• This EDM deals with the principles and procedures of separate Electronic distance measuring device (EDM) instruments that are mountable with optic/electronic theodolites.
• Original EDMs were individual units used only for distance measurements.
• EDM instruments used as a modular component in modern total stations also work under the same principle of separate EDM instruments.
• EDM was first introduced in the 1950s and has undergone several modifications.
• The early versions of the instruments, though very precise over long distances, were very large, heavy, complicated, and expensive.
• Electronic theodolite/optic theodolite mountable EDM was introduced first, and these are being used still today.
• Rapid advances at related technologies have provided lighter, simpler, and less expensive instruments.
• The latest versions of EDM instruments are used as a modular component of total stations.
• Some earlier versions of EDM instruments used natural light for the calculation of distances, but the latest version of EDM uses infrared light, laser light or microwaves.
Depending on the type of carrier wave employed, EDM instruments can be classified under the following three heads :
For the corresponding frequencies of carrier waves, the reader may refer back to as per fig no-5. It is seen that all the above three categories of EDM instruments use short wavelengths and hence, higher frequencies.
Carrier wave modulation Fig no -5
Frequency modulation of the carrier wave Fig no- 6
Impulse modulation of the carrier wave Fig no -7
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• The principle of the measurement device in EDM, which is currently used in a total station and used along with electronic/optic theodolites, is that it calculates the distance by measuring the phase shift during the radiated electromagnetic wave (such as an infrared light or laser light or microwave) from the EDM’s main unit, which returns by being reflected through the reflector, which is positioned at a measurement point (as per below figure no-1).
• This phase change can be regarded as a part of the frequency, which appears as the unit of length or time under a specific condition.
• After the slope distance L along with the slope angle Ø are measured by EDM, if the elevation of point A is the reference point, we could find the elevation of point B from the following formula (According to below figure no-2)
EMDs Structure Fig No.-1
Slope Distance (Horizontal Distance Error) by incidence angle Fig No.-2
• As per figure no-4, shows a wave of wavelength λ. The wave is traveling along the X axis with a velocity of 299,792,560.4 km/sec (approximate velocity of light in vacuum).
• The frequency of This wave is That the time is taken for one complete wavelength.
EDM Wave Fig No – 3
• As per fig, No-3 shows a modulated electromagnetic wave being emitted from an EDM instrument and being reflected and being reflected back to the instrument.
• Here the double distance is taken as 2L, which is equal to the total whole number of wavelength nλ and the particle wavelength w.
• Therefore, the distance between the EDM instrument and the reflector (L) is calculated as follows:
• The partial wavelength (w) is determined by calculating the phase shift required and reflected waves, that is, by calculating the phase delay required to match precisely the transmitted and the reflected waves.
• S = Station
• r = Reflector component of addition constant
• Z= Target
• E = References plane within the EDM for phase comparison
• λ = Modulation of wavelength
• W = Fraction to be measured of a whole wavelength of modulation Δλ
• e = Distance meter component of addition constant
• R = Reference plane the reflection of the wave transmitted by the EDM
• The instrument transmits a series of three or four modulated waves at different frequencies.
• By substituting the resulting values of λ and w in the above equation for three or four different frequencies, the value of n can be found.
• The Tools Were Created to carry out That procedure within seconds and display the value of L.
• Some EDM instruments use pulsed laser emissions, and these instruments determine the distance by measuring the time taken between the transmission of this sign and the reception of the reflected signal, by taking advantage of the pulsed laser beam.
• The velocity of light (electromagnetic waves) through the atmosphere can be affected by:
• The corrections for temperature and pressure are determined manually by referring the monograms given with all total stations (as per below fig-4), or the corrections are calculated automatically in the instrument itself by inputting the values for temperature and pressure.
Principle of Electronic Distance Measurement Fig No.-4
• For measuring short distances using EDM instruments, atmospheric corrections are relatively insignificant. For measuring long distances, atmospheric corrections become quite important.
• Personal errors include with inaccurate setups of EDM instruments and reflectors over stations, faulty measurements of reflector and instrument heights [Required for computing horizontal lengths ], and errors in determining atmospheric pressures and temperatures. These errors are largely random.
• They can be minimized by exercising the utmost care and by using good-quality barometers and thermometers.
