Reflection grating photogrammetry: a technique for absolute shape measurement of specular free-form surfaces

Abstract

While for non-reflecting surfaces a variety of optical techniques is available that allow the flexible geometric measurement of free-form surfaces, established approaches for the testing of specular surfaces are limited to basic geometries or slight deviations from an assumed reference geometry. As not only the intensified use of aspheric optics but also the increasing quality standards for technical surfaces call for an enhanced measurement range, the authors have developed two related techniques for the direct three-dimensional measurement of specular reflecting surfaces. These techniques are based on the observation of the mirror image of a grid-like reference structure and apply principles that are well-known from measurement systems for non-reflecting surfaces, such as photogrammetry and structured illumination, to the evaluation of specular surfaces. While the first of these approaches works with an active triangulation process based on one camera and a pseudo three-dimensional reference structure, the second one utilises a stereo-photogrammetric camera system in conjunction with a merely two-dimensional reference structure. Both systems allow the unambiguous measurement of reflecting free-form surfaces and may, by the use of multiple wavelength and photogrammetric stitching techniques, be extended to the measurement of rather complex geometries. Besides the fundamental mode of operation of this so-called reflection grating photogrammetry, the properties of a suitable reference structure will be presented in this contribution. Furthermore the photogrammetric calibration procedure and the used calibration models will be discussed. Finally the measurement uncertainty is evaluated based on both, experimental and theoretical considerations.