A method for calibrating an optical arrangement for determining dimensional properties of a measurement object and a coordinate measuring machine implementing the method are disclosed. The optical arrangement has a camera and a projector for projecting a first periodic pattern onto a projection area. The optical arrangement is moveable relative to a workpiece table along a first axis. A matte surface is arranged on the workpiece table at a first position relative to the optical arrangement. A second periodic pattern, which is separate from the first periodic pattern, is provided and shifted on the matte surface. Images of the second pattern are recorded using the camera and at least one distortion aberration of the camera is determined using the second periodic pattern. The first periodic pattern is projected onto the matte surface and first and second coordinates of at least one pattern point of the projected first periodic pattern are determined, the second coordinate with respect to a second axis, which is perpendicular to the first axis. The matte surface is displaced relative to the optical arrangement to a second position along the first axis and the aforementioned steps are repeated for a plurality of relative positions of the matte surface along the first axis.