1
ELECTRONIC DISTANCE MEASUREMENT (EDM)
6.1.1Electronic Distance Measurement
Electronic distance measurement (EDM), first introduced in the 1950s by the Geodimeter Inc. founders, has since those early days undergone continual refinement. The early instruments, which were capable of very precise measurements over long distances, were large, heavy, complicated, and expensive. Rapid advances in related technologies have provided lighter, simpler, and less expensive instruments these EDM instruments (EDM Is) are manufactured for use with theodolites and as modular components of Total Station instruments. Technological advances in electronics continue at a rapid rateas evidenced by recent market surveys that indicate that most new electronic instruments have been on the market for less than two years.
Current EDMIs use infrared light, laser light, or microwaves. The microwave systems use a receiver/transmitter at both ends of the measured line, whereas infrared and laser systems utilize a transmitter at one end of the measured line and a reflecting prism at the other end. Some laser EDMIs will measure short distances (100-350 m) without a reflecting prism reflecting the light directly off the feature (e.g. building wall) being measured, Microwave instruments are often used in hydrographic surveys and have a usual upper measuring range of 50 km. Although microwave systems can be used in poorer weather conditions (fog, rain, etc.) than can infrared and laser systems, the uncertainties caused by varying humidity conditions over the length of the measured line may result in lower accuracy expectations. Hydrographic measuring and positioning techniques have, in a few short years, been largely supplanted by Global Positioning System (GPS) techniques.
Infrared and laser EDMIs come in long range (10-20 km), medium range (3-10 km) and short range (0.5 to 3 km). EDMIs can be mounted on the standards or the telescope of most theodolites; additionally, they can be mounted directly in a tribrach. When used with an electronic theodolite, the combined instruments can provide both the horizontal and the vertical position of one point relative to another. The slope distance provided by an add-on EDMI can be reduced to its horizontal and vertical equivalents by utilizing the slope angle provided by the theodolite. In Total Station instruments, this reduction is accomplished automatically.
6.1.2Electronic Angle Measurement
The electronic digital theodolite, first introduced in the late 1960s (Carl Zeiss Inc.), set the stage for modern field data collection and processing. When the electronic theodolite is used with a built-in EDMI, (e.g., Zeiss EIta, Figure 5.1) or an add-on and interfaced EDMI (e.g.. Wild T-1000, Figure 6.2), the surveyor has a very powerful instrument. Add that instrument to an on-board microprocessor that automatically monitors the instrument's operating status and manages built-in surveying programs and a data collector (built-in or interfaced) that stores and processes measurements and attribute data, and you have what is known as a Total Station.
FIGURE 6.1 Zeiss Total Stations. The EIca 45 and 55 have on-board data storage (1.900data lines),whereas the EIta 50 requires an interfaced data collector. On board programs include coordinates, free stationing, polar points, heights ofobjects, connecting distances (between remote points), and setting-out angleaccuracy from 3 to 5 seconds and EDM distances to 1.500 m (single prism).(Source : Courtesy of Carl Zeiss Inc-.Thornwood. N.Y. in the Ramsay)
FIGURE 6.2 Wild T-1000 Electronic
Theodolite, shown with Dl 1000 Distomat EDM and the GRE 3 data collector. (Source : Courtesy of Leica Co. Inc..Toront in the Ramsay)
6.2Principles of Electronic Distance Measurement (EDM)
Figure 6.3 shows a wave of wavelength λ. The wave is travelling along the x axis with a velocity of 299, 792.5 ± 0.4 km/s (in vacuum). The frequency of the wave is, the time taken for one complete wavelength.
FIGURE 6.3 : Light Wave (Source : Courtesy of Leica Co. Inc..Toronto in the Ramsay)
λ = c / ƒ
where λ = wavelength in meters
c = velocity in km/s
ƒ = frequency in hertz (one cycle per second)
Figure 6.4 shows the modulated electromagnetic wave leaving the EDMI and being reflected (light waves) or retransmitted (microwaves) back to the EDMI. It can be seen that the double distance (2L) is equal to a whole number of wavelengths (n λ). plus the partial wavelength (Φ) occurring at the EDMI.
