Computing specific intensity distributions for laser material processing by solving an inverse heat conduction problem

Laser beam intensity distribution profiles for material processing techniques are most of the time restricted to be either of Gaussian or tophat shape. This often leads to different kind of problems especially at the edges of the laser-heated tracks, examples are energy losses or unnecessary overlaps. Thus, machining quality and process efficiency could be much improved by using application specific intensity profiles to generate optimal temperature distributions in the processed material. In this work, we present a numerical method to derive a specific intensity profile for a given temperature distribution. As this problem belongs to the set of inverse heat conduction problems, which are ill-posed, special regularization algorithms are needed. The only method to solve this inverse problem in reasonable time is the conjugate gradient method which we extend to the given problem of laser material processing applications. This method is an iterative approach where in each step the actual temperature distribution is calculated by using the finite element method. In general, the proposed method is applicable for materials with constant or temperature dependent coefficients, for static and dynamic distributions as well as for plane or complex geometries. However, restricting ourselves to plane geometries, intensity distributions that create tophat- or stepped temperature distributions on the plane surface of the processed material are derived and will be presented. In future work, we intend to verify these results using freeform optics as well as singly addressable V(E)CSEL arrays