Recent Developments in Inverse Problems - Abstract

Reginska, Teresa

Determining the laser beam waist from a noisy field distribution

In practical applications, the laser beam is often described as a geometrical object. For analysing this object, we define radii of the beam at any point of the beam axis z. The axial profile of the beam is defined as the plot of the radii vs. z. In general, the radii are different in directions x and y. The talk will be devoted to numerical determining the waist of the axial profile (its position and size) from noisy data. As the noisy data, we have some approximate distributions of the field and its z-derivative on a fixed beam intersection. The idea of the considered method consists in an approximation of the position and the size of the waist by the centre and the transverse semi-axis of a properly chosen hyperbola. This hyperbola is described by a generalized solution of a finite dimensional nonlinear equation. The right hand side of this equation is defined by regularized solutions of the ill-posed Cauchy problem for the Helmholtz equation at a set of points of the axis z. medskip This is a joint work with Kazimierz Regiński.