3D coordinates at first selected measurement points of a measurement object are determined using a first measurement arrangement. Surface normals at second selected measurement points of the measurement object are determined using a second measurement arrangement. Using the 3D coordinates and the surface normals, at least one of dimensional or geometric characteristics of the measurement object are determined. The second measurement arrangement includes a number of light sources and a first camera which is directed to the measurement object. A calibration data set represents individual direction dependent radiation patterns of the light sources. The surface normals are determined using the calibration data set and the 3D coordinates at the first selected measurement points.