• Mistakes (not errors) in manually recording and reading displayed distances are common and costly. They may be eliminated with a few instruments by obtaining the readings from both meters and feet as well as comparing them. Of course, data collectors also circumvent this problem. Additionally, as shown in table no-1, The misalignment of the prism may cause significant errors once the reflector is put in its 0 mm constant position.
|0 mm Constant
Prism Error (mm)
|−30 mm Constant
Prism Error (mm)
Error in Observed Distance because of Misalignment of the Prism Table no-1
• Example of a common error is failing to set the temperature and pressure in an EDM prior to receiving an observation.
• Assume this occurred using the atmospheric conditions given in the authentic index of refraction was calculated as 1.0002672. IIf the fundamental wavelength for a standard atmosphere was 10.000 m, Then then the real wavelength produced by the EDM will be 10.000\1.0002672 = 9.9972m.
• Using Equation V = f . λ Having an observed distance of 827.329 m, the error, e, at the observed distance could be
• The effect of Neglecting to account for the atmospheric conditions produces a precision of Just|-0.223 |/827.329 or 1:3700.
• This is well under the computed precision of 1:195,000
• For each 1°C change in temperature, a 1 ppm error in the distance measurement will occur. As a rule, the current temperature and pressure should be set at the time of the measurement.
• However, it is often practical to set the temperature and pressure three or four times per day: morning, midmorning, noon, and midafternoon.
• At a minimum, the temperature and pressure should be set twice a day; once in the morning and at noon. However, a lower-accuracy survey will result. Table no-2 depicts the distance error in millimeters versus the error in temperature entered into an EDM for various lengths of sight.
|Error in Temperature||Length of Sights (m)|
Table No-2, Error in Observed Distance in Millimeters versus Error in Temperature for Various Sight Lengths
• Notice that an error of 1 mm can occur for all distances over 50 m when the temperature error is more than 9°C. This temperature difference can easily occur during certain times of the year between early morning, midday, and late afternoon.
• Also, note that this error will occur with only a 3°C temperature error for sight lengths that are greater than 300 m.
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• In case EDM equipment is carefully adjusted and precisely calibrated, instrumental errors ought to be exceedingly small
• To ensure their accuracy and reliability, EDM instruments should be checked against a first-order baseline at regular time intervals.
• For this purpose, the National Geodetic Survey (NGS) has established a number of accurate baselines in each state.
• All these are approximately a mile in length and placed in relatively flat areas. Monuments are put in the ends and at intermediate points along the baseline
• Though most EDM instruments are quite stable, sometimes, they get maladjusted and create erroneous frequencies.
• This results in faulty wavelengths that hamper space measurements. Periodic checking of this equipment against a calibrated baseline will Discover the existence of observational errors. It’s particularly important to make these checks if high-order surveys have been conducted.
• The corner cube reflectors used for EDM instruments are just another source of instrumental error. Since light travels in a lower velocity in glass than in air, the”effective center” of this reflector is really behind the prism.
• Therefore, it often doesn’t coincide with the plummet, a condition that produces a systematic error in distances referred to as the reflector constant.
• This situation is shown as per below fig 5. Notice that since the retroreflector is comprised of mutually perpendicular faces, the light travels a total distance of a + b + c = 2D from the prism.
Schematic of retroreflector there D is the depth the prism fig no. -5
• Additionally, given as a refractive index for glass, which is greater than air, the velocity of light in the prism is reduced this Equation V = c/n to create an effective distance of nD where n is the index refraction of the glass.
• The dashed line in as per above fig no 5 shows the effective center thus created. The reflector constant, K in the fig., can be as large as 70 mm and will vary with reflectors.
• Once known, this electrical center of the EDM can be shifted forward to compensate for the reflector constant.
• However, when an EDM instrument is being used regularly with several unmatched reflectors, this shift is impractical. In this instance, this offset for each reflector should be subtracted from the observed distances to obtain corrected values.
• With EDM instruments that are elements of total stations and are controlled by microprocessors, this constant can be entered through the keyboard and included in the internally computed corrections.
• Equipment manufacturers also create matching reflector sets for that the reflector constant is the same, thus allowing a single constant for use to get a set of reflectors with an instrument.
• By assessing precisely known baseline lengths to observed distances, a so-called system measurement constant could be set.
• This constant can when be applied to all subsequent observations for proper correction. Although calibration by means of a baseline is favored, if one is not available, the constant can be obtained with the following procedure.
