J. M. Riieger

Electronic DistanceMeasurementAn Introduction

Fourth Edition

With 56 Figures and 18 Tables

Springer

Contents

History 1

2 Physical Laws and Units Related to EDM 3

2.1 Definitions 32.2 Frequency Spectrum 52.3 Velocity of Light in a Vacuum 62.4 Units and Their Definitions 82.4.1 Second of Time 82.4.2 Metre 82.4.3 Kelvin 92.4.4 Other Units yi EDM 9

3 Principles and Applications of EDM 11

3.1 Pulse Method 113.1.1 Principle of the Pulse Method 113.1.2 Applications of the Pulse Method 123.2 Phase Difference Method 143.2.1 Phase Difference Between Transmitted and Receiv-

ed Signal 143.2.2 Phase Difference Between Two Received Signals . . . 213.3 Doppler Methods 233.4 Interferometry 263.4.1 Principle of a Michelson Interferometer 263.4.2 Principle of Operation of the HP 5526A Laser

Measurement System 273.4.3 Vaisala Interference Comparator 29

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4 Basic Working Principles of Electronic DistanceMeters 31

4.1 Electro-Optical Instruments 314.1.1 Principle and Components 314.1.2 Methods of Modulation and Demodulation of

Light and NIR Waves 344.1.3 Methods of Phase Measurement 414.2 Microwave Instruments 444.2.1 Introduction 444.2.2 Working Principle and Components 444.2.3 Effects of Reflections in Microwave EDM

(Multipath) 46

5 Propagation of Electromagnetic Waves Throughthe Atmosphere 48

5.1 Atmospheric Transmittance 485.2 Range of EDM Instruments 495.3 Phase Refractive Index 515.4 Group Refractive Index of Light and NIR Waves

for Standard Conditions 515.4.1 First Example 535.4.2 Second Example 535.4.3 Third Example 545.4.4 Error Analysis 545.5 Group Refractive Index of Light and NIR Waves at

Ambient Conditions 545.5.1 Error Analysis 555.5.2 Omission of Humidity 565.6 Refractive Index of Microwaves 565.6.1 Error Propagation 575.7 Coefficient of Refraction 585.8 Measurement of Atmospheric Parameters 605.8.1 Measurement of Atmospheric Pressure 605.8.2 Measurement of Atmospheric Temperature 615.8.3 Measurement of Atmospheric Humidity 625.8.4 Computation of Partial Water Vapour Pressure

from Psychrometer Measurements 635.8.5 Computation of Partial Water Vapour Pressure

from Relative Humidity 655.9 Determination of the Refractive Index 665.9.1 Normal Procedures 66

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5.9.2 Limitations of Normal Procedures 675.9.3 Special Procedures 69

6 Velocity Corrections to Measured Distances 73

6.1 Reference Refractive Index 736.2 First Velocity Correction 746.2.1 Derivation of First Velocity Correction for the

Infrared Distance Meter Kern DM501 766.2.2 Derivation of First Velocity Correction for the

Infrared Distance Meter Pentax PM-81 766.2.3 Derivation of First Velocity Correction for the

Pulse Distance Meter Distomat Wild DI3000 776.2.4 Derivation of First Velocity Correction for the

Microwave Distance Meter Siemens-Albis SIALMD60 78

6.2.5 Derivation of First Velocity Correction for theMicrowave Distance Meter Tellurometer CA1000 . . 78

6.3 Real-Time Application of First Velocity Correctionby EDM Instrument 79

6.4 Second Velocity Correction 806.5 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 . . 847.1.1 First Method: Step-by-Step Solution 877.1.2 Second Method: Closed Solution 1 917.1.3 Analysis of Errors 927.2 Reduction to the Spheroid, Using Measured Zenith

Angles 937.2.1 Introduction 937.2.2 Reduction to the Spheroid: Closed S o l u t i o n . . . . . . . 957.2.3 Reduction to the Spheroid: Step-by-Step Solution . . 967.2.4 Analysis of Errors 99

