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ELECTRONIC DISTANCE MEASUREMENT
Dheeraj Kumar INTRODUCTION There are three methods of measuring distance between any two given points: 1. Direct distance measurement (DDM), such as the one by chaining or taping. 2. Optical distance measurement (ODM), such as the one by tachometry, horizontal subtense method or telemetric method using optical wedge attachments. 3. Electro-magnetic distance measurement (EDM) such as the one by geodimeter, tellurometer or distomat etc. The method of direct distance measurement is unsuitable in difficult terrain and some times impossible when obstructions occur. The problem was overcome after the development of optical distance measuring methods. But in ODM method also, the range is limited to 150 to 150 m and the accuracy obtained is 1 in 1000 to 1 in 10000. Electromagnetic distance measurement (EDM) enables the accuracies upto 1 in 105, over ranges upto 100 km. EDM is a general term embracing the measurement of distance using electronic methods. In electro-magnetic (or electronic) method, distances are measured with instruments that rely on propagation, reflection and subsequent reception of radio, visible light or infrared waves. There are in excess of fifty different EDM systems available. However, the following instruments are quite common: • • • Geodimeter Tellurometer Distomat

The EDM method is based on generation, propagation, reflection and subsequent reception of electromagnetic waves. The type of electromagnetic waves generated depends on many factors but principally, on the nature of the electrical signal used to generate the waves. E. Bergestrand of the Swedish Geographical Survey, in collaboration with the manufacturers, Messrs AGA of Sweden, developed a method based on the propagation of modulated light waves using instrument called geodimeter. Another instrument, called tellurometer was developed, using radio waves. ELECTROMAGNETIC WAVES

Fig. 1a: Periodic Sinusoidal Waves

Some of the important terms related to the wave are defined to explain the properties of electromagnetic waves The number of times the wave completes a cycle in one second is termed as frequency of the wave The frequency is represented by f hertz (Hz) 1 hertz (Hz) is one cycle per second. Thus, if the frequency f is equal to 100 Hz, it means that the waves completes 100 cycles per second. The length traversed in one cycle by the wave is termed as wave length and is denoted by λ. (metres). Thus the wavelength of a wave is the distance between two identical points (such as A and E or B and F) on the wave Wave length of a wave is the distance between two identical points (such as A and E or B and F) on the wave. The period is the time taken by the wave to travel through one cycle or one wavelength. It is represented by T seconds. The velocity (v) of the wave is the distance traveled by in one second. The frequency, wavelength and period can all vary according to the wave producing source. However, the velocity v of an electromagnetic wave depends upon the medium through which it is traveling. The velocity of wave in a vacuum is termed as speed of light, denoted by symbol c, the value of which is presently known to be 299792.5 km/s. For simple calculations, it may be assumed to be 3 x 108 m/s. The above properties of an electromagnetic wave can be represented by the relation,
f = c 1 T V=ƒλ

λ

=

PROPAGATION OF ELECTROMAGNETIC ENERGY
Velocity of EM energy ƒ is the frequency in hertz (cycles/second) & λ is the wavelength In vacuum the velocity of electromagnetic waves equals the speed of light. V = c/n n >1 n is the refractive index of the medium through which the wave propagates & c is the speed of light = 299 792 458 m/sec Therefore, f λ = c/n or λ = cf/n (i.e. λ varies with n) Note that n in any homogeneous medium varies with the wavelength λ. White light consists of a combination of wavelengths and hence n for visible light is referred to as a group index of refraction. For EDM purposes the medium through which electromagnetic energy is propagated is the earth’s atmosphere along the line being measured. It is therefore necessary to determine n of the atmosphere at the time and location at which the measurement is conducted. The refractive index of air varies with air density and is derived from measurements of air temperature and atmospheric pressure at the time and site of a distance measurement.

THE FRACTION OF A WAVELENGTH AND THE PHASE ANGLE

90°

+r
A 0° m pli tu de

λ ½λ λ ½λ λ

θ
180 °

270 °

-r

¼λ λ

¼λ λ

¼λ λ

¼λ λ

Fig. 1b: Periodic Sinusoidal Waves Another property of the wave, known as phase of the wave, and denoted by symbol φ, is a very convenient method of identifying fraction of a wavelength or cycle, in EDM. One cycle or wave-length has a phase ranging from 0° to 360°. Various points A, B, C etc. of Fig. 1 has the following phase values: Point Phase φo For θ = 0° the fraction is 0 A 0 B 90 C 180 D 270 E 360

A fraction of a wavelength can be determined from a corresponding phase angle θ For θ = 90° the fraction is ¼ For θ = 180° the fraction is ½ For θ = 270° the fraction is ¾ For θ = 360° the fraction is 1 Fig. 2 gives the electromagnetic spectrum. The type of electromagnetic wave is known by its wavelength or its frequency. However, all these travel with a velocity approximately equal to 3 x 108 m/s. This velocity forms the basis of all electromagnetic measurements.

