Electronic Distance Measurement: An Introduction

291 Pages·1996·36.889 MB·English

by  Jean M. Rüeger

Springer
Berlin
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Singapore
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J. M. RUeger
Electronic Distance
Measurement
An Introduction
Fourth Edition
With 56 Figures and 18 Tables
Springer
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.). 1944-
Electronic distance measurement : an introduction / J.M. Rueger. -
- 4th ed.
p. cm.
Includes bibliographical references and index.
1. Geodesy--Instruments. 2. Distances--Measurement. I. Title.
CB328.A1R84 1996
526'.028--dc20 96-16952
CIP
ISBN-13: 978-3-540-61159-2 e-ISBN-13: 978-3-642-80233-1
001: 10.1007/978-3-642-80233-1
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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 2.4.3 on
the introduction of the new temperature scale in 1990. 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 pro
vided by most manufacturers (or their agents) with the updating of
the tables with the instrument data was greatly appreciated.
Sydney, February 1996 1.M. RUEGER
v
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, Universi
ty 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 Survey
ing and related fields. At the same time, it is a comprehensive refer
ence 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 measure
ment principles and on proper reduction and calibration pro
cedures. 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 applica
tions 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 modu
lation/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 dis
tance 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 dis
tance 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 correc
tions and computations are discussed in Chapter 8. This chapter in
cludes numerous supplementary reductions which are required in
VII
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 eye
to-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 er
rors. The different sources of these errors are indicated, where possi
ble. 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 pro
cedures 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 (tem
perature and pressure versus elevation), critical dimensions of reflec
tors, important data of electro-optical distance meters (for correc
tion 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 (hec
topascal). 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 ap
preciated. The author is further indebted to F. K. Brunner, K.
Furuya (Tokyo Optical Co. Ltd.), K. Giger (Wild Leitz Ltd.),
VIII
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 great
ly 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 1989/1990 1.M. RUEGER
IX
Contents
1 History ...................................... . 1
2 Physical Laws and Units Related to EDM ....... . 3
2.1 Definitions .................................. . 3
2.2 Frequency Spectrum .......................... . 5
2.3 Velocity of Light in a Vacuum ................. . 6
2.4 Units and Their Definitions .................... . 8
2.4.1 Second of Time .............................. . 8
2.4.2 Metre ....................................... . 8
2.4.3 Kelvin ....................................... . 9
2.4.4 Other Units in EDM .......................... . 9
3 Principles and Applications of EDM ............. 11
3.1 Pulse Method ................................. 11
3.1.1 Principle of the Pulse Method .................. 11
3.1.2 Applications of the Pulse Method ............... 12
3.2 Phase Difference Method ....................... 14
3.2.1 Phase Difference Between 1tansmitted and Receiv-
ed Signal ..................................... 14
3.2.2 Phase Difference Between 1\vo Received Signals ... 21
3.3 Doppler Methods .............................. 23
3.4 Interferometry ................................. 26
3.4.1 Principle of a Michelson Interferometer .......... 26
3.4.2 Principle of Operation of the HP5526A Laser
Measurement System ........................... 27
3.4.3 ViiisiiHl Interference Comparator ................. 29
XI
4 Basic Working Principles of Electronic Distance
Meters ...................................... . 31
4.1 Electro-Optical Instruments .................... . 31
4.1.1 Principle and Components ..................... . 31
4.1.2 Methods of Modulation and Demodulation of
Light and NIR Waves ......................... . 34
4.1.3 Methods of Phase Measurement ................ . 41
4.2 Microwave Instruments ........................ . 44
4.2.1 Introduction ................................. . 44
4.2.2 Working Principle and Components ............. . 44
4.2.3 Effects of Reflections in Microwave EDM
(Multipath) .................................. . 46
5 Propagation of Electromagnetic Waves Through
the Atmosphere .............................. . 48
5.1 Atmospheric Transmittance .................... . 48
5.2 Range of EDM Instruments .................... . 49
5.3 Phase Refractive Index ........................ . 51
5.4 Group Refractive Index of Light and NIR Waves
for Standard Conditions ....................... . 51
5.4.1 First Example ................................ . 53
5.4.2 Second Example .............................. . 53
5.4.3 Third Example ............................... . 54
5.4.4 Error Analysis ............................... . 54
5.5 Group Refractive Index of Light and NIR Waves at
Ambient Conditions .......................... . 54
5.5.1 Error Analysis ............................... . 55
5.5.2 Omission of Humidity ........................ . 56
5.6 Refractive Index of Microwaves ................. . 56
5.6.1 Error Propagation ............................ . 57
5.7 Coefficient of Refraction ...................... . 58
5.8 Measurement of Atmospheric Parameters ........ . 60
5.8.1 Measurement of Atmospheric Pressure .......... . 60
5.8.2 Measurement of Atmospheric Thmperature ....... . 61
5.8.3 Measurement of Atmospheric Humidity ......... . 62
5.8.4 Computation of Partial Water Vapour Pressure
from Psychrometer Measurements .............. . 63
5.8.5 Computation of Partial Water Vapour Pressure
from Relative Humidity ....................... . 65
5.9 Determination of the Refractive Index ........... . 66
5.9.1 Normal Procedures ........................... . 66
XII
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 DI 3000 ...... 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 Thllurometer 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
XIII