Radius measurement and uncertainty evaluation using three-sphere reciprocity method

Three-dimensional (3D) measuring instrument has become widely applied by manufacturers due to the fast measurement capability and the flexible measuring procedure. It is also a crucial topic to evaluate or improve the measuring performance of these instruments, including the contact type like coordinate measuring machines (CMM) or the non-contact type like structure light scanners. Recently, the most commonly used standard feature is a sphere with a non-specular surface. It is because the ceramic materials is used to ensure the durability of the standard spheres, or is limited by the measuring principle of structure light scanners where the measured objects need to be lambertian surface. In the light of these limitations, the interferometry methods could not directly calibrate these standard spheres. In order to calibrate the radius and form of a non-specular sphere, this research focuses on the tactile method of spheres reciprocity method based on the previous researches. More details of the measuring principle and the formulas would be discussed. Final, the uncertainty of this method is evaluated using Monte Carlo method. The evaluated result of uncertainty is less than 10 nm for 15 mm radius sphere. This is very useful for common 3D measuring instrument calibration.