1. Module 9: Application of Electromagnetic (EM) Waves
Chapter 5
Chapter 5: Accuracy Analysis
And Evaluation of Distance
Measurement System
Precision Surveying/Chapter 5

2. Chapter 5: Accuracy Analysis of Distance Measurements
Module Objective
Be able to do the following:
Describe the general properties of Electromagnetic (EM) waves, including the spectrum
Discuss the Precision Surveying/Chapter 5 to EDM including the basic principles of EDM measurement
Perform computations related to EM wave propagation
Apply velocity corrections to EDM measurements
Analyze the accuracy of distance measurements, including sources of errors and the appropriate error budgets
Formulate error propagation for distance measurement
Evaluate geodetic EDM under field conditions (instrumental and scale errors)
Precision Surveying/Chapter

3. Introduction: Properties of Waves
Accuracy analysis and evaluation of distance measurement system is based on electromagnetic distance measurement (EDM) system
To analyze and evaluate EDM distances, general properties of waves must be understood:
A wave is a disturbance in a medium that transfers energy from one place to another. The medium itself is not transported during the process (only the disturbance)
A wave transports energy and momentum from a source through vibrations (with or without the help of a medium)
Waves continue to travel after the source is turned off
Waves can pass through one another; after passing through, they continue on their ways
When two waves overlap, the total wave is just the sum of the two waves
Precision Surveying/Chapter

4. Types of Waves There are 2 types of waves: Transverse and Longitudinal
Transverse waves – direction of waves is perpendicular to the direction of vibrations, e.g., electromagnetic waves or EM waves
Longitudinal waves – direction of waves correspond with the direction of vibrations, e.g., sound waves
We are interested in Electromagnetic (or EM) waves
Example of waves: familiar water waves illustrated in Fig. 5.1
A water (rock) drop into a lake produces waves that propagate on the surface of the water
The line joining all the crests of the wave is the wavefront
Water wave, however is a combined transverse and longitudinal waves
Different characteristics of wave propagation are shown in fig. 5.2
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5. Familiar Circular Water Waves
Fig. 5.1
 is the wavelength
Velocity of propagation
A is the amplitude of wave
Trough
Low (energy) frequency
Waves follow sine function with the
highest points as crests and the
lowest points as troughs
High (energy) frequency
Fig. 5.2
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6. Parameters Describing EM Waves
Frequency (f) and the wavelength of waves are related
by the velocity of waves (c) in a vacuum:
(5.1)
Frequency (f) is the number of times the particle of the medium at a spot moves up and back to equilibrium (likened to color or energy level)
Velocity (c) of wave which is constant and equivalent to that of light (velocity of light in a vacuum is 299,792,458 m/s ± 1.2 m/s)
Amplitude is the maximum displacement from equilibrium that any point in the medium makes as the wave goes by (how bright or intense the wave or its source is, or how much potential energy it transports); does not depend on f, v, ; it depends only on how much energy is input
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7. Electric and Magnetic Properties of EM Waves
Under certain circumstances, the electric (E) and magnetic (B) fields travel through space in so-called EM waves E B
Propagation direction
Fig. 5.3
Electric (E) and magnetic (B) components of an EM wave are perpendicular to each other and also perpendicular to the direction in which the wave is traveling as shown in Fig. 5.3
EM waves travel through space independent of the source charges,
generating and regenerating itself as it moves away from the source
Precision Surveying/Chapter

