ERRORS, CHECKING AND CALIBRATION

Although modern EDM equipment is exceptionally well constructed, the effects of age and general wear and tear may alter its performance. It is essential therefore that all field equipment should be regularly checked and calibrated. Checking and calibration are two quite separate activities. Checking is concerned with verifying that the instrument is performing within acceptable tolerances. Calibration is the process of estimating the parameters that need to be applied to correct actual measurements to their true values.

For example, in the case of levelling the two-peg test could be used for both checking and calibrating a level. The two-peg test can be used to check whether the level is within±10 mm at 20 m or whatever is appropriate for the instrument concerned. It could also be used to discover what the actual collimation error is at, say, 20 m, so that a proportional correction, depending on distance, could be applied to each subsequent reading. This latter process is calibration. In the case of levelling both checking and calibration are quite simple procedures. Rather more is involved with checking and calibrating EDM. A feature of calibration is that it should be traceable to superior, usually national, standards. From the point of view of calibration, the errors have been classified under three main headings.

4.10.1 Zero error (independent of distance)

Zero error arises from changes in the instrument/reflector constant due to ageing of the instrument or as a result of repairs. The built-in correction for instrument/reflector constants is usually correct to 1 or 2 mm but may change with different reflectors and so should be assessed for a particular instrument/reflector combination. A variety of other matters may affect the value of the constant and these matters may vary from instrument to instrument. Some instruments have constants which are signal strength dependent, while others are voltage dependent. The signal strength may be affected by the accuracy of the pointing or by prevailing atmospheric conditions. It is very important, therefore, that periodical calibration is carried out.

A simple procedure can be adopted to obtain the zero error for a specific instrument/reflector combination. Consider three points A, B, C set out in a straight line such that AB= 10 m, BC = 20 m and AC= 30 m (Figure 4.26).

Assume a zero error of+0.3 m exists in the instrument; the measured lengths will then be 10.3, 20.3 and 30.3. Now:

But the measurements 10.3+ 20.3 = 30.3

The error may be found from 10.3+ 20.3 − 30.3 = +0.3 Now as

Correction= – Error

every measured distance will need a correction of – 0.3 m. Or in more general terms

zero error= ko= lAB+ lBC− lAC (4.46)

from which it can be seen that the base-line lengths do not need to be known prior to measurement. If there are more than two bays in the base line of total length L, then

ko= (L − li)/(n− 1) (4.47)

where liis the measured length of each of the n sections.

Alternatively the initial approach may be to observe the distances between all possible combinations of points. For example, if the base line comprises three bays AB, BC and CD, we have

AB+ BC − AC = ko

AC+ CD − AD = ko

AB+ BD − AD = ko

BC+ CD − BD = ko

with the arithmetic mean of all four values being accepted.

The most accurate approach is a least squares solution of the observation equations. Readers unfamiliar with least squares methods may wish to pass over the remainder of this section until they have read Chapter 7 and Appendix A.

Let the above bays be a, b and c, with measured lengths l and residual errors of measurement r.

Observation equations: b and c as well as the zero error ko. Provided that the quality of all the observations of distance is the same

then the solutions are simply

a= (lAB+ lAC+ 2lAD− 2lBC− lBD− lCD)/4 b= (−2lAB+ lAC+ lAD+ lBC+ lBD− 2lCD)/4 c= (−lAB− lAC+ 2lAD− 2lBC+ lBD+ lCD)/4 ko= (lAB+ lBC+ lCD− lAD)/2

Substituting the values for a, b, c and koback into the observation equations gives the residual values r, which can give an indication of the overall magnitude of the other errors.

The distances measured should, of course, be corrected for slope before they are used to find ko. If possible, the bays should be in multiples of λ/2 if the effect of cyclic errors is to be cancelled.

4.10.2 Cyclic error (varies with distance)

As already shown, the measurement of the phase difference between the transmitted and received waves enables the fractional part of the wavelength to be determined. Thus, errors in the measurement of phase difference will produce errors in the measured distance. Phase errors are cyclic and not proportional to the distance measured and may be non-instrumental and/or instrumental.

The non-instrumental cause of phase error is spurious signals from reflective objects illuminated by the beam. Normally the signal returned by the reflector will be sufficiently strong to ensure complete dominance over spurious reflections. However, care should be exercised when using vehicle reflectors or reflective material designed for clothing for short-range work.

The main cause of phase error is instrumental and derives from two possible sources. In the first instance, if the phase detector were to deviate from linearity around a particular phase value, the resulting error would repeat each time the distance resulted in that phase. Excluding gross malfunctioning, the phase readout is reliably accurate, so maximum errors from this source should not exceed 2 or 3 mm.

The more significant source of phase error arises from electrical cross-talk, or spurious coupling, between the transmit and receive channels. This produces an error which varies sinusoidally with distance and is inversely proportional to the signal strength.

Cyclic errors in phase measurement can be determined by observing to a series of positions distributed over a half wavelength. A bar or rail accurately divided into 10-cm intervals over a distance of 10 m would cover the requirements of most short-range instruments. A micrometer on the bar capable of very accurate displacements of the reflector of+0.1 mm over 20 cm would enable any part of the error curve to be more closely examined.

The error curve plotted as a function of the distance should be done for strong and weakest signal conditions and may then be used to apply corrections to the measured distance. For the majority of short-range instruments the maximum error will not exceed a few millimetres.

