Articles | Volume 3, issue 2
Regular research article
17 Nov 2014
Regular research article |  | 17 Nov 2014

Data fusion of surface normals and point coordinates for deflectometric measurements

B. Komander, D. Lorenz, M. Fischer, M. Petz, and R. Tutsch

Abstract. Measuring specular surfaces can be realized by means of deflectometric measurement systems with at least two reference planes as proposed proposed by Petz and Tutsch (2004). The results are the point coordinates and the normal direction of each valid measurement point. The typical evaluation strategy for continuous surfaces involves an integration or regularization of the measured normals. This method yields smooth results of the surface with deviations in the nanometer range but it is sensitive to systematic deviations. The measured point coordinates are robust against systematic deviations but the noise level is in the order of micrometers. As an alternative evaluation strategy a data-fusion process that combines both the normal direction and the point coordinates has been developed. A linear fitting technique is proposed to increase the accuracy of the point coordinate measurements by forming an objective functional as the mean squared misfit of the gradients with respect to the point coordinates on the one hand and to the normals on the other hand. Moreover, a constraint on the maximal change of the coordinate measurements is added to the optimization problem. To minimize to objective under the constraint a projected gradient method is used. The results show that the proposed method is able to adjust the point coordinate measurement to the measured normals and hence decrease the spatial noise level by more than an order of magnitude.

Short summary
Deflectometric measurements of specular surfaces when performed with two reference planes lead to both data for surface points and surface normals. The deviations in the surface points are usually several orders of magnitude larger than those for the surface normals. In this paper we propose a method to fuse these data to increase the accuracy of the surface points. The results show that the accuracy can be increased by more than an order of magnitude.