8. Electromagnetic (EM) Spectrum
EM spectrum is the classification of energies in a chart
according to their wavelengths with each class given a
descriptive name
The sample of the EM spectrum is given in the following
chart
blue
green
red
VISIBLE
10-6
10-5
10-4
10-3
10-2
10-1 1 10
102
103
104
105
106
107
108
109
(1mm)
(1m)
Wavelength (m)
0.4
0.5
0.6
0.7 UV
INFRARED
RADIO
MICROWAVES
The sun is able to radiate a wide range of wavelengths of EM energy
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9. Module 8: Electromagnetic (EM) Wave Propagation
Important Units
Units for Frequency, f
1 Hertz (Hz) – no. of wavelengths per second
1 Kilohertz (kHz) = 1x103 Hz
1 Megahertz (MHz) = 1x106 Hz
1 Gigahertz (GHz) = 1x109 Hz
1 Terahertz (THz) = 1 x 1012 Hz
Units for Time, T
1 millisecond (ms) = 1x10-3 s
1 microsecond (s) = 1x10-6 s
1 nanosecond (ns) = 1x10-9 s
1 picoseconds (ps) = 1x10-12 s
Unit for Pressure, p
1 millibar (mb) = mmHg
mb = 760 mmHg (Standard Pressure)
Precision Surveying/Chapter

10. Modulation of EM Waves
Modulation – a process in which modulating signal is encoded on carrier wave to produce modulated signal
Carrier wave – EM wave (at higher frequencies) capable of carrying data (like a fiber material of a measuring tape – an invisible tape)
Modulating signal – data carried by carrier wave (graduations or units of length on a measuring tape)
Modulated signal – final signal with properties matching the medium in which it is traveling in
Modulation occurs by changing amplitude, frequency or phase of carrier waves – amplitude modulation, etc.
Instruments using infrared and visible-spectrum as carriers – employ amplitude (or intensity modulation)
Microwave instruments – use direct frequency modulation
Long radio wave instruments – use no modulation at all
EDM instruments are called by their carrier waves
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11. Application of EM Waves to EDM
EM waves are used in electromagnetic distance measurement (EDM) instruments.
Two main types of EDM are in common use:
Electromagnetic (Microwave) EDMs using microwave part of the spectrum
Electro-optical (Light Wave) EDMs using visible part of the spectrum
The EDM incorporated to the modern Total Station instruments is commonly of electro-optical type
Basic principles of measurement used in the two main types of EDMs are:
Time (Pulse or time-of-flight) measurement
Phase (Continuous wave) measurement
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12. EDM Pulse Measurement Principle
(5.2)
Measured distance, d, can be expressed as:
Where:
v is the speed of the electromagnetic wave;
T is the time from the start pulse to the return pulse (measured in EDM);
The speed of EM energy (v) can be expressed in terms of the speed of
of electromagnetic wave in the vacuum (c):
(5.3)
Where n is the index of refraction of the atmosphere (varying between
and ) – mainly a function of temperature and pressure
Using Equations (5.2) and (5.3), the EDM distance by pulse measurement
becomes:
(5.4)
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13. Other Applications of the Pulse Method
In pulse method, a short and intensive signal is transmitted by an instrument
Pulse technique is widely used in geodesy and in other applications
Electro-optical applications include
Lunar Laser Ranging (LLR)
Satellite Laser Ranging and Tracking (SLRT)
Microwave and radio waves applications include
Radio Detection And Ranging (RADAR)
Satellite Radar Altimeter
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14. EDM Phase Difference Measurement Principle
EDM phase difference measurement principle is based on measuring phases of a wave as the level of energy from 0 to 2π (in radian)
It can be used to describe the position of a point in a wave relative to another wave
EDM phase measurement principle is illustrated in Fig. 5.5
In the figure, the total 2-way distance (D) traveled by a measuring wave (with unit length λ/2) can be generalized as
(5.5)
where M = number of complete wavelengths () over the 2-way
measuring path (integer ambiguity)
 = the wavelength of the EDM signal
is the phase delay as a fraction of wavelength
(measured in the EDM with Δ in radians)
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15. Phase Difference Measurement in EDM
EDM phase measurement principle can be explained with the continuous
wave diagram below:
Forward Signal      
Back Signal
Figure 5.5
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16. Derived Distance and Ambiguity Resolution
The one-way distance (d) between the transmitter and the receiver can be
deduced from Equation (5.5) by dividing by 2:
(5.6)
Equation (5.6) can be re-written as
(5.7)
where d is the one-way distance to be determined,
U = λ/2 is the unit length of EDM, and
The unknowns in the Equation (5.7) are the d (which is constant for a length) and the integer ambiguity M (which varies depending on the unit length of instrument used)
The value of M is determined in the EDM as the EDM successively sends out (and receives back) signals at different frequencies
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17. Resolving EDM Ambiguity
Some EDMs can send up to 4 signals of different frequencies
Four signals of different frequencies will result in four unit lengths Ui (i = 1, 2, 3, 4); some unit lengths will range from 10m to 10km
The general equation for distance measurement in EDM based on
several unit lengths will be:
(5.8)
Where
and i is the wavelength of measuring signal modulated on the
carrier wave
The phase delay i is measured in the EDM by comparing in-coming phase with an onboard (receiver) reference
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18. EDM Ambiguity Resolution Example
Consider a case where an EDM sends 3 frequencies as shown in Figure 5.6
with phase delays p1, p2 and p2, the ambiguities Mi can be solved as
follows
Let:
P1 =
P2 =
P3 =
Signal 3
Signal 1
Signal 2
Fig. 5.6
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19. Resolving the EDM Ambiguity (1/3)
From distance Equation (5.7): or or
(5.10)
From Figure 2:
(p is phase delay in radians)
(5.11)
(5.12)
(5.13)
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20. Resolving the EDM Ambiguity (2/3)
Using the following in Equations (5.11) to (5.13):
Let:
P1 =
P2 =
P3 =
Note M3 = 0 in Equation (5.11):
approximately
Use M2 = 1 in Equation (5.12):
Precision Surveying/Chapter