Most short-range EDM instruments have values for λ/2 equal to 10 m. A simple arrangement for the detection of cyclic error which has proved satisfactory is to lay a steel band under standard tension on a horizontal surface. The reflector is placed at the start of a 10-m section and the distance from instrument to reflector obtained. The reflector is displaced precisely 100 mm and the distance is re-measured. The difference between the first and second measurement should be 100 mm; if not, the error is plotted at the 0.100 m value of the graph. The procedure is repeated every 100 mm throughout the 10-m section and an error curve produced. If, in the field, a distance of 836.545 m is measured, the ‘cyclic error’ correction is abstracted from point 6.545 m on the error curve.

4.10.3 Scale error (proportional to distance)

Scale errors in EDM instruments are largely due to the fact that the oscillator is temperature dependent. The quartz crystal oscillator ensures the frequency ( f ) remains stable to within±5 ppm over an operational temperature range of –20^◦C to 50^◦C. The modulation frequency can, however, vary from its nominal value due to incorrect factory setting, ageing of the crystal and lack of temperature stabilization. Most modern short-range instruments have temperature-compensated crystal oscillators which have been shown to perform well. However, warm-up effects have been shown to vary from 1 to 5 ppm during the first hour of operation.

Diode errors also cause scale error, as they could result in the emitted wavelength being different from its nominal value.

The magnitude of the resultant errors may be obtained by field or laboratory methods.

The laboratory method involves comparing the actual modulation frequency of the instrument with a reference frequency. The reference frequency may be obtained from off-air radio transmissions such as MSF Rugby (60 kHz) in the UK or from a crystal-generated laboratory standard. The correction for frequency is equal to

Nominal frequency− Actual frequency Nominal frequency



A simple field test is to measure a base line whose length is known to an accuracy greater than the mea-surements under test. The base line should be equal to an integral number of modulation half wavelengths.

The base line AB should be measured from a point C in line with AB; then CB−CA = AB. This differential form of measurement will eliminate any zero error, whilst the use of an integral number of half wavelengths will minimize the effect of cyclic error. The ratio of the measured length to the known length will provide the scale error.

4.10.4 Multi-pillar base lines

The establishment of multi-pillar base lines for EDM calibration requires careful thought, time and money.

Not only must a suitable area be found to permit a base line of, in some cases, over 1 km to be established, but suitable ground conditions must also be present. If possible the bedrock should be near the surface to permit the construction of the measurement pillars on a sound solid foundation. The ground surface should be reasonably horizontal, free from growing trees and vegetation and easily accessible. The construction of the pillars themselves should be carefully considered to provide maximum stability in all conditions of wetting and drying, heat and cold, sun and cloud, etc. The pillar-centring system for instruments and reflectors should be carefully thought out to avoid any hint of centring error. When all these possible error sources have been carefully considered, the pillar separations must then be devised.

The total length of the base line is obviously the first decision, followed by the unit length of the equip-ment to be calibrated. The inter-pillar distances should be spread over the measuring range of equipequip-ment, with their fractional elements evenly distributed over the half wavelength of the basic measuring wave.

Finally, the method of obtaining inter-pillar distances to the accuracy required has to be consid-ered. The accuracy of the distance measurement must obviously be greater than the equipment it is intended to calibrate. For general equipment with accuracies in the range of 3–5 mm, the base line could be measured with equipment of superior accuracy such as those already mentioned.

For even greater accuracy, laser interferometry accurate to 0.1 ppm may be necessary.

When such a base line is established, a system of regular and periodic checking must be instituted and maintained to monitor short- and long-term movement of the pillars. Appropriate computer software must also be written to produce zero, cyclic and scale errors per instrument from the input of the measured field data.

In the past several such base lines have been established throughout the UK, the most recent one by Thames Water at Ashford in Middlesex, in conjunction with the National Physical Laboratory at Teddington, Middlesex. In 2006, it was understood to be no longer operational, along with all the other UK base lines. It is hoped the situation will change. However, this is a good example of a pillar base line and will be described further to illustrate the principles concerned. This is an eight-pillar base line, with a total length of 818.93 m and inter-pillar distances affording a good spread over a 10-m period, as shown below:

2 3 4 5 6 7 8

1 260.85 301.92 384.10 416.73 480.33 491.88 818.93

2 41.07 123.25 155.88 219.48 231.03 558.08

3 82.18 114.81 178.41 189.96 517.01

4 32.63 96.23 107.78 434.83

5 63.60 75.15 402.20

6 11.55 338.60

7 327.05

With soil conditions comprising about 5 m of gravel over London clay, the pillars were constructed by inserting 8× 0.410 m steel pipe into a 9-m borehole and filling with reinforced concrete to within 0.6 m of the pillar top. Each pillar top contains two electrolevels and a platinum resistance thermometer to monitor thermal movement. The pillars are surrounded by 3 × 0.510 m PVC pipe, to reduce such movement to a minimum. The pillar tops are all at the same level, with Kern baseplates attached. Measurement of the distances has been carried out using a Kern ME5000 Mekometer and checked by a Terrameter.

The Mekometer has in turn been calibrated by laser interferometry. The above brief description serves to illustrate the care and planning needed to produce a base line for commercial calibration of the majority of EDM equipment.