1. M. Rueger

Electronic Distance Measurement An Introduction

Third Totally Revised Edition

With 56 Figures

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong

Dr. J. M. ROEGER

School of Surveying University of New South Wales P.O. Box 1 Kensington NSW 2033 Australia

ISBN-13: 978-3-540-51523-4 DOl: 10.1007/978-3-642-97196-9

e-ISBN-13: 978-3-642-97196-9

Library of Congress Cataloging-in-Publication Data. Rueger, Jean M., 1944- Electronic dis­tance measurement: an introduction 1 Jean M. Rueger. p. cm. Includes bibliographical references. ISBN-13: 978-3-540-51523-4 1. Geodesy - Instruments. 2. Distances - Measurement. I. Title. QB328.A1R84 1989 526'.028 - dc20 89-21691

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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplica­tion of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 1990

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.

lYPesetting: K + V Fotosatz GmbH, Beerfelden

2132/3145-543210 - Printed on acid-free paper

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

V

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 modem 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.),

VI

R. Niinlist and P. Kiefer for their valuable comments on Sections 5.9, 9.2.2, 9.2.3, 9.2.1 and 10.2.5.2, 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 1.M. RUEGER

VII

Contents

1

2

2.1 2.2 2.3 2.4 2.4.1 2.4.2 2.4.3 2.4.4

3

3.1 3.1.1 3.1.2 3.2 3.2.1

3.2.2 3.3 3.4 3.4.1 3.4.2

3.4.3

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 Transmitted and Receiv-ed Signal ..................................... Phase Difference Between lWo Received Signals ... Doppler Methods .............................. Interferometry ................................. Principle of a Michelson Interferometer .......... Principle of Operation of the HP 5526A Laser Measurement System ........................... Vaisala Interference Comparator .................

1

3

3 5 6 8 8 8 9 9

11

11 11 12 14

14 21 23 26 26

27 29

IX

4

4.1

4.1.1 4.1.2

4.1.3 4.2

4.2.1 4.2.2 4.2.3

5

5.1 5.2 5.3 5.4

5.4.1 5.4.2 5.4.3 5.4.4 5.5

5.5.1 5.5.2 5.6 5.6.1 5.7 5.8 5.8.1 5.8.2 5.8.3 5.8.4

5.8.5

5.9

5.9.1

x

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) .................................. .

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 Temperature ....... . 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 ........................... .

31

31 31

34 41 44

44 44

46

48

48 49 51

51 53 53 54 54

54 55 56 56 57 58 60 60 61 62

63

65 66 66

5.9.2 Limitations of Normal Procedures. . . . . . . . . . . . . . . 67 5.9.3 Special Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6 Velocity Corrections to Measured Distances ....... 73

6.1 Reference Refractive Index ...................... 73 6.2 First Velocity Correction ........................ 74 6.2.1 Derivation of First Velocity Correction for the

Infrared Distance Meter Kern DM 501 ............ 76 6.2.2 Derivation of First Velocity Correction for the

Infrared Distance Meter Pentax PM-81 ........... 76 6.2.3 Derivation of First Velocity Correction for the

Pulse Distance Meter Distomat Wild DI3000 ...... 77 6.2.4 Derivation of First Velocity Correction for the

Microwave Distance Meter Siemens-Albis SIAL MD60 ....................................... 78

6.2.5 Derivation of First Velocity Correction for the Microwave Distance Meter Tellurometer CA 1000 .. 78

6.3 Real-Time Application of First Velocity Correction by EDM Instrument ........................... 79

6.4 Second Velocity Correction ..................... 80 6.5 Refined Method of Reduction of Measured Dis-

tance to Wave Path Chord ...................... 82

7 Geometrical Corrections . ....................... 84

7.1 Reduction to the Spheroid Using Station Heights .. 84 7.1.1 First Method: Step-by-Step Solution ............. 87 7.1.2 Second Method: Closed Solution ................ 91 7.1.3 Analysis of Errors ............................. 92 7.2 Reduction to the Spheroid, Using Measured Zenith

Angles ....................................... 93 7.2.1 Introduction .................................. 93 7.2.2 Reduction to the Spheroid: Closed Solution ....... 95 7.2.3 Reduction to the Spheroid: Step-by-Step Solution .. 96 7.2.4 Analysis of Errors ............................. 99