21. Resolving the EDM Ambiguity (3/3)
Use M2 = 10 in Equation (5.13):
Final measured Distance: m
Note: All common EDM instruments used in Surveying are based on phase measurement principle, regardless of whether they use light waves, infrared waves or microwaves as carrier waves
The simple way to quickly resolve ambiguity and produce the measured distance for the Example in Fig. 5.6 is summarized in Table 5.1
Precision Surveying/Chapter

22. Simple Approach for Resolving EDM Ambiguities –Example 5.1
Refer to Figure 5.6:
Let:
P1 =
P2 =
P3 =
Position
(1)
Phase Delay
(2)
Unit Length (Ui)
(3)
(4) p1
0.2135
10 m
2.135 p2
0.0214
100 m
02.14 p3
0.1025
1000 m
102.5
Measured distance
The underlined numbers in column 4 are transferred mechanically to the distance readout of the instrument so that the final measured distance is m
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23. Distance by Phase Measurement Method – Example 5.2
An EDM capable of a maximum range of 1km has 2 unit lengths U1 = 10 m
and U2 = 1000 m . Using the EDM to measure a distance AB, the phase delay measurements (in fractions of a unit length) are and , respectively. What is the value of the distance AB?
Refer to Table 5.2
Position
(1)
Phase Delay
(2)
Unit Length (Ui)
(4) 1
0.8253
10m
8.253 2
0.4384
1000m
438.4
Distance m
The underlined numbers in column 4 are transferred mechanically to the distance
readout of the instrument giving the final measured distance as m
Precision Surveying/Chapter

24. Effect of Atmosphere on EM Waves
EDM uses half wavelength (/2) of modulated signal as a reference unit of length
EDM waves travel in all directions with the atmosphere causing:
Dissipation of energy along the travel path, causing the amplitude to be reduced
Variation of signal speed (v = f) which is dependent on refractive index (n), which changes the wavelength (since frequency (f) is constant except when there is a relative motion between the instrument and the target)
Refractive index is affected by the atmospheric temperature, pressure and humidity
Variation of direction (refraction) of wave (causing the line of sight to curve)
Variation in refractive index (n) causes variation in speed of EM waves in the atmosphere.
Precision Surveying/Chapter