L = (n λ + Φ) / 2 meters
The partial wavelength (Φ) is determined in the instrument by noting the phase delay required to precisely match up the transmitted and reflected or retransmitted waves. The instrument (e.g.. Wild Distomat) can count the number of full wavelengths (n λ). or, instead, the instrument can send out a series (three or four) of modulated waves at different frequencies. (The frequency is typically reduced each time by a factor of 10, and of course, the wavelength is increased each time also by a factor of 10.) By substituting the resulting values of λ and Φ into Equation (6-2), the value of n can be found.
FIGURE 6.4 : Principles of EDM measurement (Source : Courtesy of Kern Ins. –Leica in the Ramsay)
The instruments are designed to carry out this procedure in a matter of seconds and then to display the value of L in digital form. The velocity of light (including infrared) through the atmosphere can be affected by (1) temperature, (2) atmospheric pressure, and (3) water vapor content. In practice, the corrections for temperature and pressure can be performed manually by consulting nomographs similar to that shown in Figure 6.5, or the corrections can be performed automatically on some EDMIs by the on-board processor/calculator after the values for temperature and pressure have been entered.
For short distances using lightwave EDMIs, atmospheric corrections have a relatively small significance. For long distances using lightwave instruments and especially microwave instruments, atmospheric corrections can become quite important. The following chart shows the comparative effects of the atmosphere on both lightwaves and microwaves.
ERROR parts per millionParameter / Error / Light Wave / Microwave
t, temperature / +1º / - 1 / - 1.25
p, pressure / +1 mm Hg / + 0.4 / + 0.4
e, partial water / 1 mm Hg / - 0.05 / + 7 at 20ºC
vapor pressure / + 17 at 45ºC
At this point, it is also worth noting that several studies of general EDM use show that more than 90 percent of all distance determinations involve distances of 1000 m or less and that more than 95 percent of all layout measurements involve distances of 400 m or less. The values in the preceding chart would seem to indicate that, for the type of measurements normally encountered in the construction and civil field, instrumental errors and centering errors hold much more significance than do the atmosphere-related errors.
FIGURE 6.5 : Atmospheric correction
graph.(Source : Courtesy of
Sokkia Co. Ltd in the Ramsay)
6.3EDMI CHARACTERISTICS
Following are the characteristics of recent models of add-on EDMIs. Generally the more expensive instruments have longer distance ranges and higher precision.
Distance range
800 m to 1 km (single prism with average atmospheric conditions) Short-range EDMIs can be extended to 1300 m using 3 prisms, Long-range EDMIs can be extended to 15 km using 11 prisms(Leica Co.)
Accuracy range
±(15 mm + 5ppm) for short-range EDMIs ±(3mm + 1 ppm) for long-range EDMIs
Measuring time
1.5 seconds for short-range EDMIs to 3.5 seconds for long-range EDMIs Both accuracy and time are considerably reduced for tracking mode measurements.
Slope reduction
Manual or automatic on some models Average of repeated measurements: available on some models Battery capability is 1400 to 4200 measurements, depending on the size of the battery and the temperature
Temperature range
-20°C to +50°C. Nonprism measurements: available on some models with distances from 100 to 350 m (3 to 5 km with prisms)
6.4PRISMS
Prisms are used with electro-optical EDMIs (light, laser, and infrared) to reflect the transmitted signals (see Figure 6.6). A single reflector is a cube corner prism that has the characteristics of reflecting light rays back precisely in the same direction as they are received. This retro-direct capability means that the prism can be somewhat misaligned with respect to the EDMI and still be effective. A cube corner prism is formed by cutting the corners off a solid glass cube. The quality of the prism is determined by the flatness of the surfaces and the perpendicularity of the 90° surfaces.
Prisms can be tribrach-mounted on a tripod, centred by optical plummet, or attached to a prism pole held vertical on a point with the aid of a bull's-eye level. However, prisms must be tribrach-mounted if a higher level of accuracy is required.