Fig. 2: Electromagnetic Spectrum

MEASUREMENT OF TRANSIT TIMES Fig. 3 (a) shows a survey line AB, the length D of which is to be measured using EDM equipment placed at ends A and B. Let a transmitter be placed at A to propagate electromagnetic waves towards B, and let a receiver be placed at B, along with a timer. If timer at B starts at the instant of transmission of wave from A, and stops at the instant of reception of incoming wave at B, the transit time for the wave from A and B is known.

Fig. 3: Measurement of Transit Time From this transit time, and from the known velocity of propagation of the wave, the distance D between A and B can be easily computed. However, this transit time is of the order of 1x 10-6 s which requires very advanced electronics. Also it is extremely difficult to start the timer at B when the wave is transmitted at A. Hence a reflector is placed at B instead of a receiver. This reflector reflects the waves back towards A, where they are received (Fig. 3 (b)]. Thus the equipment at A acts both as a transmitter as well as receiver. The double transit time can be easily measured at A. This will require EDM timing devices with an accuracy of ±1 x 10-9 s. PRINCIPLES OF ELECTRONIC DISTANCE MEASUREMENT If an object moves at a constant speed of V over a straight distance L in a time interval ∆t, then L= V∆t = (c/n) ∆t (1) Knowing the speed of light c and being able to determine the refractive index, we could measure the time interval it takes for an electromagnetic wave to move from A to B to determine the distance D between A and B. But since the speed of light (c) is very high, the time interval ∆t would need to be measured extremely accurately. Instead, the principle of EDM is based on the following relationship: In Fig. 3 (b), the wave transmitted from A towards B is instantly reflected from B towards A, and is then received at A, as shown by dotted lines. The same sequence is shown in Fig.3 (c) by opening out the wave, wherein A and A' are the same. The distance covered by the wave is 2D = n λ + ∆ λ (2) Here D is the distance between transmitter and reflector, n is an integer number of whole wavelengths, ∆ is a fraction of a wavelength, λ is the wavelength, n is the no. of complete cycle. So D can be determined from λ, n and ∆ Measurement of ∆ λ is known as phase comparison

Phase comparison Generally, the various commercial EDM systems available do not measure the transit time directly. Instead, the distance is determined by measuring the phase difference between the transmitted and reflected signals. This phase difference can be expressed as fraction of a cycle which can be converted into units of time when the frequency of wave is known. Modern techniques can easily measure upto 1/1000 part of a wavelength.
1 2 3 4 5 6 7 8 9 10 11 12

A λ λ λ λ λ λ λ 2D Fig. 3 Phase comparison ∆λ= ∆λ=
phase _ difference _ in _ deg ree xλ 360 0 (ϕ 2 −ϕ 1) o xλ 360 o

A’ λ λ λ λ λ ∆

OR

(3) (4)

φ1 is the phase of wave as it is transmitted at A φ2 is the phase of wave as it is received at A
Determination of nλ in the above equation is referred as resolving the ambiguity of the phase comparison It can be determined by: 1. By increasing the wave length manually in multiples of 10, so that a coarse measurement of D is made and enabling n to be deduced. 2. By measuring the line AB using three different wavelengths (closely related) so as to form three simultaneous equations of the form : Solving for the integer number (n) of (Resolving the ambiguity in the number of whole wave lengths): whole wavelengths

Additional waves of known lengths λ3 = kλ2 and λ2 = k λ1 (k is a constant), are introduced to measure the same distance 2D: 2D = (n3 + ∆3) λ3 2D =(n2 + ∆2 ) λ2 2D =(n1 + ∆1) λ1 (5) (6) (7)

Determining ∆1 ∆2 and ∆3 by measuring phase angles φ1 φ2 and φ3 and solving the above equations simultaneously yields 2D (Note: For 2D < λ3, ∆ 3 = 0).