25. Atmospheric Refractive Index
(5.17)
Refractive index (n) can be expressed as:
Where v is the actual velocity of light in the atmosphere;
c is the velocity of light in the vacuum (299,792,458 m/s ± 1.2 m/s
Wavelength (λa) corresponding with the actual refractive index (na) in the atmosphere or
(5.18)
Reference wavelength (λREF) (based on the manufacturer’s Lab temperature and
pressure):
(5.19)
Refractive index is calculated using internationally approved formulas
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26. Calculation of Refractive Index (n)
The actual refractive index n for electro-optical instruments is determined
using the following equation (IUGG in Helsinki, 1960):
(5.20)
Where p is the atmospheric pressure (in mb) (valid between 533mb mb;
t is the atmospheric temperature (in C) (valid between -40C to +50C);
e is the measured partial water vapor pressure (in mb)
ng is the group refractive index (for all frequencies making up the wave):
(5.21)
Very often, e is disregarded in formulae provided by manufacturers
Refractivity or refractive number (N) is used instead of n:
N = (n-1) × 106
N is change in refractive index in ppm
Precision Surveying/Chapter

27. Effect of Errors in Weather Measurement (Electro-optical)
Refractive index (n) is better represented as refractive number
or refractivity (N):
N=(n-1)× 106
So that dN = dn × 106
Or dn = dN × 10-6 meaning that change in refractivity (dN) is in ppm
Whatever is expressed with refractive index (n) can also be expressed in refractivity (N) as long as the difference in their units is considered
In electro-optical instruments:
Error in temperature of 1C is likely to affect n and distance by 1ppm
Error in pressure of 1.0mb is likely to affect n and distance by 0.3ppm
Error in humidity (or e) of 1.0mb is likely to affect n and distance by 0.04ppm
It is recommended that humidity should be considered for more precise and over long distances when using electro-optical instruments
Precision Surveying/Chapter

28. Refractive Index of Microwave Instruments
The actual refractive index n for microwave instruments is determined
using the following equation (IUGG in Helsinki, 1960):
(5.31)
with the usual notations, and valid for carrier wavelengths m
In microwave instruments:
Error in t of 1C is likely to affect n and distance by 1.4ppm
Error in p of 1.0mb is likely to affect n and distance by 0.3ppm
Error in humidity (or e) of 1.0mb is likely to affect n and distance by 4.6ppm
Critical parameter in microwave measurement is humidity – since e cannot be precisely determined, this limits the accuracy of microwave instruments compared to electro-optical ones
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29. Effects of Atmosphere - Comments
An accuracy better than 3 ppm in the refractive index of microwave cannot easily be achieved, even if the humidity (e) is measured very precisely at both instrument stations
Microwave measurement is less accurate than that of electro-optical instrument
During normal field measurement, the effect of atmospheric conditions is corrected for by entering a setting into the instrument, determined from ambient temperature and pressure measurement – this applies the first velocity correction
Some EDMs reduce all measurements automatically for the first velocity correction assuming the refractive index at the instrument is representative of the whole wave path
Precision Surveying/Chapter

30. First Velocity Correction
Two corrections due to atmosphere: First velocity correction (k ) &
Second Velocity Effect (k" )
(5.35)
First Velocity Correction:
By using refractivity instead of reactive indices:
Note: na is approximately equal to 1
For dn = nREF – na and dN = NREF - Na
dn = dN (ppm)
(with dN in ppm)
Precision Surveying/Chapter