8 Miscellaneous Corrections, Computations andNumerical Examples 101

8.1 Correction of Measured Distance to Zenith AngleRay Path 101

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

8.1.2 Correction for Theodolite-Mounted EDMInstruments 103

8.1.3 Correction for Telescope-Mounted EDMInstruments 104

8.2 Eye-to-Object Corrections for Zenith Angles andDistances 105

8.2.1 Eye-to-Object Correction for Zenith Angles 1058.2.2 Eye-to-Object Correction for Distances 1068.2.3 Numerical Example 1078.3 Height Difference from Measured Zenith Angle(s)

and Slope Distance 1088.3.1 Single Zenith Angle Measurement 1088.3.2 Reciprocal Zenith Angle Measurements 1108.4 Determination of the Coefficient of Refraction

from Reciprocal Zenith Angle Measurements I l l8.4.1 Derivation of the Equation for the Coefficient of

Refraction I l l8.4.2 Error Analysis 1138.5 Reduction to Centre of Distances 1148.5.1 Angles and Distances Measured at Satellite Station 1148.5.2 Angles Measured at Centre Station, Distances at

Satellite Station 116

8.6 Numerical Examples 1178.6.1 Reduction of a Long Distance 1178.6.2 Reduction of a Short Distance 120

9 Electro-Optical Distance Meters 123

9.1 Classification of Electro-Optical Distance Meters . . 1239.1.1 Classification According to Range 1239.1.2 Classification According to Accuracy 1249.1.3 Classification According to the Degree of

Integration with Theodolites 1249.1.4 Special Features of Modern Short Range Distance

Meters 1289.2 Design of Some Electro-Optical Distance Meters . . 1359.2.1 Kern DM500 1359.2.2 Topcon ET-1 1399.2.3 Distomat Wild DI3000 1419.2.4 Kern Mekometer ME5000 145

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10 Reflectors 148

10.1 Introduction 14810.2 Glass Prism Reflectors 15010.2.1 Accuracy of Reflectors 15210.2.2 Shape and Size of Reflectors 15310.2.3 Phase and Group Refractive Index in Glass 15510.2.4 Reflector Constant 15610.2.5 Effects of Errors of Reflector Alignment 15810.2.6 Temperature Effects 16310.2.7 Care of Reflectors 164

11 Batteries and Other Power Sources 165

11.1 Review of Power Sources 16511.2 Batteries Used in EDM 16711.2.1 Primary Batteries 16711.2.2 Secondary Batteries 16711.3 Sealed Nickel-Cadmium Batteries 16811.3.1 Construction and Principle 16811.3.2 Discharge Characteristics 17011.3.3 Charge Characteristics 17111.3.4 Capacity and Life of Battery 172

12 Errors of Electro-Optical Distance Meters 174

12.1 Additive Constant 17412.2 Short Periodic Errors '*; 17512.2.1 Electrical or Optical Crosstalk Errors 17512.2.2 Analogue Phase Measurement Errors 17712.2.3 Multipath Errors 17812.2.4 Experimental Results 17812.2.5 Reduction of Short Periodic Errors 179

12.3 Scale Errors / . . . 17912.3.1 Oscillator Errors 17912.3.2 Diode Errors 18112.4 Non-Linear Distance-Dependent Errors 18112.5 Summary and Mathematical Model of Errors 183

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13 Calibration of Electro-Optical Distance Meters 186

13.1 Introduction 18613.1.1 Reasons for Calibration 18613.1.2 Concept of Calibration 18713.2 Calibration on EDM Baselines 18913.2.1 Geometric Design of EDM Baselines 18913.2.2 Physical Design 19513.2.3 Measurements on EDM Baselines 19713.2.4 Analysis of Baseline Measurements 19913.2.5 Determination of Baseline Lengths 20713.3 Calibration on Cyclic Error Testlines 20813.3.1 Design of and Measurements on Cyclic Error

Testlines 20913.3.2 Semi-Graphic Determination of Short Periodic Errors 21113.3.3 Analytical Determination of Short Periodic Errors . 21313.4 Calibration of Modulation Frequency 21713.4.1 Frequency Measuring Techniques 21713.4.2 Calibration of Ageing and Warm-Up Effects 21813.4.3 Frequency Versus Temperature Characteristic 220

13.5 Accuracy Specifications of EDM Instruments 220

Appendices 222

A. First Velocity Correction for Precise Electro-OpticalDistance Measurement 222

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

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

E. Technical Data of a Selection of Short RangeDistance Meters 241

F. Technical Data of a Selection of Pulse Distance• Meters 251

G. Technical Data of a Selection of Long RangeDistance Meters 255

H. Critical Dimensions of a Selection of Reflectors . . . 257

References 259

Subject Index 269

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