Three-dimensional small angle measurement using a single image

The paper presents a new method of measuring 3D small angles. In the method, a collimated parallel ray is projected on a double-face-reflector, a CCD detects the position changes of the returned light points. Compared with the traditional autocollimation system, the presented system can distinguish the small change of angle around axis z, therefore, the system realizes the measurement of 3D small angles. By matrix transform, the paper sets up the mathematics model between the position changes of the imaging points on CCD and the changes of spatial small angles. It describes the characteristics of this method and gives its resolving method. By simulations, the paper testifies the correctness of the system model and its resolving method. Furthermore, the paper analyses the effect of the system parameters on the system resolutions. The results can be used as the reference and basis while designing system. When the system parameters apply the values supposed in the paper, the resolutions of alpha and beta can reach 0.025". The resolution of gamma, less than that of alpha and beta, is about 2".