Section 5 Electronic Distance Measurement Systems

Essentially the instruments mentioned in this chapter consist of a transmitter, set up at one end of the length to be measured, sending out a continuous wave, to the receiver at the other end. This wave, termed the carrier wave, is then modulated and the length determined as explained later.

Choice of frequency

This is a fundamental problem in EDM systems. The electromagnetic spectrum is continuous from visible light with frequencies of the order of 1014 HZ, corresponding to wavelengths of the order of 10-6 m, to long radio waves with frequencies of 104 or 105 Hz, corresponding to wavelengths of the order of 104 m. The relationship between frequency and wavelength is shown in Fig 1.

It is convenient to divide the instruments in current use into three distinct categories depending on the frequency of the carrier signal:

(1) low frequency radio systems with carrier frequencies of the order of 105 to 106Hz (wavelengths of the order of 103 or 102m),

(2) microwave radio systems with carrier frequencies of the order of 1010 Hz (wavelengths of the order of 10-2 m),

(3) visible and infra-red light systems with carrier frequencies of the order of 1014Hz (wavelengths of the order of 10-6m).

Generally speaking it is found that the lower frequency signals provide greater range but require larger transmitters, and being affected by the atmosphere are therefore less accurate for EDM purposes than those of higher frequency. However, for marine and air navigation and for much hydrographic work long range is vital, accuracy requirements are comparatively low and permanent or semi-permanent transmitters are appropriate. All these factors point to the use of low frequency signals and indeed most position-fixing systems operate in the low or medium frequency range. In these ranges wavelengths are of the order of 102 or 103m and the phase differences can be measured directly in terms of the basic wave.

For practical field instruments for engineering and land surveying the higher frequencies are most useful as the instruments can be made small and transportable and the propagation through the atmosphere is more stable. However, at these frequencies it is more difficult to measure the phase differences, as discussed later, and the wavelengths are so small that it is impractical to use directly the waves themselves for the measurements. The solution adopted is to modulate the high frequency carrier with a lower frequency wave and to use the modulated wave for measurement

purposes.

Modulation is a process whereby certain characteristics of the carrier wave are varied or selected in accordance with another signal. The carrier signal does not have to be at a precisely determined frequency but it must be produced efficiently and in such a form that it can be modulated easily. The modulation signal, being the one used for the actual measurement has to be at an accurately controlled frequency. It is often produced by a crystal-controlled oscillator which may be housed in a thermo-statically-controlled oven to enhance the stability of the signal: a warming-up time should be allowed for the most precise results.

Some instruments use an amplitude modulation, whilst others use a frequency modulation, the differences being indicated in Fig. 2, but the difference is unimportant from the point of view of the operator. In amplitude modulation the amplitude of the carrier wave is varied above and below its unmodulated value by an amount proportional to the amplitude of the modulation signal and the frequency of that signal. The amplitude of the carrier remains constant in frequency modulation but now its frequency is continuously varied by an amount proportional to the instantaneous amplitude of the modulating signal and at the frequency of that signal.

Phase difference and distances

There are two options available in the use of microwaves for distance measurement, either pulse transit times or phase changes being measured. In the former case the unmodulated carrier is usually a pulse train or series of pulses, not the continuous wave referred to previously. When resolution of distance to 0.01m or better is required the latter system is usually adopted, being based on the relationship between the transmitted and received signal.

Consider a transmitter sending out an oscillating signal at a constant frequency, f, to a receiver touching it. Were the two touching, then the transmitted signal and received signal would be in phase, but as the receiver moves away from the transmitter the received signal will lag behind the transmitted signal due to the time of travel of that signal. Thus there will be a phase difference between the signals, and if the difference in phase between the signals at the transmitter and the receiver is measured the distance between them can be deduced. When that distance is equal to the wavelength the phase difference will be 2π and the signals will be in phase, as in fact they will be each time the distance apart is an integral wavelength. Therefore within an unknown distance, d, all that one measurement of phase difference will give is the residual part of d over and above an integral number of completed wavelengths.

It is not possible to compare instantaneously the phase of the signals at a transmitter and distant receiver. Therefore EDM systems adopt the technique of either retransmitting the signal back to the transmitter (microwaves) or reflecting the signal back to the transmitter (electro-optical) and making the phase comparison there. Thus it is always a double path which is measured.

The fundamental equation which relates slope distance to phase delay or phase difference may be written as

dna2where d = double distance, i.e. total travel of wave λ= modulation wavelength = V0/μf

n = number of complete wavelengths within d

φ= phase difference between the outgoing and incoming signals

a = an additive constant related to geometrical and electrical eccentricities μ= refractive index f = frequency

Generally n is unknown and d can be found by repeating the measurements of phase difference at frequencies differing from a 'fine' measuring frequency. In certain instruments this process is carried out automatically whereas in others the process is carried out by the operators.