8 Miscellaneous Corrections, Computations and Numerical Examples. . . . .. . . . . . . . . . . . . . . . . . . .. . 101

8.1 Correction of Measured Distance to Zenith Angle Ray Path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

XI

8.1.1 Correction for Unequal Heights of Theodolite, EDM Instrument, Thrget and Reflector ........... 101

8.1.2 Correction for Theodolite-Mounted EDM Instruments ................................... 103

8.1.3 Correction for Telescope-Mounted EDM Instruments ................................... 104

8.2 Eye-to-Object Corrections for Zenith Angles and Distances ..................................... 105

8.2.1 Eye-to-Object Correction for Zenith Angles ....... 105 8.2.2 Eye-to-Object Correction for Distances ........... 106 8.2.3 Numerical Example ............................ 107 8.3 Height Difference from Measured Zenith Angle(s)

and Slope Distance ............................ 108 8.3.1 Single Zenith Angle Measurement ............... 108 8.3.2 Reciprocal Zenith Angle Measurements ........... 110 8.4 Determination of the Coefficient of Refraction

from Reciprocal Zenith Angle Measurements ...... 111 8.4.1 Derivation of the Equation for the Coefficient of

Refraction .................................... 111 8.4.2 Error Analysis ................................ 113 8.5 Reduction to Centre of Distances ................ 114 8.5.1 Angles and Distances Measured at Satellite Station 114 8.5.2 Angles Measured at Centre Station, Distances at

Satellite Station ............................... 116 8.6 Numerical Examples ........................... 117 8.6.1 Reduction of a Long Distance ................... 117 8.6.2 Reduction of a Short Distance .................. 120

9 Electro-Optical Distance Meters ... . . . . . . . . . . . . . . 123

9.1 Classification of Electro-Optical Distance Meters. . 123 9.1.1 Classification According to Range. . . . . . . . . . . . . . . 123 9.1.2 Classification According to Accuracy. . . . .. . . . . . . . 124 9.1.3 Classification According to the Degree of

Integration with Theodolites .................... 124 9.1.4 Special Features of Modern Short Range Distance

Meters. ....... . .. ........ ..... . . ......... . ... 128 9.2 Design of Some Electro-Optical Distance Meters .. 135 9.2.1 Kern DM500.................................. 135 9.2.2 Topcon ET-1 .................................. 139 9.2.3 Distomat Wild 013000. ..... . ... . . .. . . . ... . .... 141 9.2.4 Kern Mekometer ME5000 ...................... 145

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10 Reflectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

10.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 10.2 Glass Prism Reflectors. . . . . . . . . . . . . . . . . . . . . . . . . 150 10.2.1 Accuracy of Reflectors ......................... 152 10.2.2 Shape and Size of Reflectors. . . . . . . . . . . . . . . . . . . . 153 10.2.3 Phase and Group Refractive Index in Glass. . . . . . . 155 10.2.4 Reflector Constant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 10.2.5 Effects of Errors of Reflector Alignment. . . . . . . . . 158 10.2.6 Temperature Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 10.2.7 Care of Reflectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

11 Batteries and Other Power Sources. . . . . . . . . . . . . . . 165

11.1 Review of Power Sources ... . . . . . . . . . . . . . . . . . . . . 165 11.2 Batteries Used in EDM......................... 167 11.2.1 Primary Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 11.2.2 Secondary Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 11.3 Sealed Nickel-Cadmium Batteries. . . . . . . . . . . . . . . . 168 11.3.1 Construction and Principle. . . . . . . . . . . . . . . . . . . . . 168 11.3.2 Discharge Characteristics ....................... 170 11.3.3 Charge Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . 171 11.3.4 Capacity and Life of Battery. . . . . . . . . . . . . . . . . . . . 172

