Electronic Distance Measurement

Historically, the development of electro-optical distance meters evolved from techniques used for the determination of the velocity of light. Fizeau determined the velocity of light in 1849 with his famous cogwheel modulator on a line of 17.2 km length: Light passed through the rotating cogwheel, travelled to a mirror at the other end of the line, was reflected and returned to the wheel where the return light was blocked off by the teeth at high revolutions of the wheel. Fizeau’s experiment employed for the first time the principle of distance measurement with modulated light at high frequencies. Later, Foucault employed a rotating mirror in 1862 and Michelson (1927) a rotating prism in 1926 for similar experiments. According to Zetsche (1979), the first electro-optical distance meter was developed by Lebedew, Balakoff and Wafiadi at the Optical Institute of the U.S.S.R. in 1936. In 1940, Hüttel published a technique for the determination of the velocity of light using a Kerr-cell modulator in the transmitter and a phototube in the receiver. This inspired the Swedish Scientist E. Bergstrand to design the first “Geodimeter” (for geodetic distance meter) for the determination of the velocity of light in 1943. The first commercial instrument (Geodimeter NASM-2) was produced by the Swedish company AGA and became available in 1950. With the early Geodimeters, longer distances could only be measured at night. An important development was the introduction of the heterodyne technique to electro-optical distance meters by Bjerhammar in 1954, which enabled the execution of more accurate phase measurements at more convenient low frequencies (Bjerhammar 1971). The first instrument to employ the heterodyne principle was the Geodimeter Model 6A. Subsequently, the principle was employed in distance meters of all makes. The (laser) Geodimeter with the longest range (60 km), the Model 8, was released in 1968. It has been used widely in high order geodetic networks throughout the world.

The frequency f and the wavelength λ of electromagnetic waves are related by the following fundamental equations: where c = velocity of electromagnetic waves in a medium, usually referred to as the velocity of light in the medium f = frequency of signal λ = wavelength in the medium.

There are many ways to measure distances by electronic means. Four basic principles will be presented although only one will be discussed in greater depth.

EDM instruments are classified according to the type of carrier wave employed. Instruments using light or IR waves are classified as electro-optical instruments. Instruments based on radio waves are generally called microwave instruments. Because of the different structure of these two types of instruments, they will be discussed separately.

The transmittance of the atmosphere is usually described by the quotient of incident radiant power divided by transmitted radiant power. It is a measure of the attenuation and extinction of wave propagation. The transmittance is a function of numerous variables: wavelength, distance, temperature, barometric pressure, gaseous mixture, rain, snow, dust, aerosols, bacteria and, in more detail, the size of particles of all these constituents. The limitations of atmospheric transmittance are given by the scattering and absorption of the emitted radiation. Scattering by air molecules (Rayleigh Scattering) and scattering by larger aerosol particles (Mie scattering) can be distinguished. Absorption in several spectral regions is mainly caused by water vapour, carbon dioxide and ozone. Figure 5.1 depicts the transmittance of atmosphere as a function of wavelength for a part of the visible and near-infrared (NIR) spectrum under specific conditions. The figure shows that only a limited part of the NIR spectrum is suitable for EDM.

The basic formula for the computation of d was introduced in Sections 2.1 and 3.1.1. Equation (3.1) may be written, after substitution of Eq. (2.4) for c, to describe the distance value d’ actually displayed on a distance meter.

In principle, the wave path d₁ is obtained after applying the two velocity corrections to an actual observation of the length. Unless the length is subsequently processed in a three-dimensional network adjustment, it has to be reduced to the equivalent spheroidal distance on a geodetic reference surface, for example the Australian Geodetic Datum. Selected methods of reduction to the spheroid will now be reviewed, prior to a discussion of additional corrections and computations.

Occasionally, some additional EDM corrections are required in order to achieve the collinearity requirements between EDM wave path and zenith angle ray paths which were assumed during the derivation of the geometrical corrections in Sect. 7. A number of approaches to the problem are discussed below. These derivations are followed by the discussion of three EDM-related computational problems, namely the computation of height differences from measured zenith angles and slope distances (EDM-Trigonometric Heighting), the computation of the coefficient of refraction from reciprocal zenith angle (and slope distance) measurements and the centring of measured zenith angles and slope distances from satellite stations to their respective centre stations. This section then concludes with fully worked examples for the reduction to the spheroid of the measurements of a short and a long EDM line.

Distance meters featuring visible light or near infrared (NIR) radiation as carrier waves are called electro-optical EDM instruments. These carrier waves follow the laws of geometrical optics; normal telescopes are used for transmitting and receiving the signals.

Apart from military laser rangers, electro-optical EDM instruments need a device at the target station which reflects the light (or infrared) beam back to the instrument. Reflecting devices should have the following properties:

Power sources are very important in electronic distance measurement as no power means no distance measurements. The most common types of power sources are:

All electro-optical distance meters suffer from a large number of usually very small instrumental errors, irrespective of the use of the pulse measurement or phase measurement principle. The errors may be inherent to the electrical and optical design and/or caused by manufacturing and component tolerances. The magnitude of these errors is kept small by the manufacturers and usually accounted for in the accuracy specifications of instruments. In view of the fact that a small number of errors must be calibrated by the user of EDM instruments and that errors occasionally exceed the specified accuracy and may change with time, the user must be aware of the main error pattern of instruments.

In this context, the calibration of a distance meter is defined as the determination of its instrument correction and associated precision. The instrument correction IC [see Eq. (12.13), for example] is added to distance measurements to obtain the correct distance. It has been shown previously that the instrument correction is a function of a number of independent variables, the most important being distance, temperature and time. The instrument correction is determined for a particular instrument-reflector combination. All distance-dependent and the constant terms require re-evaluation when using the distance meter with another type of reflector.