Calibration of revolution axis for 360 deg surface measurement

Two methods are proposed to calibrate the revolution axis of a 360 deg, multiview fringe projection system for surface measurement. The first method is based on minimizing the distance between calculated and measured points; the second method is based on minimizing the difference between thus obtained vectors. Both are able to retrieve the revolution axis of a turntable, which is then used to transform surface patches measured at different viewing angles to a common coordinate. In the point-based method, a nonlinear minimization problem has to be solved by the Levenberg-Marquardt algorithm; in the vector-based method, the minimization problem is resolved into several linear equations, and an analytic solution is obtained efficiently. Results of simulation and experiments show that the error of calibration can be less than 0.05 deg for the axis's orientation and 0.3 mm for the axis's position (a point on the axis), which is about 0.1% of the measured volume.