CompMath Seminar - Safiere Kuijpers, University of Groningen

Title: Bayesian shape inversion for scattering transmission problems

Abstract:

In the field of nano-optics, one works with very small objects, which cannot be made in the exact shape intended due to the manufacturing process. Therefore, it is useful to know how these objects deviate from their intended shape to predict their experimental behavior better. This can be determined from experimental measurements using Bayesian inversion and assuming that the involved wave obeys the Helmholtz equation. I prove that the resulting inverse problem is well-posedness in a wave number-explicit way. To solve the forward problem numerically, finite elements are used as well as a mapping approach to a reference configuration to handle the sample-dependent geometry and a perfectly matched layer to approximate the radiation condition at infinity. The posterior distribution is approximated using sequential Monte Carlo with adaptive tempering. I will show numerical results to demonstrate the feasibility and potentiality of this approach as well as the effect of the frequency on the posterior concentration.