Let's now summarize where we were in the last lecture and then note some practical implications of synthetic aperture radar. In this slide, we summarize the important geometric properties of radar imaging, including how the width of the recorded swath depends upon the system parameters. We know now how to resolve the landscape into pixels using radar. Our objective from this point on is to understand what the pixels tell us about the landscape. Along the way, we have to consider a number of related matters, including some further properties of electromagnetic radiation and sources on geometric and radiometric distortion in radar images. The first important point to take note of is that the wave form within the ranging pulse does not have a constant frequency, but chirps over a limited range about a center frequency. That chirp range is very small but nevertheless, it is a major determined for achieving high range resolution. Understanding that is beyond this series of lectures, but the book referenced provides the details for those interested. The chirp range is small enough, that we can regard the imaging wavelength as equivalent to that of the center frequency. A second practical matter and one which has significant implications for understanding the properties of radar images, is to do with the polarization of the incident and reflected waves. Power or power density is carried forward as a result of both an electric field and a magnetic field, that oscillates at right angles to each other and to the direction of propagation as illustrated by the field vectors in the left-hand diagram on this slide. There is a fixed relationship between the magnitude of the magnetic field and the magnitude of the electric field. They are always at right angles each other. Thus, we only need to consider electric field from now on. The direction in which the electric field vector points, defines the plane of polarization depending on the transmitting antenna used at the platform, the radiation incident at the earth's surface can be vertically or horizontally polarized as illustrated in this slide. The transmitted signal can either be vertically or horizontally polarized. Irrespective of the polarization of the incident radiation, the scattered signal can also have both horizontal and vertical components. Whether either or both of those components can be received, again, depends upon the properties of the receiving antenna. Generally, the same antenna is used for transmission and reception. Whether it can transmit and receive both polarizations will depend on its design. There are four possible radar configurations. Transmit horizontal and receive horizontal, which is called HH, transmit horizontal and receive vertical, which is called VH, transmit vertical and receive horizontal, which is called HV, or transmit vertical and receive vertical, which is called VV. Note that the first in the double letter convention is they received polarization, while the second is the transmitted polarization. Most systems are the HH or VV, and are called single polarization radars. Whereas more sophisticated radars accommodate all four configurations, and are set to be fully or quad-polarized radars. This slide shows a radar image example over the city of Darwin, Australia in two different polarizations, HH and VV. It was recorded by the ASAR C band imaging radar carried on the Envisat platform. Although much of the image seem similar in the two polarizations, there are some notable differences as indicated. In many cases, polarization is an important discriminator in radar imagery. Here is another Envisat ASAR example over the city of Kalgoorlie, in Western Australia. This time, one of the images is cross polarized as indicated. Again, note the differences between the lock and cross polarized responses. Note the comment on the bottom left-hand side of the slide. Monostatic radar, main choosing the same antenna for transmission and reception. Later we will relax that requirement, but for monostatic systems which are by far the most common, we assume the two cross polarized responses are identical. In this example, we see all four polarization configurations. The image was recorded by the TerraSAR-X Satellite Program. The color composite image was constructed by displaying the horizontally polarized image as red, the vertically polarized image as green, and the two cross polarized responses as blue after they have been added. Bringing all this together, we say that operational radars in remote sensing are defined by three important system parameters. The operating wavelength, the polarization, and the incidence angle, or range of angles. Ever since radar was developed during the Second World War, the range of wavelengths has been described by a letter designation. It is not unique, but the frequency and wavelength ranges shown here are the most usual in remote sensing. Of this set, L, C, and X are the most often encountered. You may wish to take note of the formula on the right-hand side of this slide, which relates operating wavelength in meters and frequency in megahertz. In this slide, we see the technical characteristics of a number of satellite and aircraft radar remote sensing missions. You can convert between wavelength and frequency, using the formula from the previous slide. We've seen that the radar resolution cell or pixel size in a displayed image product, is defined by the ground branch resolution and the azimuth resolution. The ranging pulses are chirps about the operating frequency or wavelength. Although that requires some sophisticated signal processing to resolve targets in the range direction, better sensitivity to weak targets is possible. The important parameters of an imaging radar are the wavelength, polarization, and look angle. Operating wavelengths or frequencies are described by letter designations, reputedly chosen as a means for discussing the operating frequencies of aircraft detection radars during the Second World War. These questions are designed to consolidate your understanding of the geometric properties of a radar image.
