Multiple reflectors based autocollimator for three-dimensional angle measurement

Abstract

This paper designs a multiple reflectors based autocollimator, and proposes a direct linear solution for three-dimensional (3D) angle measurement with the observation vectors of the reflected lights from the reflectors. In the measuring apparatus, the multiple reflectors is fixed with the object to be measured and the reflected lights are received by a CCD camera, then the light spots in the image are extracted to obtain the vectors of the reflected lights in space. Any rotation of the object will induce a change in the observation vectors of the reflected lights, which is used to solve the rotation matrix of the object by finding a linear solution of Wahba problem with the quaternion method, and then the 3D angle is obtained by decomposing the rotation matrix. This measuring apparatus can be implemented easily as the light path is simple, and the computation of 3D angle with observation vectors is efficient as there is no need to iterate. The proposed 3D angle measurement method is verified by a set of simulation experiments.