In Fig 3 two modulation frequencies are shown with the phase delays then arising due to the distance d of travel. The wavelengths are such that five given by one frequency occupy the same length as four given by the other (lower) frequency. This particular length (200m) is also covered by one whole wavelength whose frequency is equal to the difference of the two modulation frequencies. Moreover the difference in phase between the two is always equal to the phase of the wave given by the difference frequency. Thus, measuring the two phase delays consequent to travelling over a double distance up to 200m is equivalent, on subtraction, to measuring the phase which would have been given had the difference frequency been applied. A phase difference of 2

π applies to a distance of 200m, and so if a phase difference of 1.54π be deduced on subtraction, a double distance of 1.54π×200/2πm is involved, i.e. 154m. Naturally when a distance in excess of 200m is being measured, this particular difference frequency gives an unknown number of whole lengths of 200 m plus a part length of 200 m. Thus a set of different frequencies has to be applied, which when related to the basic 'fine' frequency allows stages of double distance such as 2000 m, 20000 m and 200 000 m to be evaluated without ambiguity.

In the measurement illustrated the phase difference with the lower wavelength was 1.70πand since this corresponds to 1.70π×40 / 2π, i.e. 34.0 m, the distance measured must therefore have been (n×40 + 34.0) where n is an integer. The measurement with the second wavelength was made primarily to enable n to be identified.

The figures in the illustration have been arranged to be exact, and so the distance calculated using the difference frequency works out exactly as 154m, i.e. (3×40+34). In practice there may be small inaccuracies in the measurements and the result from the difference frequency may not tally exactly with the first measurement, e.g. if the phase in the second measurement had been 0.15π the result would have been 1.55π×200/2π, i.e. 155 m but the distance was known to be (n× 40+ 34.0) and the result is close enough to enable n to be identified as 3 giving the distance as 154.0m as before. This is an important point which should be well understood as it is this which is the reason for the unique accuracy of EDM. If the wavelength is correct and the integral number of wavelengths is correctly identified then the major part of the distance is determined without error; the only part of the distance which is measured is the residual part over and above an integral number of wavelengths.

Effective wavelength

It has been mentioned above that the length of the double path is always measured by EDM systems.

To measure a distance D with a signal of wavelength λ and a double distance d = 2D with a signal of wavelength 2λgives an identical result in respect of both numbers of complete wavelengths and residual phase difference. Instead of determining the actual double distance travelled by the signal and then dividing it by two, it is convenient to use an effective wavelength of half the true wavelength and thence to calculate the single distance directly. By using effective wavelengths of λA = 20m andλE= 25m the same single distance of 77 m would have been derived.

In practice to achieve high precisionλA is kept comparatively short, 10 m being a common value.

Precision is determined also by the accuracy of measurement of φ. Some instruments can resolve to only 1% phase others to 0.1% or better.

Phase measurements may be achieved in various ways, i.e.

(1) by a resolver which consists of a stator and rotor, the latter being placed into an angular position with respect to the former corresponding to the phase difference between the transmitted and returned signals,

(2) by a variable light path,

(3) by a digital system in which the transmitted wave when passing through zero voltage activates a counter which counts pulses of a selected frequency until stopped by the returned wave.

It is recommended that reference be made to Electromagnetic Distance Measurement, second edition (Granada Technical Books) by C. D. Burnside for more detailed information on this and other aspects of the subject.

In modern instruments the phase difference between the outgoing and incoming signals is not measured at the operating frequencies but is transformed to a corresponding difference at much lower frequency. This greatly improves the accuracy of measurement of phase difference such that resolution to one thousandth part of a cycle can be readily obtained.

New Words and Expressions

Electronic Distance Measurement：电子测距仪 transmitter：发射机；传送机，传递器 send out：发送，派遣，放出 receiver：接收机 carrier wave：载波

modulate：vt 调整，调制 frequency：频率

fundamental：基础的，基本的

electromagnetic spectrum：电磁波谱，电磁波 visible light：可见光 wavelength：波长 radio wave：无线电波

category：种类，类别，范畴 carrier signal：载波信号

low frequency radio system：低频无线电系统 microwave：微波

carrier frequency：载波频率

visible and infra-red light：可见光和红外光 generally speaking：一般来说 atmosphere：大气，空气，气氛

marine and air navigation：航海和航空导航 hydrographic work：水利工程 permanent：永久的，持久的 land surveying：土地测量 higher frequency：高频

transportable：可运输的；便携式电视机（或计算机） propagation：传播

in accordance：一致，依照

crystal-controlled oscillator：晶（体）控（制）振荡器 thermo-statically-controlled oven ：热静控制腔 warming-up time：预热时间 amplitude modulation：调幅 frequency modulation：调频

proportional：成比例的，相称的，

constant：不变的，持续的；常数，恒量

instantaneous amplitude：瞬时振幅 Phase difference：相位差，相位差分 pulse transit times：脉冲经过次数 phase change：相位变化 pulse train：脉冲列，脉冲链 resolution：分辨率 oscillate：振荡

lag behind：落在后面，滞后于 integral：完整的，整体的，积分的 electro-optical：光电的 refractive index：折射率 phase delay：相位延迟

consequent：作为结果的，随之发生的 equivalent：相等的，相当的

ambiguity.：含糊，模糊，不明确 identify：.识别，鉴别

comparatively：比较地，相当地 precision：精确，精密度，精度 resolve：解决，决定

phase measurement：相位测量 resolver：分相器，分解器；溶剂 stator：定子，固定片

rotor：转子，回转轴，转动体 voltage：电压，伏特数 returned wave：回波