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1 Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo

2 J. M. RUeger Electronic Distance Measurement An Introduction Fourth Edition With 56 Figures and 18 Tables Springer

3 Dr. J. M. RUEGER School of Geomatic Engineering University of New South Wales Sydney NSW 2052 Australia Library of Congress Cataloging-in-Publication Data Rueger. J. M. (Jean M.) Electronic distance measurement : an introduction / J.M. Rueger th ed. p. cm. Includes bibliographical references and index. 1. Geodesy--Instruments. 2. Distances--Measurement. I. Title. CB328.A1R '.028--dc CIP ISBN-13: : / e-isbn-13: This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1996 The use of general descriptive names, 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 protective laws and regulations and therefore free for general use. Typesetting: K + V Fotosatz GmbH, Beerfelden SPIN / Printed on acid-free paper

4 Preface to the 1996 Edition As the basic principles of EDM instruments have changed little since the third edition of 1990, there was no need for significant changes. This edition differs from its predecessor in that it contains corrections of a number of errors and misprints, totally revised tables in Appendices D, E and F and a new note in Section on the introduction of the new temperature scale in The author is indebted to the many readers who reported the many small errors and misprints. T. Black, H. Buchanan, R. Da-Col, R. Kochle, P. H. Lam, 1. Nolton, 1. R. Pollard and A. Quade were particularly helpful. All known errors have been corrected. The assistance provided by most manufacturers (or their agents) with the updating of the tables with the instrument data was greatly appreciated. Sydney, February M. RUEGER v

5 Preface The book has evolved from the author's continuing teaching of the subject and from two editions of a text of the same title. The first edition was published in 1978 by the School of Surveying, University of New South Wales, Sydney, Australia. Like its predecessors, this totally revised third edition is designed to make the subject matter more readily available to students proceeding to degrees in Surveying and related fields. At the same time, it is a comprehensive reference book for all surveyors as well as for other professionals and scientists who use electronic distance measurement as a measuring tool. Great emphasis is placed on the understanding of measurement principles and on proper reduction and calibration procedures. It comprises an extensive collection of essential formulae, useful tables and numerous literature references. After a review of the history of EDM instruments in Chapter 1, some fundamental laws of physics and units relevant to EDM are revised in Chapter 2. Chapter 3 discusses the principles and applications of the pulse method, the phase difference method, the Doppler technique and includes an expanded section on interferometers. The basic working principles of electro-optical and microwave distance meters are presented in Chapter 4, with special emphasis on modulation/demodulation techniques and phase measurement systems. Important properties of infrared emitting and lasing diodes are discussed. Various aspects of the propagation of electromagnetic waves through the atmosphere are treated in Chapter 5, such as the range of EDM instruments, phase and group refractive indices, coefficient of refraction, measurement of temperature, pressure and humidity and different approaches to the problem of the determination of ambient refractive indices. Chapter 6 continues with the derivation of first velocity corrections for electro-optical and microwave distance meters and concludes with the second velocity correction and a review of more refined methods of velocity corrections. All equations for the geometrical reduction of electronic distance measurements to the spheroid (or to sea level) are derived in Chapter 7, both, for reductions using station elevations and for reductions using measured zenith angles. Numerical examples are given. Error analyses indicate critical parameters. Additional corrections and computations are discussed in Chapter 8. This chapter includes numerous supplementary reductions which are required in VII

