We are now going to change direction completely and spend the rest of this course looking at the technology of imaging radar as a remote sensing tool. In the first module of this course, we looked at the Planck radiation law. Remember, it shows how bodies at different temperatures emit radiation or energy. As seen on the diagram to the right of this slide, the earth at 300K is a low emitter by comparison to the sun or a burning fire. But let's focus on the curve for the earth itself in more detail in the next slide. Here we see the earth curve expanded. Look particularly at the right-hand side covering the microwave range and note that the emission from the earth at microwave frequencies is much lower than its emission in the visible and infrared range. Although there is a very small level of radiation from the earth at microwave frequencies, we can, for all intents and purposes, assume the earth is dark. We can therefore take advantage of that by irradiating the earth with an artificial source of microwave radiation, just as we use a torch or a flashlight at night when there is little natural light available. When we use radar to image the earth's surface, we do so to the side of the platform, whether that be a satellite, an aircraft, or a drone. The reasons for this will become clear soon. There are two things we then need to understand. First, we need to understand how the energy reflected back to the platform is representative of the properties of the landscape. Secondly, we need to understand how such an arrangement gives us spatial resolution in both the across track and along track directions. Just as with radio, television, and mobile or cell phones, clouds are not a problem with radar imaging. This is a huge advantage because clouds can completely stop remote sensing imaging at optical wavelengths. Also, since the platform carries its own source of irradiating energy, imaging can be carried out anytime of day or night. The energy radiated to the surface is not continuous, but consists of a regular sequence of pulses, as shown in this slide. Importantly, those pulses travel at the speed of light, which is 300 megameters per second or 300 million meters per second. Reflections from targets closer to the platform will appear back at the radar earlier than those from the targets further from the platform, as illustrated by A, B, and C in the diagram here. The pulses are actually the envelopes of a burst of microwave radiation at the frequency or wavelength of interest. Just as with optical imaging, in which the earth responds differently at different wavelengths, the same is true of radar. The frequency inside the pulse will determine the property of the earth that we are measuring. The pulse transmitted in the previous slide is actually repeated on a regular basis called the pulse repetition frequency. The rate at which the pulses are transmitted is synchronized with the forward velocity of the platform so that the strips of ground image by each of the pulses align with each other as shown in this diagram. This provides continuous coverage. It is actually the property of the antenna used to radiate the pulse that gives the so-called footprint on the ground. The angle with which the radiation is transmitted to the side of the platform is called the look angle. Its corresponding version on the ground is called the incidence angle. They will be the same for a low-flying platform and a flat surface. There will be slightly different, however, at spacecraft altitudes where the earth's curvature might be important and also for ambulating terrain. We now need to understand quantitatively, how the radar separates targets, or regions on the ground as different distances as from the platform. In the diagram here, we show two targets A and B separated in the direction and from the platform. We call that the ground range direction, in contrast to the slant direction which is parallel to the beam from the radar as shown. Suppose the two tablets are delta r apart, in the slant range direction. Given that the radiation travels at the speed of light c, and that it travels to and from the platform. The difference in time between the two echoes is given by delta t, which is twice the distance divided by the speed of light. If the pulse duration is tall, as in the previous slide, then the two targets can be resolved provided there are no closer together then c2 divided by 2. We call that limit the slant range resolution, because we cannot resolve between the pulses if they overlap. This is illustrated on the bottom of the slide. Of course, as remote sensing uses, we are interested in the resolution along the ground range direction, rather than that in the slant direction. From trigonometry we can see that to be the formula at the bottom of the slide, there is a sine theta in the denominator. From the last formula, we can make some important observations. First, there is no special resolution directly under the platform. That is, when theta equals zero. That is why the system has to be side looking. Some early aircraft radars of this type were called side looking airborne radars or SLARs. Secondly, the slant and ground range resolutions are independent of the altitude of the platform. That's an amazingly useful property. Thirdly, ground range resolution is a function of incidence angle, and thus will vary across the swath. It is best in the far swath where theta is largest and poorest in the near swaths where theta is smallest. This is opposite to that for optical sensors which have their best resolution closest to the platform. Just as we can see more detail in the near range when we look at the window of an aircraft. Finally, if the antenna radiated to both sides of the aircraft