31. Second Velocity Correction
Second velocity correction is expressed as
(5.44)
Actual length is at lower curvature (effect is negligible in electro-optical)
where k is the coefficient of refraction (0.13 to 0.25);
d is the measured distance, displayed on instrument;
R is the mean radius of curvature of the spheroid along the line measured for mean refractive index for both ends used
 is the actual path of wave with R< 
Geometric correction (Wave path to Chord Correction):
(5.47)
d1 is the measured distance corrected for first and second velocity corrections
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32. EDM Instrumental Errors
EDM instrumental or internal errors consist of:
Zero error (system constant)
Cyclic and phase drift
Phase measurement error
Phase drifts
Long-term variations in EDM modulation frequency
Vertical tilt axis error (affecting the centering of instrument)
Of all of the above, only phase measurement error is not systematic (but random) in nature are
The most important of the errors are the zero, cyclic and phase measurement errors

33. Important Systematic Errors in EDM
Zero error – electronic/mechanical centers of EDM and optical/mechanical centers of reflector vary
the systematic error is provided by manufacturer or through calibration
Cyclic error – due to electric cross-talk in EDM, is negligible in modern instrument
Phase measurement error (drift) – depends on accuracy of phase resolver (usually accurate)
Variation in EDM modulation frequency – depends on stability of frequency generation with time
Frequency stability must be checked in the lab
The instability affects scale of distance measurement (S1); the correction can be calculated for f1 and f2 as the old and new frequencies respectively, as
(5.48)

34. Random Errors in EDM
Accuracies of phase measurements and of modulation frequencies are usually very high
After correcting measurements for systematic errors, residual errors remaining become random errors (due to inability to determine the systematic errors exactly)
The sources of random instrumental (internal) errors are:
Leveling errors of EDM instrument (usually not significant)
Errors in the manufacturer’s determination of the velocity of light, modulation frequency, and refractive index; the combined effect is usually expressed as instrument’s accuracy specification, such as ± (a + b ppm) – very significant
Error in reading vertical angles of theodolite for slope reduction (usually not significant)
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35. EDM External Errors External sources of EDM errors:
Atmospheric conditions (cause first-velocity corrections), which change the speed of signal propagation in the atmosphere is systematic in nature
Refraction (second-velocity corrections) and earth curvature (geometric correction) is systematic in nature
Centering and leveling of EDM instrument and prism on survey markers are sources of random errors
Reading atmospheric conditions is a source of random errors
Manually reading vertical angles of theodolite for slope reduction is a source of random errors
EDM/theodolite/prism height relation, which results in optical pointing error is systematic in nature
The most significant source of random errors is the centering of EDM and prism

36. Order of Correcting EDM Measurements
Uncorrected distance can be given:
(5.49)
REF = wavelength of modulation signal
REF/ 2 = unit length for distance measurement
Order of correcting EDM measurements:
Apply system constant correction (z0)
Apply scale difference correction (if there is frequency variation)
Apply first and second velocity corrections (scale difference due to atmospheric conditions, na)
Apply geometric corrections (ΔS)

37. Error Propagation of Distance (1/2)
A corrected EDM distance can be given as (Phase difference):
(5.54)
Propagated error in distance:
(5.55)
Let the approximate two-way distance be 2S = M =
Errors are due to phase measurement, velocity of propagation in a vacuum, modulation frequency determination, actual refractive index, zero error, geometric reduction errors

38. Random Error Propagation of Distance (2/2)
Using approximation 2S =
(5.57)
Propagation formula is similar to usual representation of accuracy
of EDM distance:
(5.58)
where:
(5.60)
(5.61)
(Expressed in ppm)

39. Properties of Propagated Error
b = s/S or ppm (e.g. 5ppm is 5 mm in 1 km) – effect is predominant in long S
a is due to the following errors (predominant in short S):
Zero, Cyclic, and phase measurement
b is due to the following errors:
atmospheric refraction (error in determining refractive index)
error in determining the velocity of light in the vaccum
error in calibration of modulation frequency
Values of a and b are higher in microwave EDMs due to ground reflections and relative humidity
Short range, electro-optical EDMs are used in engineering surveys
Kern ME5000 has a = 0.2 mm, b = 0.2 ppm
Refer to numerical Examples in Section 5.6.1

