Now look at some further unusual scattering behaviors, one of which is sea-surface scattering. This treatment will finalize our consideration of scattering by looking at some unusual mechanisms that occur because of the coherent nature of the incident radiation. We will look first at Bragg scattering, which occurs when there are periodic structures on the ground, and then we will look at sea surface scattering, which is in fact related to Bragg scattering. Just before that though, we want to look at another feature of the double bounce dihedral corner reflector model for buildings, particularly in urban and city regions where houses and buildings often occur in rows along streets laid out in a regular grid patterns. In one of the quiz questions in the last lecture, you were asked to consider what would happen to the response of a dihedral corner reflector if the incoming beam was not precisely aligned with the face of the reflector. This is generally not a problem for tree trunks as a result of their cylindrical nature, but for flat vertical structures, such as the sides of buildings, if the incoming beam is inclined as illustrated in the diagram, the backscatter drops very quickly. Thus, buildings will only stand out in an image if the direction of radar illumination is at right angles to the wall in the horizontal plane. This leads to what is called the cardinal effect, an example of which is seen in the next slide. The word cardinal here derives from the cardinal points on a compass, that is north, east, south, and west. Here we see a portion of a survey image acquired over Montreal, Canada in 1984 demonstrating the cardinal effect. The bright central portion of the image is where cross streets are aligned orthogonally to the incoming radar energy. Whereas the darker portions to the north of about the same urban density have street patterns that are not orthogonal to the radar beam. We now come to a non unusual scattering mechanism which had its origins in crystallography. The Australia father and son team of William and Lawrence Bragg received the Nobel Prize in 1915 for x-ray diffraction, which has the same basis as what we're now going to consider in radar scattering. The wavelengths that are used in radar remote sensing that is about 3-50 centimeters are not too different from some of the periodicities we see in the landscape, such as row crops. Consider the interaction of an incoming radar front with the surface shown in the diagram on this slide, which is periodic in the plane of irradiation. It could represent, for example, the cross-section of a newly plowed field. When this region is irradiated, there will be moderately strong reflections from regularly spaced parts of the surface as indicated. It is a set of those reflections which constitute the backscatter that occurs from the radar resolution cell or pixel. Note that some returns travel further than others, so when looking at reconstructing the composite pixel response, we have to convert those additional travel distances into phase angles. Thus, the pixel response is made up of a set of signals with different phase angles. Those phase differences will be related to the angle of incidence and the spatial wavelength of the surface periodicity. Sometimes the signals will add constructively, giving a brighter than average return, whereas at other times they will add destructively. We saw the same effect when we considered speckle but here the interference results from periodicities in the landscape rather than randomly distributed incremental scatters. Usually, when we considered the different mechanisms within a pixel which contribute to backscatter, we simply add the backscattered powers. With Bragg scattering, however, we add the electric fields, which then squares the backscatter power density, making the pixel much brighter than if the periodicity were not present. There is one important condition to all this, and that is that the row-like periodicity has to be aligned orthogonally to the incoming wave front, otherwise the phase reinforcement will not occur. When it does, the condition for constructive reinforcement is that the surface and electromagnetic wavelengths are related by the formula shown, which is called Bragg's Law, and the behavior is called Bragg resonance. Here we see an example of Bragg Resonance with circular pivotal irrigated agricultural fields in Libya. The strong returns are much likely associated with Bragg Resonance. The radar of illuminations from the bottom of the scene, so that plowed furrows running across the scene give the enhanced returns. We now turn to how scattering occurs from the ocean and work on Bragg scattering is important here. A flat sea will behave like a specular reflector and will appear dark in radar imagery. To receive measurable backscatter, the sea surface must be made rough by some physical mechanism. The principle means for surface roughening is the formation of waves. There are two broad types of wave, both excited by the action of the wind blowing across the surface, they are distinguished by the mechanism that tries to restore the water surface against the driving effect of the wind. Gravity waves depend on gravitation acting on the disturbed massive water to counteract the effect of the wind, their wavelengths tend to be long, typically in excess of a few centimeters. Capillary waves have wavelengths shorter than a few centimeters, and rely on surface tension to work against the disturbance caused by wind action. They appear to ride on the gravity waves. For both waves, amplitude and wavelength is a function of wind speed, fetch, that is the distance over which the wind is in contact with the surface of the water, and the duration of the wind event. The bottom left-hand diagram here shows the so-called energy spectrum of typical capillary waves. It peaks around the wave number, roughly aligned with C band radar. Importantly though, this diagram tells us that presence among the capillary waves are components, in a farrier analysis sense, that can match the wavelength of an incoming radar beam and thus cause Bragg resonance to occur. From the spectrum, we see there is more energy at smaller wave numbers, and from the expression for Bragg resonance, we see that for a given radar wavelength lambda, we can select a smaller wave number on the capillary wave spectrum if we make the incidence angle small. Thus, oceanographic radar imaging is usually best done with small incidence angles. These images, recorded by SeaSat and SIR-A over a region of the Californian coastline of Santa Barbara, illustrate the importance of incidence angle in sea surface scattering. The seawater detail is much better expressed in the 20-degree imagery than in the 40-degree imagery. Note however the terrain distortion, at 20 degrees and the consequent difficulty in assessing terrain detail. Note also the strong dihedral corner reflector responses from oil rigs in the channel, easily seen at 40 degrees but less so at 20 degrees. Finally, notice what happens in radar images of the ocean. If the capillary waves are damped, oil slicks attenuate, considerably, the amplitudes of the capillary waves, meaning that incident radar energy has nothing to couple into, making those regions on an image look dark as seen here. Note also the effect that ship wakes have capillary waves and thus on the radar response. Summarizing here; First, the dihedral corner reflector effect requires the incoming radar beam to be orthogonal to the reflecting elements. Secondly, the cardinal effect shows how the alignment of straight patterns affects strong reflections in urban zones. Next, Bragg scattering occurs when the earth's surface has regular periodic features, it is also a strong reflection mechanism. Next, sea scattering entails coupling of the incoming electromagnetic radiation in the radar beam with capillary waves on the ocean's surface, it is strongest at small incidence angles. Finally, oil slicks damp the capillary waves and thus considerably reduce radar backscatter from the sea surface. When looking at the second question here, keep in mind that radar reflections are separated spatially in an image if the returns for the radar happen at different times.