and a single receiver were used, then there would be a right-left ambiguity in the received signal. That can be circumvented using two antennas and receivers, but most often that is not the case. Most systems encountered in practice radiate to one side of the platform. Having looked at how we achieve resolution in the ground range direction, that's from the platform. We now need to see how we achieve spatial resolution along the track of the platform. Although a curious line it is called azimuth resolution. It is determined by the properties of the antenna used on the platform for transmitting and receiving the microwave pulses. In particular, it is the so-called beam width of the antenna in the azimuth direction that sets the azimuth resolution in the manner we will now describe. From antenna theory, the width of the beam transmitted by an antenna is directly proportional to the operating wave length and inversely proportional to the length of the antenna, as shown on the slide. That means that a longer antenna will give a narrow beam width on the ground and thus a smaller strip irradiated action. What we want to know now is the width of that strip because that defines the azimuth resolution. From the previous slide, we had the top equation as the beam width of the antenna expressed in radians, at a range of R subscript nought that projects onto the ground, l dimension of R subscript l meters. That is the width of the illuminated strip and thus the azimuth resolution. Note from this formula, the azimuth resolution gets worse with increasing slant range and better with increasing antenna length. At this point, it is worth doing a simple calculation as on the next slide. Consider an aircraft situation, the slant range is 2000 meters. The radar antenna is three meters long in the azimuth direction and the operating frequency is 10 gigahertz. That corresponds to a wavelength of three centimeters. Substituting those values into the formula, we see that an azimuth resolution of 20 meters results, which is acceptable. However, if the same radar is placed on a spacecraft with a slant ranges 1,000 kilometers, the azimuth resolution will be 10 kilometers, which is totally unacceptable. Clearly, a better method is needed to achieve good azimuth resolution at spacecraft altitudes. What if we use a short antenna and thus irradiated a broad region on the ground as shown in this diagram? Clearly, the azimuth resolution should be very poor. The length of the region illuminated in the along track direction is the slant range to the ground multiplied by the beam width of the small antenna, which is as shown in the equation on the slide. What happens, though, if there's more than one pulse transmitted while the point target is in view of that large right at beam? To answer that, consider the geometry on the next slide. Here we see the platform moving past the target. The radar just encounters the target when the target first comes into the beam and loses it when it leaves the beam. All the time the platform is transmitting pulses, which incidentally are called ranging pulses, and it's receiving echoes. By processing those echoes using a signal processing technique called matched filtering, we are able to make the length of the spacecraft travel look like a long antenna or aperture as shown in the figure. That travel distance is equal to the projected beam width on the ground of the real short antenna. The effective long antenna is called a synthetic aperture, leading to the name synthetic aperture radar or SAR for the technology. What beam width does a synthetic aperture create, and what footprint does that lead to on the ground? Remember the beam width in radians is the operating wavelength divided by the antenna length. For the synthetic antenna, that is as given by the formula in the center of the slide. The two in the denominator comes about because the transmission is from the antenna to the target and then back to the antenna. When projected onto the ground, this gives an along track or azimuth resolution as shown at the bottom of the slide. Truly an amazing result because it tells us that the azimuth resolution in synthetic aperture radar is directly proportional to the antenna length in the azimuth direction and not inversely proportional as before. We will look at the implications of that in the next lecture. By way of summary, we note so far, first that imaging at microwave frequencies makes use of the fact that very little natural microwave energy emanates from the Earth's surface. We can thus irradiate the surface ourselves with a source of microwave energy carried on a remote sensing platform. Secondly, as with optical remote sensing systems, the forward motion of the platform sweeps out a swath of recorded image data of the Earth's surface. Thirdly, imaging radars are side looking; range resolution is best at far swath, that is large incidence angles, and worse at near swath that is, with small incidence angles. Fourthly, good azimuth resolution is obtained by using a signal processing technique called matched filtering, that allows a small real antenna to be used on the platform but achieves a very high spatial resolution equal to half the size of the real antenna; this is called synthetic aperture radar. Finally, in SAR, both the ground range and azimuth resolutions are independent of the platform altitude and operating wavelength, which is the wavelength of the frequency burst modulated by the ranging pulse. Again, this is a significant practical advantage. In the first question here, your attention is drawn to the node to receive sufficient energy that the brightness of a pixel is of a measurable value and well above any noise that might be present in the system.