6 certain cases as well as the computation of height differences from measured zenith angles for EDM tacheometry and EDM height traversing, the derivation of the coefficient of refraction and eyeto-object corrections for distances and zenith angles. A description of four typical distance meters is given in Chapter 9, together with a discussion of classification criteria and special features of modern electro-optical distance meters. Chapter 10 presents a number of different types of EDM reflectors and many important aspects of reflectors such as the reflector constant (and its computation) and the effect of misaligned reflectors on distance and angle measurements. Chapter 11 discusses the properties of NiCd rechargeable batteries. A review of other suitable power sources has been added. Chapter 12 gives a comprehensive introduction into major errors of electro-optical distance meters, including additive constant, short periodic errors, scale errors and non-linear distance-dependent errors. The different sources of these errors are indicated, where possible. A mathematical model covering most known error patterns is given. The last chapter provides the neccessary information on how errors can be determined by the user of a distance meter. Included in Chapter 13 is a large section on the calibration of distance meters on EDM baselines. The geometric design of three types of EDM baselines, the physical design, the measurement and analysis procedures and-the determination of the baseline lengths are discussed. Other sections describe the calibration procedures on cyclic error testlines and the measurement of the modulation frequency and discuss the accuracy specifications of distance meters. The appendices include an improved refractive index formula for high precision measurements as well as tables on saturation water vapour pressures (versus temperature), a standard atmosphere (temperature and pressure versus elevation), critical dimensions of reflectors, important data of electro-optical distance meters (for correction and calibration purposes) and technical data of a selection of short range distance meters, pulse distance meters and long range distance meters. The text uses SI units for all quantities but pressure. Pressures are stated in millibars (mb) rather than the equivalent unit hpa (hectopascal). However, common conversion rates to and from non-si units are given. Most equations are numbered for easier reference. The definitions of parameters of equations are repeated below the relevant final formulae in order to facilitate the use of the book as a compendium of formulae. The more important symbols are also included in the list of symbols at the beginning of the text. The writing of this third edition was suggested by F. K. Brunner. His continued encouragement and valuable advice was highly appreciated. The author is further indebted to F. K. Brunner, K. Furuya (Tokyo Optical Co. Ltd.), K. Giger (Wild Leitz Ltd.), VIII

7 R. Niinlist and P. Kiefer for their valuable comments on Sections 5.9, 9.2.2, 9.2.3, and , respectively, and to C. Rusu for the preparation of a number of diagrams. The book benefited greatly from the comments made by many readers with respect to the two earlier editions and from the assistance provided by colleagues in editing these earlier editions. The cooperation of manufacturers or their Australian agents with the collection of the technical data for the tables in the appendices is gratefully acknowledged as is the competent support by the staff of the Springer-Verlag. Sydney, Summer 1989/ M. RUEGER IX

8 Contents 1 History Physical Laws and Units Related to EDM.... Definitions.... Frequency Spectrum.... Velocity of Light in a Vacuum.... Units and Their Definitions.... Second of Time.... Metre.... Kelvin.... Other Units in EDM Principles and Applications of EDM... Pulse Method... Principle of the Pulse Method... Applications of the Pulse Method... Phase Difference Method... Phase Difference Between 1tansmitted and Received Signal... Phase Difference Between 1\vo Received Signals... Doppler Methods... Interferometry... Principle of a Michelson Interferometer... Principle of Operation of the HP5526A Laser Measurement System... ViiisiiHl Interference Comparator XI

9 Basic Working Principles of Electronic Distance Meters.... Electro-Optical Instruments.... Principle and Components.... Methods of Modulation and Demodulation of Light and NIR Waves.... Methods of Phase Measurement.... Microwave Instruments.... Introduction.... Working Principle and Components.... Effects of Reflections in Microwave EDM (Multipath) XII Propagation of Electromagnetic Waves Through the Atmosphere.... Atmospheric Transmittance.... Range of EDM Instruments.... Phase Refractive Index.... Group Refractive Index of Light and NIR Waves for Standard Conditions.... First Example.... Second Example.... Third Example.... Error Analysis.... Group Refractive Index of Light and NIR Waves at Ambient Conditions.... Error Analysis.... Omission of Humidity.... Refractive Index of Microwaves.... Error Propagation.... Coefficient of Refraction.... Measurement of Atmospheric Parameters.... Measurement of Atmospheric Pressure.... Measurement of Atmospheric Thmperature.... Measurement of Atmospheric Humidity.... Computation of Partial Water Vapour Pressure from Psychrometer Measurements.... Computation of Partial Water Vapour Pressure from Relative Humidity.... Determination of the Refractive Index.... Normal Procedures

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