Development of a Stitch Algorithm Using the Approximated Reference Shape

Abstract

For the mass production of large, severe aspherical optics, we have developed a new stitch algorithm named ARSA (Approximated Reference Shape Algorithm) which can be used for free-form measurement machines. The stitching measurement, which combines plural partial measurements into a whole shape, has been developed based on interferometry and is now widely used. The well known algorithm calculates the stitching parameters so as to minimize the mismatch in the overlapping area. However, with a free-form measurement machine using a scanning probe, the measured data are sparse and contain 3D points, causing significant calculation errors such as interpolation errors in the overlapping area. ARSA is based on minimizing the error of estimating the approximated reference shape. This algorithm has the unique feature that the calculation error is smaller in the case of severer asphericity and the interpolation error is also small for the same reason as in the case of interferometry. We classify the workpiece's shape into three spatial frequency domains and assess the performance for each case by simulation. The simulated measurement data are three sets of 3D points in fan-shaped partial measurements, and the workpiece's shape is a convex hyperboloid whose asphericity is 1.282mm for the full aperture of 1200mm. In all three domains the calculation results coincide with the theoretical values to within nanometer level. These results show the validity of this new algorithm.