Toshiyuki Takatsuji

The first measurement of a three-dimensional coordinate by use of a laser tracking interferometer system based on trilateration

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.

Geometric calibration of a coordinate measuring machine using a laser tracking system

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.

Whole-viewing-angle cat's-eye retroreflector as a target of laser trackers

A spherical cats-eye retroreflector made from a glass material having a refractive index of two was developed. The geometrical sphericity of the cats 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.

The relationship between the measurement error and the arrangement of laser trackers in laser trilateration

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.

Restriction on the arrangement of laser trackers in laser trilateration

Laser trilateration is an effective technique for measuring three-dimensional coordinates. Taking advantage of a fourth laser tracker, the positions of all four laser trackers can be determined by a self-calibration algorithm. We show a restriction on the arrangement of laser trackers, namely, no tracker must exist on the plane defined by the other three trackers. A method of evaluating the measurement results is also discussed.

Design of laser interferometric measuring device of involute profile

The vibration and noise of gears is one of the serious problems for devices, such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are considerably affected by the tooth flank form deviation of micrometer order. The quality of product gears is controlled using a gear measuring instrument and calibrated with an involute artifact. However, the conventional calibration of the involute artifact cannot achieve a sufficient accuracy. In this report, a direct method of measuring the involute artifact using a laser interferometer is proposed. Fundamental experiments are carried out, in which the effects of the surface condition of the measured object and the effect of the driving of the artifact are investigated. It is confirmed that the proposed method enables the measurement of the detailed form of an involute tooth flank and has the potential of accomplishing a highly precise measurement of an involute artifact.

Nanometric lateral scale development using an atomic force microscope with directly traceable laser interferometers

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).

Phase-shifting interferometry with equal phase steps by use of a frequency-tunable diode laser and a Fabry–Perot cavity

A phase-shifting interferometry (PSI) with equal phase steps by use of a frequency-tunable diode laser and a Fabry-Perot cavity is proposed for the Carré algorithm. The measurement accuracy of the Carré algorithm depends on the equality of the phase steps. Using the Fabry-Perot cavity as a highly stable optical frequency reference, a high degree of phase step equality can be realized in PSI with an optical frequency shift. Our experimental scheme realizes an optical frequency step equality higher than 5.1 x 10(-5) and a measurement repeatability of lambda/800.

High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine

A high-performance laser tracker that is used for the calibration of a coordinate measuring machine (CMM) is introduced. A specially designed hemispherical-shape articulating mirror is used in the tracking mechanism, which enables reduction of the measurement uncertainties so that they are not more than 0.3 ?m. The uncertainty analysis of the laser tracker is also described.

Bilateral comparison of 25 nm pitch nanometric lateral scales for metrological scanning probe microscopes

One-dimensional (1D) and two-dimensional (2D) gratings are some of the most important transfer standards for the calibration of nanometrological instruments. National Metrology Institutes (NMIs) demonstrate their calibration capability through international comparisons among themselves and provide pitch calibration services for their customers. In the past, international comparisons were performed three times for gratings with large pitches such as 4000 nm, 1000 nm, 700 nm and 300 nm. Additionally, a bilateral comparison was conducted for 100 nm and 50 nm between the Japanese National Metrology Institute (NMIJ) and the German National Metrology Institute (PTB). The industry, however, requires calibration services for increasingly smaller pitches. In a previous study, NMIJ developed a nanometric lateral scale, a special 1D grating with 25 nm pitch consisting of Si/SiO2 multilayer thin-film structures, and calibrated the pitch of this scale by using the NMIJs atomic force microscope equipped with differential laser interferometers (DLI-AFM). In this paper, we will report results of an informal bilateral comparison for the nanometric lateral scale between NMIJ and PTB.