40. EDM Calibration & Testing Procedures
Calibration and Testing provide:
precision (repeatability) of instrument, such as standard its deviation
instrument (additive constant & cyclic error) & scale error
Calibration is needed in the following:
to verify manufacturer’s specified scale and additive constant
before carrying out control surveys
as a statutory requirement of some Survey Acts, such as calibrating the EDM every 12 months
after the repair of instrument for a damage
Calibration procedure
Use distance measurements in all combinations on baselines of between 6 & 8 stations; measure temp., pressure, humidity, with appropriate sensors.
Use forced-centering pillars with inter-pillar spacing of 100m – 2 km
Maximum baseline distance should correspond to the maximum range of EDM
Baselines are measured regularly by appropriate government agencies

41. Methodology for EDM Calibration
Some of the information to be considered in calibration:
Operating manual of EDM, including all necessary self-checks
Equipment are in good adjustment and in good working order
Allowable range of weather conditions for the instrument calibration
Number of times (at least twice) to measure pillar-to-pillar slope distances
Meteorological conditions (temperature, pressure, wind speed, cloud cover, visibility) taken with standardized sensors at both the instrument and target stations for all distances
Redundant measurements allow least squares adjustment with increased reliability and precision of unknown parameters
Scale and additive constant errors are parameters
Precision Surveying/Chapter

42. Meteorological Sensors for EDM Calibration
Inaccurate meteorological observations can contribute up to 1-2 ppm error in scale determination of an EDM
Use appropriate temperature sensor type:
Hygro-thermometer – displays humidity/temp & humidity/wet bulb
Precision psychrometer with accuracy of 1- 2% relative humidity and ± 0.1ºC resolution of temperature
Precision thermometer (0.02C) – thermistors (0.2C)
Use appropriate pressure and relative humidity sensor types:
Precision barometer (or digital barometer) with accuracy of ± 1.0 mbar
Handheld multibarometers with accuracy ± 5.0 mbar for pressure and 1C for temperature
Microbarometers with an accuracy of microbar
Digiquartz pressure sensor with accuracy of 0.01%
Hygristor sensor (a typical relative humidity sensor) measures humidity to accuracy of 0.25% relative humidity

43. EDM Baseline Designs
EDM baselines must be well designed to allow all possible systematic errors in EDM to be detected when used
Three basic EDM design types (Hazelton, 2009): Aarau, Hobart and Heerbrugg
Important parameters of the designs are summarized in the following table
Remember: System constant & scale factor error of EDM are usually determined from baseline measurements
Precision Surveying/Chapter

44. EDM Baseline Designs Aarau design Hobart Design Heerbrugg design
Geometry
Straight baselines with up to 4 or 9 points
Set up at 2 points (zero pillar point & a pillar point that is half the unit length of the EDM from the zero pillar
Array 7 collinear points (set on tripods for forced-centering interchange) with spacing based on unit length of EDM and the length that is as long as the intended use of EDM; setting out of baselines follows some formulas in Eqn. (5.92) – (5.98) with EDM range (d) and unit length (U) as important parameters
Type of measurements
Measured in multiples of some numbers, such as 60 m
Distances are measured to all the other points on the line
Redundant measurements (with 21 one-way distances between 7 stable points)
Other determinations
Separate cyclic error can be determined within the baselines
Combined zero & reflector offsets and cyclic errors can be determined for unknown baseline distances
Advantages
Fewer measurements are made
Least squares estimation is possible
Disadvantages
More measurements required
Restricted to few instruments with certain unit lengths
Precision Surveying/Chapter

