Reconstructing surface profiles from curvature measurements
This paper investigates the accuracy with which surface profiles can be reconstructed from curvature data. The stability of the reconstructions is examined with respect to the presence of measurement noise and the accuracy of the initial values. The assessment of the reconstruction accuracy is based on an analytical solution (up to numerical integration) derived for the case when the measurement results are given in Cartesian coordinates, and on numerical results in the polar case. The results presented for the latter case allow, in particular, conclusions to be drawn regarding the minimum accuracy of data and initial values required for reconstructing aspheres from curvature measurements with nanometer accuracy.
Document Type: Original Article
Affiliations: 1: Physikalisch-Technische Bundesanstalt Berlin, Abbestrasse 2–12, D-10587 Berlin, Germany 2: Physikalisch-Technische Bundesanstalt Braunschweig, Bundesallee 100, D-38116 Braunschweig, Germany
Publication date: 2002-07-01