Data from: Waterjet and laser etching: the nonlinear inverse problem

In waterjet and laser milling, material is removed from a solid surface to create a new shape. The inverse problem consists of defining the 2D beam path to arrive at a prescribed freeform surface. WaterJet Machining (WJM) and Pulsed Laser Ablation (PLA) are studied in this paper since a generic nonlinear material removal model is appropriate for both of these processes. The inverse problem is usually solved for this kind of process by simply controlling dwell time in proportion to the required depth of milling at a sequence of pixels on the surface. However, this approach is only valid when shallow surfaces are etched, since it does not take into account either the footprint of the beam or its overlapping on successive passes. We propose a discrete adjoint solution algorithm that allows for nonlinear effects and non-straight passes. Tests are performed to validate the proposed method, which show that tracking error is typically reduced by a factor of two in comparison to the pixel-by-pixel approach and the classical raster path strategy with straight passes. The tracking error can be as low as 2-5% and 1-2% for WJM and PLA respectively, depending on the complexity of the target surface.