With the original Gunter’s chain, the surveyor simply looked at the chain and estimated the fractional part of the last link that should be included in the measurement. Those links were tangible. Since the wavelengths of a modulated carrier are not, the EDM must find the fractional part of its measurement electronically. Therefore, it does a comparison. It compares the phase angle of the returning signal to that of a replica of the transmitted signal to determine the phase shift. That phase shift represents the fractional part of the measurement. This principle is used in distance measurement by both EDM and GPS systems.
How does it work? First, it is important to remember that points on a modulated carrier are defined by phase angles, such as 0°, 90°, 180°, 270° and 360° (shown above and in Figure 1.6 from the textbook). When two modulated carrier waves reach exactly the same phase angle at exactly the same time, they are said to be in phase, coherent, or phase locked. However, when two waves reach the same phase angle at different times, they are out of phase or phase shifted. For example, in the image, the sine wave shown by the dashed line has returned to an EDM from a reflector. Compared with the sine wave shown by the solid line, it is out of phase by one-quarter of a wavelength. The distance between the EDM and the reflector, ρ, is then:
N = the number of full wavelengths the modulated carrier has completed
d = the fractional part of a wavelength at the end that completes the doubled distance.
In this example, d is three-quarters of a wavelength because it lacks its last quarter. But how would the EDM know that? It knows because at the same time an external carrier wave is sent to the reflector, the EDM keeps an identical internal reference wave at home in its receiver circuits. In Figure 1.8, the external beam returned from the reflector is compared to the reference wave and the difference in phase between the two can be measured. Both EDM and GPS ranging use the method represented in this illustration. In GPS, the measurement of the difference in the phase of the incoming signal and the phase of the internal oscillator in the receiver reveals the small distance at the end of a range. In GPS, the process is called carrier phase ranging. And, as the name implies, the observable is the carrier wave itself.
The image shows again the EDM sending out the transmitted wave in blue with the phase angles indicated as before. The signal goes to the retro prism and returns. When it returns, shown in the dashed red line, notice the phase angles, and it is clear that the return signal does not come back exactly in phase with the transmitted wave. The key element here is that the EDM generates another wave that is exactly the same as the wave it transmitted. However, it keeps the additional wave at home in the circuits of the EDM so that it can compare it with the reflected wave when it arrives. By comparing the returned wave—the one here in the dashed red line—with the exact replica of the transmitted wave, it can determine how much the returned wave is phase shifted, out of phase, with the original transmitted wave. The distance between the EDM and the reflector is then indicated by this formula, Rho equals N, the number of full wavelengths the modulated carrier has completed, plus d, the fractional part of the N ; all of that divided by 2. Why divide it by 2? Because in two-way ranging, the signal has traveled the distance twice, going out and coming back.