λ2
1 2 3 4 5 6

∆3
7 8 9 10 11

∆2

12

A λ λ λ λ λ λ λ D
Fig. 4: Resolving the ambiguity by waves of different wavelength

A’ λ λ λ λ λ p1

MODULATION As stated above, EDM measurements involve the measurement of fraction ∆ λ of the cycle. Modern phase comparison techniques are capable of resolving to better than 1/1000 part of a wavelength. Assume ±10 mm to be the accuracy requirement for surveying equipment, this must represent 1/ 1000 of the measuring wavelength. This means that λ == 10 x 1000 mm = 10 m, which is a maximum value. However, by use of modem circuitry, λ can be increased to 40 m, which corresponds to f= 7.5 x 106 Hz. Thus, the lowest value of f that can be used is 7.5 x 106 Hz. At present, the range of frequencies that m be used in the measuring process is limited to approximately 7.5 x 106 to 5 X 108 Hz. In order to increase the accuracy, it is desirable to use an extremely high frequency of propagation. However, the available phase comparison techniques cannot be used at frequencies greater than 5 x 108 Hz which corresponds to a wavelength λ = 0.6 m. On the other hand, the lower frequency value in the range of 7.5 x 106 to 5 x 108 Hz is not suitable for direct transmission through atmosphere because of the effects of interference, reflection, fading and scatter. The problem can be overcome by the technique of modulation wherein the measuring wave used for phase comparison is superimposed on a carrier wave of much higher frequency. EDM uses two methods of modulating the carrier wave: (a) Amplitude modulation. (b) Frequency modulation. In amplitude modulation, the carrier wave has constant frequency and the modulating wave (the measuring wave) information is conveyed by the amplitude of the carrier waves. In the frequency modulation, the carrier wave has constant amplitude, while its frequency varies in proportion to the amplitude of the modulating wave. Frequency modulation is used in all microwave EDM instruments while amplitude modulation is done in visible light instruments and infrared instruments using higher carrier frequencies.

Measuring wave

measuring wave

Amplitude modulation

Frequency modulation

Fig 5: Modulation TYPES OF EDM INSTRUMENTS Depending upon the type of carrier wave employed, EDM instruments can be classified under the following three heads: 1. Microwave instruments, 2. Visible light instruments 3. Infrared instruments. All the above three categories of EDM instruments use short wavelengths and hence higher frequencies.

1. Microwave instruments These instruments come under the category of long range instruments, where in the carrier frequencies of the range of 3 to 30 GHz enable distance measurements upto 100 km range. Tellurometer comes under this category. Phase comparison technique is used for distance measurement. This necessitates the erection of some form of reflector at the remote end of the line. If passive reflector is placed at the other end, a weak signal would be available for phase comparison. Hence an electronic signal is required to be erected at the reflecting end of the line. This instrument, known as remote instrument is identical to the master instrument placed at the measuring end. The remote instrument receives the transmitted signal, amplifies it and transmits it back to the master in exactly the phase at which it was received. This means that microwave EDM instruments require two instruments and two operators. Frequency modulation is used in most of the microwave instruments. The method of varying the measuring wavelength in multiplies of 10 is used to obtain an unambiguous measurement of distance. The microwave signals are radiated from small aerials (called dipoles) mounted in front of each instrument, producing directional signal with a beam of width varying from 20 to 200. Hence the alignment of master and remote units is not critical. Typical maximum ranges for microwave instruments are from 30 to 80 km, with an accuracy of ±15 mm to ± 5 mm/km. Tellurometer It is an EDM which uses high frequency radio waves (micro-waves) for measuring distances. It is a highly portable instrument and can be worked with 12 to 24 volt battery. For measuring distance, two Tellurometer are required, one to be stationed at each end of the line, with two highly skilled persons, to take observations. One instrument is used as a master unit and the other as a remote unit. Just by pressing a button a master can be converted in to remote unit and vice-versa. A speech facility (communication facility) is provided to each operator to interact during measurement. 2. Visible light instruments These instruments use visible light as carrier wave, with a higher frequency, of the order of 5 x 1014 Hz. Since the transmitting power of carrier wave of such high frequency falls off rapidly with the distance, the range of such EDM instruments is lesser than those of microwave units. A geodimeter comes under this category of EDM instruments. The carrier, transmitted as light beam, is concentrated on a signal using lens or mirror system, so that signal loss does not take place.

Fig. 6: Corner Cube Prism Since the beam divergence is less than 1 °, accurate alignment of the instrument is necessary. Corner-cube prisms, shown in Fig. 6 are used as reflectors at the remote end. These prisms are constructed from the corners of glass cubes which have been cut away in a plane making an angle of 45° with the faces of the cube.

