Principles of EDM measuring distances

EDM (Electronic Distance Measurement) is the measurement of a distance using the velocity and the travel time (or phase change) of a modulated electromagnetic wave (light, infrared or microwave) sent from an instrument to a reflector and back.

Principle

The instrument at A transmits a modulated wave to a reflector (prism or transponder) at B. The reflected wave returns to A. The distance is found from the time taken or from the phase shift of the returned wave. The wave travels with a known velocity $v = c/n$, where $c = 299{,}792{,}458$ m/s is the velocity in vacuum and $n$ is the refractive index of the air.

  EDM at A ------ outgoing wave ------> Prism at B
        <------ reflected wave ------
           Double path = 2D

1. Pulse (time-of-flight) method

A short pulse of energy is sent and the time $t$ between sending and receiving it is measured.

$$D = \frac{v\,t}{2}$$

It needs a very accurate clock: a time error of 1 ns gives about 15 cm error in distance. It is used for long ranges and in reflectorless laser total stations.

2. Phase-comparison method

A continuous carrier wave is modulated with a fixed frequency $f$ (wavelength $\lambda = v/f$). The phase difference $\phi$ between the transmitted and the received wave is measured. The double path $2D$ contains $N$ complete wavelengths plus a fraction:

$$2D = N\lambda + \frac{\phi}{2\pi}\lambda \quad\Rightarrow\quad D = \frac{1}{2}\left(N + \frac{\phi}{2\pi}\right)\lambda$$

The instrument measures the fraction, but the whole number $N$ is unknown. It is found by using several modulation frequencies (a coarse and a fine wavelength), so $N$ is resolved automatically. This is the common method in total stations.

Steps in operation

1. Set up the EDM/total station over one point and a reflector over the other point.
2. Enter the temperature, pressure and prism constant.
3. Sight the reflector and press measure.
4. The instrument corrects for the atmosphere and gives the slope distance, horizontal distance and height difference.

EDMs give high accuracy (typically $\pm$(a few mm + 1 to 5 ppm)), speed and long range.