Abstract: Laser scanning apparatus and a related method for scanning a workpiece in a raster scan pattern, to remove a series of thin, overlapping layers in the workpiece and thereby provide a stepwise approximation to a contoured, three-dimensional shape. In one embodiment, the beam follows a raster scan pattern with scans that are parallel to the removed layer's boundary. The wall bounding the layer is made to be substantially perpendicular to the plane of the removed layer, regardless of the wall's orientation, by tilting the beam about an axis normal to a specified reference plane and by elliptically polarizing the beam to a selected degree. A substantially constant proportion of the beam's average intensity is thereby absorbed at each point along the boundary wall, regardless of the wall's orientation relative to the reference plane. In another embodiment, the beam scans repeatedly along an axis parallel to a specified reference plane.