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Displacement detection of a small sphere with high sensitivity is required for realizing the micro tactile probe used in micro-coordinate-measuring machines (CMMs). Therefore, the authors have proposed a new technique for detecting the three-dimensional displacement of a small sphere by a kind of astigmatic method, termed the “eccentric astigmatic method (EAM).” In the EAM, a spherical mirror as a spherical tactile probe is placed on the focus of an objective lens. At this position, three eccentric beams, focused by the objective lens, are incident on the mirror surface at right angles and the reflected rays return on the incident paths. In contrast, when the sphere moves from this position even by a small distance, the return path of each reflected ray changes drastically. This change can be detected by the EAM using a condenser lens and a photodetector. The changes in the spot radius caused by the EAM were calculated using a ray-tracing code. As a result, a change in the spot shape was found to occur only for displacement along one axis. Moreover, simulations based on wave optics were performed, whose results confirmed the feasibility of detection of the three-dimensional displacement of a sphere by the EAM.

Property Evaluation of Eccentric Astigmatic Method to Apply Micro Tactile Probe