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Fujimoto I.,Okuwa Technical Research Center | Sato S.,Tokyo University of Science | Kim M.Y.,Kyungpook National University | Ando S.,Tokyo University of Science
Measurement Science and Technology | Year: 2011

Significant propagation properties of optical vortex beams with an on-axis single singular point for displacement measurement applications are proposed: the preservation of the singularity structure, including the conically shaped structure of the amplitude distribution, especially, its sharp structure, and the circulating structure of the phase distribution around the singular point through free-space propagation. Through theoretical analyses, simulations and basic experiments, it is verified that optical vortex beams are very effective for performing both rotational and translational displacement measurements simultaneously in the surveying field. © 2011 IOP Publishing Ltd. Source


Fujimoto I.,Okuwa Technical Research Center | Takatsuji T.,Japan National Institute of Advanced Industrial Science and Technology | Nishimura K.,Mizukoshi Keiki Co Ltd. | Kim M.Y.,Kyungpook National University
Applied Optics | Year: 2012

An autonomous method for calibrating the reference flat surface of an interferometer is proposed with the uncertainty analysis. The method consists of three phases; the first step is multiple rotating shifts of a specimen, the second is a linear shift, and the last is multiple rotating shifts again. The profile of the reference flat surface is basically determined by the linear shift. The linear shift errors that occurred during the linear shift are identified by the rotating shifts. The rotating shift errors caused by the rotating shifts can be compensated and the residual uncertainty can be reduced in proportion to the square root of the number of rotating shifts per one revolution. Finally, the uncertainty analysis is carried out in detail. © 2012 Optical Society of America. Source


Fujimoto I.,Okuwa Technical Research Center | Nishimura K.,Mizukoshi Keiki Co Ltd. | Takatsuji T.,Japan National Institute of Advanced Industrial Science and Technology | Pyun Y.-S.,Sun Moon University
Precision Engineering | Year: 2012

In this paper, a three-point method with an autonomous calibration function is proposed to measure the flatness of next-generation 450 mm wafers. The measuring method is comprised of the following two processes: (1) the measurement of the flatness of the wafer across the circumference of the circle by three displacement sensors that are built-in to the wafer holder and (2) the measurement along several straight lines that pass through the rotational center point and two points on the circumference of the circle while changing the straight line for measurement by rotating the wafer step by step. Through these two processes, the flatness of the wafer can be determined by the proposed algorithm, which can automatically reduce the influence of motion errors and the zero-difference of the three sensors. The conceptual design and the algorithm utilized in the proposed method are explained using theoretical analyses and numerical calculations. The results of this study are as follows: the expanded uncertainty of wafer flatness is approximately 6.8 and 0.3 μm when the sampling number for the measurement across the circumference of the circle with a radius of 220 mm is 10 3 and 10 6, respectively. The measurements were observed under the practical conditions that: (a) the sampling number for the measurement along several straight lines that pass through the rotational center point and two points on the circumference of the circle that has a radius of 220 mm is 100, (b) the radius of the circular sensor is 1 mm, (c) the standard deviation of the sensor is 0.1 μm, and (d) the adjacent sensor interval is 30 mm. © 2011 Elsevier Inc. All rights reserved. Source


Fujimoto I.,Okuwa Technical Research Center | Takatsuji T.,Japan National Institute of Advanced Industrial Science and Technology | Nishimura K.,Mizukoshi Keiki Co Ltd. | Pyun Y.-S.,Sun Moon University
Measurement Science and Technology | Year: 2012

In this paper, the relationship between the uncertainty components of displacement sensors and the measurement uncertainty of a surface straightness measurement system with the three-point method is analytically studied. The uncertainty components include the linearity, sensitivity, etc of the sensors. First, the three-point method which can automatically calibrate the zero-difference is outlined, and the relationship between input displacement and output voltage of a sensor, and the uncertainty components of a sensor are particularly explained. Next, the uncertainty analysis and numerical experiment are carried out. The main results of this study are as follows: (1) the influence of the uncertainty components including the linearity and sensitivity of the sensor on the measured shape of an object target can be reduced in proportion to the magnitude of the sensitivity coefficient and the square root of the sampling number for measurement. (2) When both the sampling numbers n r for calibrating the system and the sampling numbers n x for measuring the shape of an object target are 1000, and the measuring length is 600mm, the expanded uncertainty can be reduced to less than 38% of that in the case of n x = 100, and become less than 1m in the case of n x 300 while it is 1.58m in the case of n x = 100. As well, these results do not include the influence of uncertainty factors such as the systematic error, which cannot be compensated because the true value is unknown. © 2012 IOP Publishing Ltd. Source


Fujimoto I.,Okuwa Technical Research Center | Nishimura K.,Mizukoshi Keiki Co Ltd. | Takatuji T.,Japan National Institute of Advanced Industrial Science and Technology | Pyun Y.-S.,Sun Moon University
Measurement Science and Technology | Year: 2011

An autonomous method for calibrating the zero difference for the three-point method of surface straightness measurement is presented and discussed with respect to the relationship between the measurement uncertainty and the size of the disk gauge used for calibration. In this method, the disk gauge is used in two steps. In the first step, the disk gauge rotates a few revolutions and moves parallel to three displacement sensors built into a holder. In the second step, the geometrical parameters between the sensors and the disk gauge are acquired, and the zero differences are computed by our recently proposed algorithm. Finally, the uncertainty of the zero differences is analyzed and simulated numerically, and the relationship between the disk gauge radius and the measurement uncertainty is calculated. The use of a disk gauge of larger radius results in smaller uncertainty of straightness measurement. © 2011 IOP Publishing Ltd. Source

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