An arrangement, process and mask for implementing single-scan continuous motion sequential lateral solidification of a thin film provided on a sample such that artifacts formed at the edges of the beamlets irradiating the thin film are significantly reduced. According to this invention, the edge areas of the previously irradiated and resolidified areas which likely have artifacts provided therein are overlapped by the subsequent beamlets. In this manner, the edge areas of the previously resolidified irradiated areas and artifacts therein are completely melted throughout their thickness. At least the subsequent beamlets are shaped such that the grains of the previously irradiated and resolidified areas which border the edge areas melted by the subsequent beamlets grow into these resolidifying edges areas so as to substantially reduce or eliminate the artifacts.