in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudioCalamar, Figueres/BerlinPrinted on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my family Preface "When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science." -Lord KelvinThe act of measuring, which is used for determining the size, amount or degree of a parameter by an instrument through comparison with a standard unit, or used indirectly by calculation based on theory, makes science and technology different from imagination. Measurement is also essential in industry, commerce and daily life. If we focus on the manufacturing industry, we can easily find that dimensional metrology plays an increasingly important role not only in the traditional field of manufacturing but also in the advanced field of nanomanufacturing, represented by ultra-precision machining and semiconductor fabrication.Nanomanufacturing is a process of using precision machines that can generate precision tool motions to fabricate designed surface forms/dimensions with nanometric tolerances. Dimensional measurement of the workpiece and the machine is always an essential process for the purpose of quality control in all kinds of manufacturing. Because accuracy is the most important requirement for nanomanufacturing, the dimensional measurement is a much more crucial process for nanomanufacturing than other kinds of manufacturing. Figure 0.1 shows tolerances with respect to the dimensions of the workpieces and machines in nanomanufacturing. It can be seen that most of the workpieces and machines have sizes ranging from micrometers to meters while the corresponding tolerances range from 100 nm to 0.1 nm. In addition, more and more precision workpieces are required in a shorter amount of time in order to reduce manufacturing costs. Shapes of the precision workpieces are also becoming more and more complex. These factors are bringing greater challenges to the existing measuring technologies of precision metrology and nanometrology.Precision metrology has a long history tracing back to the inventions of the micrometer (J. Watt 1772), gage b...

Influences of angular misalignments of a small cylinder on its roundness measurement by the method referred to as the stitching linear scan method are theoretically investigated. To compensate for the influences, a technique for measuring angular misalignments of a small cylinder by utilizing the linear-scan surface form stylus profilometer, which is employed for roundness measurement, is newly proposed. In addition, for roundness measurement, a holder unit capable of compensating for the angular misalignments of a small cylinder is developed, and the feasibility of the proposed technique is verified in experiments. Furthermore, a measurement uncertainty analysis of the stitching linear-scan method is carried out through numerical calculations based on a Monte Carlo method.

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A measurement method based on a confocal probe on the second harmonic generation that can measure linear and angular displacements in the focusing point is proposed. In the proposed method, a pinhole or an optical fiber placed in front of the detector in conventional confocal probes is replaced by a nonlinear optical crystal, which is utilized as a medium generating second harmonic wave whose light intensity changes by the linear and angular displacements of a target under measurement. The feasibility of the proposed method is verified by theoretical calculations and experiments with the newly designed optical setup. Experimental results have demonstrated that the developed confocal probe has a resolution of 20 nm and 5 arc-seconds for measurement of linear and angular displacements, respectively.