12 Errors of Electro-Optical Distance Meters ........ 174

12.1 Additive Constant.. ....... . . ....... ...... ..... 174 12.2 Short Periodic Errors .......................... 175 12.2.1 Electrical or Optical Crosstalk Errors............ 175 12.2.2 Analogue Phase Measurement Errors ............ 177 12.2.3 Multipath Errors .............................. 178 12.2.4 Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 178 12.2.5 Reduction of Short Periodic Errors .. . . . . . . . . . . . . 179 12.3 Scale Errors .................................. 179 12.3.1 Oscillator Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 12.3.2 Diode Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 12.4 Non-Linear Distance-Dependent Errors. . . . . . . . . . . 181 12.5 Summary and Mathematical Model of Errors. . . . . 183

XIII

13 Calibration of Electro-Optical Distance Meters .... 186

13.1 Introduction .................................. 186

13.1.1 Reasons for Calibration ........................ 186 13.1.2 Concept of Calibration ......................... 187

13.2 Calibration on EDM Baselines .................. 189

13.2.1 Geometric Design of EDM Baselines ............. 189 i3.2.2 Physical Design ............................... 195 13.2.3 Measurements on EDM Baselines ................ 197 13.2.4 Analysis of Baseline Measurements .............. 199 13.2.5 Determination of Baseline Lengths ............... 207

13.3 Calibration on Cyclic Error Testlines ............. 208 13.3.1 Design of and Measurements on Cyclic Error

Testlines ...................................... 209 13.3.2 Semi-Graphic Determination of Short Periodic Errors 211 13.3.3 Analytical Determination of Short Periodic Errors. 213

13.4 Calibration of Modulation Frequency ............ 217

13.4.1 Frequency Measuring Techniques ................ 217 13.4.2 Calibration of Ageing and Warm-Up Effects ...... 218 13.4.3 Frequency Versus Temperature Characteristic ...... 220

13.5 Accuracy Specifications of EDM Instruments ..... 220

Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 222

A. First Velocity Correction for Precise Electro-Optical Distance Measurement ......................... 222

B. Tables of Saturation Water Vapour Pressures . . . . . . 225 C. Parameters of the ICAO Standard Atmosphere. . .. 230 D. Data of a Selection of Electro-Optical Distance

Meters as Required for the Derivation of the First Velocity Correction and for Calibration Purposes .. 232

E. Technical Data of a Selection of Short Range Distance Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

F. Technical Data of a Selection of Pulse Distance Meters......... . . ... ....... .................. 244

G. Technical Data of a Selection of Long Range Distance Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

H. Critical Dimensions of a Selection of Reflectors . . . 248

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

XIV

List of Symbols

A = amplitude or maximum strength of electromagnetic signal A = baseline design parameter (Sect. 13.2) A = parameter of precision formula Ajj = coefficients of instrument correction B = baseline design parameter (Sect. 13.2) B = parameter of precision formula C = baseline design parameter (Sect. 13.2) C = parameter of first velocity correction CE = short periodic (cyclic) error D = baseline design parameter (Sect. 13.2) D = parameter by first velocity correction Ds = density factor of dry air (Appendix A) Dw = density factor of water vapour (Appendix A) Ew = saturation water vapour pressure at "wet bulb" temperature over water EicE = saturation water vapour at "wet bulb" temperature over ice Ew = saturation water vapour pressure at "dry bulb" temperature over water Hj = spheroidal height of "i"th station dH ~ height difference = H2 - HI HM = mean height = 0.5 (HI + H~ I = electric current IC = instrument correction Ilh = threshold current (Sect. 4.1.2.1) 1 = radiant intensity at distance d 10 = radiant intensity at emitter K' = first velocity correction K" = second velocity correction KI = first arc-to-chord correction (d l to d~ K2 = slope correction (d2 to dJ K3 = sea level correction (d6 to d3)

K4 = second chord-to-arc correction (d3 to d4)

K23 = chord-to-chord correction (d2 to d3)

Ks = slope correction (d2 to ds) K6 = sea level correction (ds to d3)

