This paper proposes a calibration method for a coordinate measuring machine (CMM) using a laser tracking system. The laser tracking system can measure three-dimensional coordinates based on the principle of trilateration with high accuracy and is easy to set up. The accuracy of length measurement of a single laser tracking interferometer (laser tracker) is about 0.3 µm over a length of 600 mm. In this study, we first measured 3D coordinates using the laser tracking system. Secondly, 21 geometric errors, namely, parametric errors of the CMM, were estimated by the comparison of the coordinates obtained by the laser tracking system and those obtained by the CMM. As a result, the estimated parametric errors agreed with those estimated by a ball plate measurement, which demonstrates the validity of the proposed calibration system.
A laser tracking interferometer system developed by us is capable of measuring the coordinates of a target retroreflector. In this system, a self-calibration algorithm is used to determine system parameters such as the arrangement of laser trackers and the initial lengths of interferometers. The self-calibration algorithm is a least-squares method, hence in the algorithm a residue of measurement results is evaluated as a criterion of convergence. The relationship between the measurement error and the arrangement of the laser trackers was experimentally investigated. On the basis of these investigations, a new definition of the residue used in the self-calibration algorithm is proposed.
A spherical cat's-eye retroreflector made from a glass material having a refractive index of two was developed. The geometrical sphericity of the cat's eye and the sphericity examined optically were approximately 100 nm and 500 nm respectively. The discrepancy between these two values is discussed. This optical device is very versatile in terms of applications since it is free from viewing angle restrictions.
One-dimensional grating standards with sub-hundred nanometre pitches are required for calibration of nanometrological instruments. Nanometric lateral scales (design pitches: 100, 60 and 50 nm) for the calibration of nanometrological instruments were designed and fabricated by electron beam cell projection lithography. An offset-locked laser system consisting of an I2-stabilized He–Ne laser and a slave laser was installed in an atomic force microscope with differential laser interferometers (DLI-AFM) for the realization of a continuously, directly length-standard-traceable system and the pitches of the lateral scales were calibrated using the new DLI-AFM. The average pitches were quite close to the design pitches and the expanded uncertainties (k = 2) were less than 0.6% of the design pitches. The developed nanometric lateral scales are of sufficiently high quality and are candidates for certified reference materials (CRMs).
A three-dimensional coordinate of a target position was measured using a laser tracking interferometer system based on laser trilateration. Laser interferometers, which are mounted on two-directional rotating stages, track the motion of the target retroreflector. By applying the principle of trilateration, the position of the retroreflector is estimated using the optical path difference caused by the motion of the target. Four laser interferometers were used, which produced redundancy in the measurement. By taking advantage of the redundancy, the position of the interferometers and the initial position of the target is self-calibrated and consequently the target position was calculated. The measurement error of a preliminary experiment was about m for a 1 m measurement.
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