The light wave, directed into the cut-face is reflected by highly silvered inner surface of the prism, resulting in the reflection of the light beam along a parallel path. This is obtainable over a range of angles of incidence of about 20° to the normal of the front face of the prism. Hence the alignment of the reflecting prism towards the main EDM instrument at the receiver (or transmitting) end is not critical. The advantage of visible light EDM instruments, over the microwave EDM instruments is that only one instrument is required, which work in conjunction with the inexpensive comer cube reflector. Amplitude modulation is employed, using a form of electro-optical shutter. The line is measured using three different wavelengths, using the same carrier in each case. The EDM instruments in this category have a range of 25 km, with an accuracy of ± 10 mm to ± 2 mm/km. The recent instruments use pulsed light sources and a highly specialized modulation and phase comparison techniques, and produce a very high degree of accuracy of ± 0.2 mm to ± 1 mm/km with a range of 2 to 3 km. Geodimeter This instrument which works based on the propagation of modulated light waves, was developed by E. Bergestrand of the Swedish Geographical Survey in collaboration with the manufacturer M/s AGA of Swedish. The instrument is more suitable for night time observations and requires a prism system at the end of the line for reflecting the waves. Infrared instruments The EDM instruments in this group use near infrared radiation band of wavelength about 0.9 µm as carrier wave which is easily obtained from gallium arsenide (Ga As) infrared emitting diode. These diodes can be very easily directly amplitude modulated at high frequencies. Thus, modulated carrier wave is obtained by an inexpensive method. Due to this reason there is predominance of infrared instruments in EDM. Wild Distomat fall under this category of EDM instruments. The power output of the diodes is low. Hence the range of these instruments is limited to 2 to 5 km. However, this range is quite sufficient for most of the civil engineering works. The EDM instruments of this category are very light and compact, and these can be theodolite mounted. This enables angles and distances to be measured simultaneously at the site. A typical combination is Wild DI 1000 infra-red EDM with electronic theodolite ('Theomat'). The accuracy obtainable is of the order of ± 10 mm, irrespective of the distance in most cases. The carrier wavelength in this group is close to the visible light spectrum. Hence infrared source can be transmitted in a similar manner to the visible light system using geometric optics, a lens/mirror system being used to radiate a highly collimated beam of angular divergence of less than 15'. Corner cube prisms are used at the remote end to reflect the signal. Electronic tacheometer, such as Wild TC 2000 'Tachymat' is a further development of the infrared (and laser) distance measurer, which combines theodolite and EDM units. Microprocessor controlled angle measurement give very high degree of accuracy, enabling horizontal and vertical angles, and the distances (horizontal, vertical, inclined) to be automatically displaced and recorded. Distomat DI 1000 It is a very small, compact EDM, particularly useful in building construction and other Civil Engineering works, where distance measurements are less than 500 m. It is an EDM that makes the meaning tape redundant. To measure the distance, one has to simply point the instrument to the reflector, touch a key and read the result.

ERRORS IN EDM The accuracy obtained with EDM instruments are affected by the factors: 1. 2. 3. 4. 5. 6. Refractive index (n) Modulation frequency (f) Measurement of phase differences (φ) Instrument constant (k) Zero and non-linearity correction (Z) and, Centering of the instrument (e)

The Refractive Index (n) is a function of the following atmospheric parameters: temperature, pressure, and humidity. The error in determination of the n depends on the type of meteorological instruments. The trend in today's EDM instrument production is to emphasize automation in shortdistance survey and measurement The Basic Modulation Frequency (f) in modern instruments is produced by quartz oscillators, which can reach accuracies of about 10-6 within certain temperature limits. For short-distance surveys an error of 10-5 is tolerated. Phase measurement Phase Measurement is the measurement of the phase shift. This phase shift can be measured with an accuracy of 10-4. Since error in phase measurement is of random nature, the repetition of measurements over the same line reduces this error. Instrument Constant (k) is specified in the manuals Zero and Non-linearity Correction can be determined by several ways. The best approach is to select an about 1 km long line and divide it into several sections. From these sections, all possible combinations of distances are accurately measured by the EDM to be tested. This procedure yields the least-squares solution for the zero correction and its standard deviation. Centering of the Instrument is usually done by the use of an optical plummet. The accuracy obtained depends on the skill of the operator in handling the instrument. From the error sources summarized, the error σp in measuring the phase difference. The error σz in determining the zero correction and the error σe in centering the instrument are all independent of the distance as well as of each other. Their combined effect 1S denoted as a. The error σn in the determination of the refractive index and the error σf in the factory calibrated modulation frequency are dependent on the measured distance D Their combined influence on the measured length is usually denoted as b in general literature of EDM. The predicted standard deviation in the measurement then can be expressed as:

σ = a 2 + (bD) 2

(8)

In manufacturer's specification it is usually expressed in the simplified symbolic form: Accuracy = ± (a + bD) (9)

Where, the second term reads: millimeters per kilometer when D is given in kilometers. The above procedure is the way the instrument manufacturers determine the accuracy specifications in their instrument manuals, with exclusion of the entering error, which bears no relation to any type or quality of instrument.