45. EDM Calibration on Known Baseline
See sample test baseline in Fig. 5.8 – consists of 7 stations
Processing the Distance measurements on baselines:
Measure all possible combinations of one-way slope distances (21 distances for 7 points); one line is measured 4 times with the average taken as one distance for the line; HI, temperature, pressure, humidity
Correct slope distance for first velocity (due to weather)
Reduce slope to mark-to-mark distances
Use published distance (p) and mark-to-mark distance (m): p = C+Sm
Perform least squares adjustment (weighting distances) to determine system constant (C), scale factor (S) and their standard deviations with (p, m) as observations
Perform the following statistical tests, given the manufacturer standard deviation of EDM as a ± b ppm:
Are C, 1-S significantly different from zero? Use z-test
Are sig(C) & a and sig(S) & b acceptable? Use Chi-square test
Advantages of using known baselines: Stability of pillars; Fast setup; HI & HR are fairly constant; High precision of C; Distances spread over whole range of EDM

46. Measuring Arrangement for EDM Calibration
mij is the distance measurement
between pillars i and j
Fig. 5.8
Precision Surveying/Chapter

47. EDM Testing on Unknown Baselines (1/3)
3 approaches: Standard, modified standard, approximate
They are all based on collinear arrays of points represented by a series of tribrachs on tripods using forced centering interchange
Cannot determine scale factor (S), but only system constant (C)
All distances are corrected for weather conditions & slope reductions
Challenges include aligning all the points and centering on the points; it is time consuming; they produce poor accuracy

48. EDM Testing on Unknown Baselines (2/3)
Standard
Modified Standard
Approximate
Measured quantities
21 one-way distances between 7 points, weather, zenith angles
Each distance measured 3 times and averaged
The same weights are used for the averaged distances in least squares adjustment
Same as in the standard approach; standard deviation of each measurement from repeated readings are used for weighting the measurement in least squares adjustment
A line (forming an array of collinear points) of unknown length is measured in several sections (not in all combinations); number of points in the array depends on desired accuracy with a minimum of 3 points for unique determination of C)
Data processing
Form and solve 21 parametric least squares equations; solve for six unknown distances between baseline points; system constant C and its standard deviation; and standard deviation of measuring a distance with the EDM
7 points in a straight x-axis of a coordinate system with 6 unknown x-coordinates and C to be determined from 21 distance measurements by least squares method; standard deviation of C and standard deviation of measuring a distance with the EDM are also determined
Overall distance (M) of a line and the section distances (mi) are used to formulate the equation for the unknown C; the approximate value of C can be determined uniquely
Statistical Tests
Perform test on C & its standard deviation; and on the standard deviation of measuring a distance with the EDM
using the a posteriori variance factor of unit weight
Perform test on C only
Precision Surveying/Chapter

49. EDM Testing on Unknown Baseline: Approximate Approach
Fig. 5.9 A line for approximate method
System constant C can be determined from n sections as follows
(Note: number of sections in Fig. 5.9 is n = 4):
(5.126)

50. EDM Standardization
EDM standardization refers to the comparison of the instrument to a standard of length traceable to the National Standard
It is the determination of the scale of an instrument (affected by refractive index, shift in modulation frequency)
2 different ways of standardizing EDM instrument:
Measuring frequencies of EDM, which is more precise
Problem: calibrated frequency counters sufficiently accurate for EDM standardization are normally not available to surveyors
Determining a scale factor from a baseline of known length (baseline previously known by invar taping, interferometric method, or by a precision EDM instrument)
Problem: results may be affected by the instrumental errors or errors in reductions
Precision Surveying/Chapter

51. EDM Standardization – Frequency Method
Module 9: Application of Electromagnetic (EM) Waves
EDM Standardization – Frequency Method
If the actual frequency (f2) is significantly different from the nominal frequency (f1) for which the instrument is designed, the measured distance (Smeas) can be corrected for scale errors, giving the corrected distance (Scorr) as:
(5.127)
Note: Scale error is not very critical; it may be assumed to be fairly
constant during the period of observation in a project
How to use Calibration parameters (system constant C & scale factor S) when distance m is measured with the calibrated EDM:
On known calibration baseline: d = C + Sm
On Unknown baseline: d = C + m
d is the corrected distance.
Precision Surveying/Chapter