Extrinsic calibration of a laser displacement sensor in a non-contact coordinate measuring machine

In order to implement 3D scanning of those complicated parts such as blades in the aviation field, a non-contact optical measuring system is established in the paper, which integrates a laser displacement sensor, a probe head, the frame of a coordinate measuring machine (CMM), etc. As the output of the laser sensor directly obtained possesses the 1D length of the laser beam, it needs to determine the unit direction vector of the laser beam denoted as (l, m, n) by calibration so as to convert the 1D values into 3D coordinates of target points. Therefore, an extrinsic calibration method based on a standard sphere is proposed to accomplish this task in the paper. During the calibration procedure, the laser sensor moves along with the motion of the CMM and gathers the required data on the spherical surface. Then, both the output of the laser sensor and the grating readings of the CMM are substituted into the constraint equation of the spherical surface, in which an over-determined nonlinear equation group containing unknown parameters is established. For the purpose of solving the equation group, a method based on non-linear least squares optimization is put forward. Finally, the system after calibration is utilized to measure the diameter of a metallic sphere 10 times from different orientations to verify the calibration accuracy. In the experiment, the errors between the measured results and the true values are all smaller than 0.03 mm, which manifests the validity and practicality of the extrinsic calibration method presented in the paper.