• Three stations, A, B, and C, ought to be established in a straight line on flat ground, with stations A and C in a distance that is multiple units of the fundamental wavelength of the instrument apart.
• The fundamental wavelength from most instruments today is typically 10 m. Station B should be at between stations A and C, also at a multiple of the fundamental wavelength of the EDM. For example, the lengths AB and BC might be set at 40 m and 60 m, respectively, for an instrument with an as fundamental wavelength of 10 m.
• The length of AC, as well as the two components, AB and BC, ought to be observed several times together with the instrument-reflector constant set to zero and also the way of each length determined. From these observations, the following equation could be written:
• AC + K = (AB + K ) + (BC + K)
• for which K = AC – (AB + BC)
• where K = the system measurement constant to be added to correct the observed distances
• The procedure, including the centering of the EDM instrument and reflector, should be repeated several times very carefully, and the average value of that K adopted.
• Since different reflectors have varying offsets, this test should be performed with any reflector that will be used with the EDM, and this results marked on each to avoid confusion later.
• For the most precise calibration, this length AB and BC should be carefully laid out as even multiples of the instrument’s shortest measurement of wavelength.
• Failure to do this can because an incorrect value of K to be obtained. As shown as per above fig no 5, due to the construction of the reflector and the pole being located near this center of the reflector, the system measurement constant is typically negative.
• The video EDM-Reflector Offset Constant Determination, which is available on the companion website for this book, discusses this method.
• While the above procedure provides a method for determining a specific instrument-reflector constant, it is highly recommended that EDM instruments be calibrate using NGS calibration baselines.
• These baselines are established throughout the country to be used by surveyors. Their technical manual Utilization of Calibration Base Lines, that can be listed in the bibliography at the end of this chapter, provides guidelines on using the baselines and reduction in the observations providing the instrument-reflector offset constant and a scaling factor.
• Natural mistakes in EDM surgeries stem chiefly from atmospheric variations in pressure, temperature, and humidity, which affect the index of modify and refraction the wavelength of electromagnetic energy.
• The values of the variables have to be measured and used to correct observed distances. As demonstrated in humidity can generally be neglected when using electro-optical instruments, but this variable was important when microwave instruments were employed.
• The National Weather Service of adjusts atmospheric pressure readings to sea-level values.
• Since atmospheric pressure changes by approximately 1 . Of mercury (Hg) per 1000 feet of altitude, under no conditions ought to radio broadcast values for atmospheric pressure be utilized to fix distances.
• Instead, atmospheric pressure should be the measured by an aneroid barometer that is calibrated against a barometer not corrected to sea level.
• Many collage and high school and physics departments have these barometers. EDM instruments with total stations have onboard microprocessors that use atmospheric variables, input through the keyboard, to compute corrected distances after making observations before displaying them.
• For older instruments, varying this transmission frequency made corrections, or they could be computed manually after the observation.
• Equipment manufacturers provided charts and tables that assisted in this process. The magnitude of error in EDM due to errors in observing atmospheric pressure and temperature is indicated as per below fig No-6. Note a 10°C temperature error, or a pressure difference of 25 mm (1 in.) of mercury, each produce a distance error of about 10 ppm.
• Thus in case a radio broadcast atmospheric pressure is entered into an EDM in Denver, Colorado, the resulting Distance error might be as good as 50 ppm, and a 200-m distance could in error by up to1 cm.
Errors in EDM produced by pressure or temperature errors. Fig No-6
• A microclimate can exist at the layers of the atmosphere immediately above a surface like the ground. Field experiments prove that temperatures on or close to the ground maybe 10° into 25° higher or lower than those at shoulder height.
• Since this microclimate can substantially change this index of refraction, it’s important to maintain a line of sight that’s at least 0.5 m above the surface of the ground.
• On long lines of sight, the observer ought to be cognizant of intervening ridges or other items that can exist between the instrument and reflector, which might lead to problems in meeting this condition.
• If this condition can’t be met, the height of the reflector might be increased. Under certain conditions, it could be required to set an intermediate point on the encroaching surface to ensure light in the EDM doesn’t travel through those lower layers.
• For the most precise work, long lines, a sampling of those atmospheric conditions along the line of sight ought to be observed.
• In this case, it may be required to elevate the meteorological instruments. This may be difficult where the terrain gets considerably lower than the sightline. In such cases, the atmospheric measurements for the ends of this line could be measured and averaged.
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