Measurement System: Operator EDM tribrach tripod Atmosphere (temp, press, humidity Prism tribrach tripod

There are three types of errors that may occur in EDM measurement. Constant or zero error related to misalignments in the EDM and prism First velocity correction related to meteorological conditions Scale error due to oscillator frequency changes

BASIC COMPONENTS OF EDM
Electro - Optical Instruments 1. The Light Sources a. Ga Al As (Gallium Aluminium Arsenide) Infra - red diode (0.950 µm) b. Ga Al As Lasing diode (0.800 µm) c. He - Ne Laser (0.63 µm) d. Xenon Flash Tube (0.480 µm) 2. The Modulator for modulation of carrier wave at a modulation frequency produced by oscillator. 3. The Transmitter (lens system) 4. The Reflector to reflect rays parallel to the incoming ones. 5. The Receiver (lens system) 6. The Photo Detector transforms light bean intensity into variation of current. 7. The Oscillator produces the modulation frequency [Temperature - Compensated Crystal Oscillator (TCXO) are commonly used in short range EDM instrument. 8. The Resolver Shifts the phase of the reference signal. 9. The Phase Detector provides the phase comparison between the return and reference signal. 10. The Display - readout the distance. Microwave Instruments: 1. The Microwave Sources - The klystron (a resonator) or Gunn Diodes (Instruments of X-band (18 mm) and K-band (30 mm) are most popular. 2. Antenna to transmit and receive the signals. 3. The Mixer to mix transn1itted and received signals. 4. The Demodulator / Discriminator to demodulate modulated signals into alternating current.

5. The oscillator 6. The Resolver 7. The Phase Detector 8. The Display Reflector In the Electro-optical instruments, the Carrier Wavelength is close to the visible light spectrum and is transmitted in the similar manner to the visible light system. These devices should have the following properties: 1. Good reflectivity. 2. Complete illumination of the receiver optics of the instrument. 3. No change in direction of emerging rays through small movements of the reflecting device. To satisfy the above conditions, fo11owing reflectors have proved to be more suitable reflector system. Spherical Optical System It is a spherical mirror set at the rear end, which focuses the waves into parallel beam. Corner Cube Prisms They were first employed by the U.S. Army Map Service in 1953 and are now almost extensively used. These prisms are constructed from corners of glass cube, which have been cut away in a plane making an angle of 45° with the faces of the cube. The light wave, directed into cutface is reflected by highly silvered inner surfaces of the prism, resulting in the reflection of the light beam along a parallel path. The beam entering and leaving the corner cube, although parallel, are separated by finite distance called translation. The size of the corner cube refers to the area of the front face, which may be either circular or rectangular. The dimension of the corner cube depends on how much translation is required to shift the transmitted ray from the transmitting optics to the receiving optics in the instrument, after being reflected from the corner cube. Therefore, it is important for surveyors to use only the kind of prisms specified by the manufacturer. Offset The zero point of the electronic distance measurement should lie in the standing axis of the theodolite on which the EOM instrument in mounted. If not, the offset of the zero point from the standing axis has to be taken into account. A sin1ilar situation applies to the reflector and the reflector offset has also to be taken into account. The sum of the two corrections in known as the additive constant C (C = Instrument offset + Prism offset). This constant will vary according to the combination of Instrument and prism used. It is normally set to zero by the manufacturer for a given combination. (The reflector constant may be eliminated by advancing the electrical center of the EDM by a corresponding amount during manufacture). Batteries The batteries presently used as power sources for EOM instruments are: Alkaline/Lithium Batteries.

The use of primary batteries in EDM is not common, as the cost may be prohibitive. However, some instruments permit alternative operation with primary batteries Sealed Nickel-Cadmium Batteries (Rechargeable batteries) Most EDM instruments employ above batteries, which are series combinations of individual cylindrical cells assembled in packs. The individual cells are usually rated at 1.2 V DC

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