For flexible 3D positioning of a complex 3D mechanism, it is needed to measure 3D displacement of the end-effecter of the mechanism in high precision and by non-contact method. It was common to use plural sensors or scales together to measure the 3D displacement. However, it is difficult to calibrate the sensitivities of the plural sensors or scales. A novel 3D displacement measurement is proposed using an optical system in which lens focuses are collected at the center of the sphere, which has been used for the radius measurement of the sphere. Instead of facing in the XY direction that has high sensitivity, new ideas are necessary for the measurement in the Z direction of the optics where focuses are collected at the center of the sphere. The displacement in the XY direction and the one in the Z direction can be measured at the same time by using a ring-shaped laser beam instead of a simple ray.