Data processing method based on surface and tangent vector deviations for freeform surface

Abstract

Surface measurement and analysis are important to freeform surface optical systems. The deviation from designed surface is generally regarded as a judging criterion of real surface quality. In off-axis optical systems, some freeform surfaces contain no reference points. Measured data of such surfaces can only constitute a fitted surface, but the spatial position of the fitted surface is difficult to be determined to make a smallest deviation from designed surface by internal algorithms. In freeform surface optical systems, besides the surface deviations, the tangent vector variations of lattice data of measured surface can also affect the image quality. Consequently the quality of freeform surface should be appraised by both of tangent vector variations and surface deviations. This paper presents one method using first-order differential to directly analyze and process the measured lattice data of freeform surfaces. This method assesses the tangent vector variations of measured data and the smoothness of real surfaces, while does not involve the fitting procedure with designed surfaces. In this paper, this method is applied to evaluate a set of measured lattice data of some reflective freeform surfaces. Furthermore, some fitting algorithms are applied to assess the surface deviations between the measured and designed surfaces as contrasts.