In control surveys, tribrach-mounted prisms can be detached from their tribrachs and then interchanged with a theodolite (and EDMI) similarly mounted at the other end of the line being measured. This interchangeability of prism and theodolite (also targets) speeds up the work, as the tribrach mounted on the tripod is centred and levelled only one lime. Equipment that can be interchanged and mounted on tribrachs already set up is known as forced-centring equipment.
Prisms mounted on adjustable-length prism poles are very portable and as such, are particularly suited for stakeout surveys. Figure 6.7 shows the prism pole being steadied with the aid of an additional target pole. The height of the prism is normally set to equal the height of the instrument. It is particularly important that prisms mounted on poles or tribrachs be permitted to tilt up/down so that they can be perpendicular to infrared signals that are being sent from much higher or lower positions.
FIGURE 6.6 : Various target and
reflector systems in tribach mounts.
FFIGURE 6.7 : Steadying the EDM reflectorwith the aid of a second target pole
6.5EDMI ACCURACIES
EDMI accuracies are stated in terms of a constant instrumental error and a measuring error proportional to the distance being measured.
Typically accuracy is claimed as ±[5 mm + 5 parts per million (ppm)] or ±(0.02 ft + 5 ppm). The ±5 mm (0.02 ft) is the instrument error that is independent of the length of the measurement, whereas the 5 ppm (5 mm/km) denotes the distance-related error.
Most instruments now on the market have claimed accuracies in the range of ±(3mm 4- 1 ppm) to ±(10 mm + 10 ppm). The proportional part error (ppm) is insignificant for most work, and the constant part of the error assumes less significance as the distances being measured lengthen. At 100 m, an error of ±5 mm represents 1/20,000 accuracy, whereas at 1,000 m the same instrumental error represents 1/200,000 accuracy.
When one is dealing with accuracy, it should be noted that both the EDMI and the prism reflectors must be corrected for off-centre characteristics. The measurement being recorded goes from the electrical centre of the EDMI to the back of the prism (allowing for refraction through glass) and then back to the electrical centre of the EDMI. The difference between the electrical centre of the EDMI and the plumb line through the tribrach centre is compensated for by the EDMI manufacturer at the factory. The prism constant (30 to 40 mm) is eliminated either by the EDMI manufacturer at the factory or in the field.
The EDMIs prism constant value can be field-checked in the following manner: A long line (>1 Km) is laid out with end stations and an intermediate station (see Figure 6.8). The overall distance AC is measured, along with partial lengths AB and BC. The constant value will be present in all measurements; therefore,
AC — AB — BC = instrument/prism constant (6-3)
Alternatively, the constant can be determined by measuring a known baseline if one can be conveniently accessed.
6.6EDMI OPERATION
Figures 6.8 to 6.10 show a variety of first-generation short- to medium-range EDMIs, The operation of all EDMIs involves the following basic steps: (1) set up (2) aim (3) measure (4) record.
6.6.1Set Up
Tribrach-mounted EDMIs are simply inserted into the tribrach (forced centring) after the tribrach has been set over the point by means of the optical plummet. Telescope or theodolite yoke-mounted EDMIs are simply attached to the theodolite either before or after the theodolite has been set over the point. Prisms are set over the remote station point either by inserting the prism into an already setup tribrach (forced centring) or by holding the prism vertically over the point on a prism pole. The EDMI is turned on and a quick check is made to ensure that it is in good working order—for example, battery, display, and the like. The height of the instrument (telescope axis) and the height of the prism (centre) are measured and recorded; the prism is usually set to the height of the theodolite when it is mounted on an adjustable prism pole.
FIGURE 6.8 : Method of determining the instrument-reflector constant
FIGURE 6.9 Pentax PM 81 EDM
mounted on a 6-second Pentax
theodolite and also shown as tribrach mounted. EDM has a triple-prism
range of 2 km (6.600 ft) with SE =
+/—(5 mm + 5 ppm). (Source : Courtesy of
Pentax Corp.,Colo in the Ramsay.)
6.6.2Aim
The EDMI is aimed at the prism by using either the built-in sighting devices on the EDMI or the theodolite telescope. Telescope or yoke-mount EDMIs will have the optical line of sight a bit lower than the electronic signal. Some electronic tacheometer instruments (ETIs) have a sighting telescope mounted on top of the instrument. In those cases, the optical line of sight will be a bit higher than the electronic signal.
