Hello, this part of the lesson about distances is dedicated to the electronic measurement of distances. We will first see the basic principles of these electronic measurements; then we will see how to determine a distance, what is the method used, and finally, what are the factors which influence the quality of the measurement. <i>The principle of electronic measurements of distances.</i> Firstly, we consider the following device with a theodolite having a distance meter on which we have a transmitter (written) as well as a receiver. At the other end, we have a prism, placed on a cane, on the point of interest and in between, we have waves that permit us to transmit a signal. One can determine here the path Go then the path Back; the principle consist of measuring a travelling time... (written...) ... of the signal between going and coming back. Namely, 2 times the distance that interests me. The signal travels at the speed of light... (written) .... in this case, <i>C</i>. Then, 2 times my distance is equal to my delta t times the speed of light. We have here the value of this speed of light in vacuum, together with the refraction index that we apply for the atmosphere. The type of waves that we use are infrared waves with this type of lengths and gas lasers with here, also, these lengths expressed in nanometers. One can measure with these techniques, a few meters, tens of meters, hundreds of meters for topography work and for more important work, we can go up to several kilometers or tens of kilometers. I invite you to reflect on the resolution of time measurements for determining a distance. The first method of measuring electronic distances is a method called "by pulse". Firstly, we have carrier wave of high frequency.... (written) on which we will graft a short signal, (written) that we call "pulse". We see in this figure, this grafted signal on its carrier that will go to the reflector, and return to the receiver, and thus we will have a measurement of delta t with the back and forth path. We can determine as follows: 2 s as delta t times the speed of light. The second method of determining is the measurement method called "phase shift". We will use here the properties of the carrier, which had a wavelength here, (written) as can be seen in this figure... and the principle consist of determining a phase shift phi, between the transmitter and receiver. (written) Measuring the phase difference can be very accurate. However, one problem remains to be solved, which is to determine the total number of the wavelengths To resolve this ambiguity, we have the following solution, which consist of using the different wavelengths, with an initial length, here, lambda 2 which gives us a rough measure and then a lambda 1 that permits us to get a fine measurement. The combination of these two observations allow us to unambiguously determine the distance between the observer and the prism or reflector. To illustrate this principle, we take an example here with three wavelengths. First of all we have a rough measurement, with a measured phase shift, here phi 3 and for example here, 390 meters. We have an intermediate measurement here, phi 2 that will give us here, 93 meters. It remains to get the phase-shift measurement phi 1, that is the fine measurement, with here, 2.84 meters. It remains after to sum all the significant parts of these observations, namely 392.84 meters. We have thus our distance <i>D</i> determined by the combination of phase observations. The electronic measurement of distances will be influences by the atmospheric properties. Indeed, a change in temperature or pressure will have an impact on the refraction index Here we have the Barrel and Sears formula that creates a relation between pressure values and temperature values, and that give here a correction, or a scale factor, expressed in ppm. We have on this chart on the right, the values of these correction factors, for example for a pressure of 900 millibars and a temperature of 20 degrees, I will have 40 ppm of correction. 40 ppm (written) that means 40 millimeters for a distance of 1 kilometer. Please note that this formula is valid for one type of waves. Here, in this case, infrared waves. So, one must consult with the documentation of the measuring devices to find an adequate formula for the given wave of the device carrier. To illustrate this formula, we take here a small numerical example. We have measured a distance of 1000 meters with a temperature value of 20 degrees and a pressure of 970 millibars. We can see here our chart at 20 degrees and then 970 millibars, and we find here on the correction curve +20 ppm. So we can note here +20 ppm which corresponds to 20 millimeters per kilometers In this case, our corrected distance will be 1000.021 meters. To summarize this part of the lesson dedicated to electronic measurement of distances, it can be said that the properties of the electromagnetic waves are used to determine these distances, mainly relying on infrared type of carriers or laser and that these waves are influenced by atmospheric properties, namely the temperature and pressure. There exists formulas that allows for calculating a correction factor in ppm and attention must be paid to the fact that, for each device, depending on the frequency, the formula will be different.