Error analysis and surface reconstruction for swing arm profilometry

Abstract

Aiming to develop a prototype swing arm profilometer for several meter-class aspheres, we first present detailed error analysis including error motions of the swing rotary table and the part rotary table, and misalignment of the axes of the two rotary tables. The induced probing error in the normal direction of the reference sphere is calculated by considering the error motions in the coordinate transformation. A surface reconstruction algorithm is then proposed to separate the error motions of the part rotary table by stitching multiple traces. The error motions are optimally recognized and then removed from the trace measurement based on the least squares principle. We model the objective function by relating the normal error to the rigid body transformation of each trace. The basic idea is to minimize the inconsistency of all intersection points of different traces simultaneously. Finally the algorithm is verified through simulations. It shows that error motions of sub-milliradian scale are even tolerant with the surface reconstruction algorithm.