Most instrument manufacturers provide prism/target assemblies, which permit fast optical sightings for both optical and electronic alignment (see Figure 6.6). That is, when the crosshair is on target, the electronic signal will be maximized at the centre of the prism.
The surveyor can (if necessary) set the electronic signal precisely on the prism centre by adjusting the appropriate horizontal and vertical slow-motion screws until a maximum signal intensity is indicated on the display (this display is not available on all EDMIs). Some older EDMIs have an attenuator that must be adjusted for varying distances the signal strength is reduced for short distances so that the receiving electronics are not overloaded. Newer EDMIs have automatic signal attenuation.
6.6.3Measure
The slope distance measurement is accomplished by simply pressing the "measure" button and waiting a few seconds for the result to appear in the display. The displays are either LCD (most) or LED. The measurement is shown to two decimals of a foot or three decimals of a meter: a foot/meter switch readily switches from one system to the other. If no measurement appears in the display, the surveyor should check on the switch position ,battery status, attenuation, and crosshair location (sometimes the stadia hair is mistakenly centred).
EDMIs with built-in calculators or microprocessors can now be used to compute horizontal and vertical distances, coordinates, atmospheric, curvature, and prism constant corrections. The required input data (vertical angle, ppm, prism constant, etc.) are entered via the keyboard.
Most EDMIs have a tracking mode (very useful in layout surveys, which permits continuous distance updates as the prism is moved closer to its final layout position. Handheld radios are useful for all EDM work, as the long distances put a halt to normal voice communications. In layout work, clear communications are essential if the points are to be properly located. All microwave EDMIs permit voice communication—which is carried right on the measuring signal.
Figure 6.10 shows a remote device (Kem RD 10). which is attached to the prism. The display on the EDMl is transmitted to the RD 10 so that the surveyor holding the prism is immediately aware of the results. In tracking mode, the RD 10 display will show the remaining left/right and near/far (+/-) layout distances so that the surveyor holding the prism can quickly proceed to the desired layout point—even on high-noise construction sites.
FIGURE 5.10 Kern RD 10 remote EDM display shown attached to EPM reflecting prism. Slope. horizontal, and vertical distances (from the EDM to the prism) are displayed on the RD 10, Maximum range is 1,300 feet (400 m). (Source : Courtesy of Pentax Corp.,Colo. In the Ramsay)
6.6.4Record
The measured data can be recorded conventionally in HOLD note format, or they can be manually entered into an electronic data collector. The distance data must be accompanied by all relevant atmospheric and instrumental correction factors. Total Station instruments, which have automatic data acquisition capabilities, are discussed in Section 6.8.
6.7GEOMETRY OF ELECTRONIC DISTANCE MEASUREMENT
Figure 6.11 illustrates the use of EDM when the optical target and the reflecting prism are at the same height (see Figure 6.6—single prism assembly). The slope distance (S) is measured by the EDMI, and the slope angle (a) is measured by the accompanying theodolite. The heights of the EDMI and theodolite (hi) are measured with a steel tape or by a graduated tripod centring rod; the height of the reflector/target is measured in a similar fashion. As noted earlier, adjustable-length prism poles permit the surveyor to set the height of the prism (HR) equal the height of the instrument (hi), thus simplifying the computations. From Figure 6.11, if the elevation of station A is known and the elevation of station B is required:
Elev. STA. B = elev. STA. A + hi ± V - HR (6-4)
FIGURE 6.10 : Geometry of an EDM calculation (Source : Land Surveying, Ramsay)
When the EDMI is mounted on the theodolite and the target is located beneath the prism pole, the geometric relationship can be as shown in Figure 6.12. The additional problem encountered in the situation depicted in Figure 6.12 is the computation of the correction to the vertical angle (Δα) that occurs when Δhi and ΔHR are different. The precise size of the vertical angle is important, as it is used in conjunction with the measured slope distance to compute the horizontal and vertical distances.