

Inverse problems in astronomical adaptive optics

Adaptive optics (AO) is a technology used in ground-based astronomy to correct for the wavefront aberrations and loss of image quality caused by atmospheric turbulence. Provided some difficult technical problems can be overcome, AO will enable future astronomers to achieve nearly diffractionlimited performance with the extremely large telescopes that are currently under development, thereby gre...

Inverse Medium Scattering Problems in Near-field Optics

A regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium deposited on a homogeneous substrate from data accessible through photon scanning tunneling microscopy experiments. In addition to the ill-posedness of the inverse scattering problems, two ...

0 Problems in Optics

Inverse Scattering in Near-field Optics

A regularized continuation method is developed for a two-dimensional inverse medium scattering problem in near-field optics, which reconstructs the scatterer of an inhomogeneous medium deposited on a homogeneous substrate from data accessible through photon scanning tunneling microscopy (PSTM) experiments. In addition to the ill-posedness of inverse scattering problems, two difficulties arise b...

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.