EDM operation principles and errors

Principles of operation of EDM

An EDM instrument sends a modulated electromagnetic wave (infrared, laser or microwave) to a reflector at the other end of the line. The reflected wave returns to the instrument, and the distance is obtained by measuring either the time taken or the phase difference of the wave.

1. Pulse method: $D = \dfrac{v\,t}{2}$, with $v = c/n$ the velocity in air and $t$ the round-trip time.
2. Phase-comparison method: the carrier wave is modulated with frequency $f$ ($\lambda = v/f$). The phase shift $\phi$ is measured and

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

The integer $N$ is solved by using two or more modulation frequencies. A microprocessor applies the atmospheric corrections and displays the distance.

Sources of errors in EDM

The final error is usually expressed as $\pm(a\ \text{mm} + b\ \text{ppm})$.

Distance-independent errors (constant)

• Zero error (instrument/reflector constant), due to the difference between the electrical centre and the mechanical centre.
• Centring errors of the instrument and the reflector over the stations.
• Phase measurement (resolution) error.
• Error in measuring the height of the instrument and the target.

Distance-dependent errors (proportional)

• Error in the atmospheric refractive index from wrong temperature, pressure and humidity readings. This is the largest source.
• Error in the modulation frequency (instrument oscillator drift).
• Error in the velocity of light used.

Other errors

• Cyclic error (phase non-linearity) inside the instrument.
• Reflection from other objects (ground swing) and multipath.
• Poor line of sight, beam passing close to the ground or heat shimmer.
• Operator mistakes, e.g. wrong prism constant.

Errors are reduced by regular calibration, using accurate temperature and pressure, careful centring, and taking several readings.