L = fraction of unit length U N = refractivity N = number of baseline stations (Sect. 13.2) Po = radiant power output Ps = partial pressure of dry air (Appendix A) P w = partial water vapour pressure (Appendix A) Q = cofactor R = mean radius of curvature of spheroid along a line RM = mean radius of curvature of spheroid for a specific area Rj = range of distance meter Ro = range of distance meter Ry = range of distance meter to y prisms S = grid distance (Sect. 8.6.2) T = atmospheric transmittance

xv

T = thermodynamic temperature U = unit length of an EDM instrument a = height of cube corner above front face of prism b = distance between front face and vertical/horizontal axis of prism c = phase velocity of light in a medium c = additive constant (Sect. 13.2) cy = cyclic error correction (Sect. 13.3) cg = group velocity of light in a medium Co = velocity of light in a vacuum d = measured distance, including first velocity correction do = slope distance between ground marks d' = measured distance (displayed on instrument) d1 = wave path length ( = d' + K' + K") d2 = wave path chord d3 = spheroidal chord d4 = spheroidal distance ds = horizontal distance at height of EDM instrument station d6 = d2 +K2 d* = distance between satellite stations dv = meteorological range, visibility range dTH = distance along zenith angle ray dEDM = wave path chord (dz) (Sect. 8.1.1) e = partial water vapour pressure e = eccentricity of satellite station (Sect. 8.5) e = eccentricity of EDM instrument (Sects. 9.1.3.4, 9.1.3.5) f = frequency of signal f D = Doppler frequency fnom = nominal modulation frequency fact = actual (measured) modulation frequency h = relative humidity (Sects. 5.5, 5.8.4) hEDM = height of trunnion axis of EDM instrument above survey mark hR = height of reflector above survey mark hTH = height of trunnion axis of theodolite above survey mark hT = height of target above survey mark k = coefficient of refraction ki = ambiguity increments (Sect. 3.2.1.4) ko = central scale factor (Sect. 8.6) kL = coefficient of refraction of light waves kM = coefficient of refraction of microwaves Ii = normalized phase measurement m = ambiguities n = phase refractive index of a medium n = number of observations (Chap. 13) nA = group refractive index of light and IR waves in air no= group refractive index of light and IR waves in glass nOph = phase refractive index of light and infrared waves in glass nL = group refractive index of light waves for ambient atmospheric condi-

tions nM = refractive index of microwaves for ambient atmospheric conditions nREF = reference refractive index of a specific EDM instrument ng = group refractive index of atmosphere for standard conditions p = atmospheric pressure r = radius of curvature of wave path s = chord distance (Sect. 6.5)

= standard deviation (Chap. 13) s* = reduced cyclic error testline data

= time (Sect. 2)

XVI

t* = period of sinusoidal signal At = time lead of electromagnetic signal .M = time interval (Sect. 3.3) At' = flight time of a signal between transmitter and receiver t = "dry bulb" temperature t' = "wet bulb" temperature u = number of unknowns (Chap. 13) v = speed v = residual (Chap. 13) y = sinusoidal signal Zj = measured zenith angle at station Pi Zjj = zenith angle at station Pi to Pj z = attenuation or extinction coefficient (Sect. 5.1) zo = zenith angle between ground marks Q = eye-to-object correction for zenith angle <I> = phase angle of electromagnetic signal <I>B = diameter of return beam <I>p = diameter of aperture of reflector <I>T = diameter of transmitter optics A<I> = phase lead of electromagnetic signal A<I> = measured phase difference (Sect. 3.22) fl = coefficient of expansion of air (= 0.003661) (Sect. 5.5) fl = azimuth of the measured line, clockwise through 3600 from true north

(Sect. 7.1) fl = vertical angle (Sect. 8.3.1) fl = horizontal angle (Sect. 8.5) measured at centre station fl* = horizontal angle measured at satellite station (Sect. 8.5) flA = angle of incidence flO = angle of refraction f3 = angle of refraction (Sect. 10.2.5.2) f3 = angle between the wave path normals through the terminals of a line o = refraction angle o <I> = periodic error o () = differential Ei = deviation of vertical at station Pi ~ = spheroidal zenith angle at station Pi v = angle (Sect. 8.3.1) A. = wavelength v = radius of curvature of the spheroid in the prime vertical Q = radius of curvature of the spheroid in the meridian cr = vacuum wave number (Appendix A) cr = standard deviation (Sect. 8.3.2, 8.4.2) (J = optical length (Sect. 6.5) \jI = phase lead of contaminated signal (Sect. 12.2.1) (0 = angular velocity

XVII