 Hello everyone, welcome to the next lecture in the course remote sensing principles and applications, we are discussing the topic of active microwave remote sensing with imaging radar. In the last lectures we got introduced to the concept of like how radar image is acquired, what sort of like image distortions will occur, the concept of resolution in a radar image all those things. In this lecture we are going to see the actual signal contained within a radar image like what characterizes it and what are the terrain properties that will influences the reflection of objects in the radar signal. First we will get introduced to what is known as the radar equation. So, we are not going to discuss everything in detail or derive anything here, but we are going to understand what is actually contained in a radar image. So, when I introduced the concept of radar image I told you that it will collect the power that is being reflected back from the object. So, here the term reflection mean the signal which is reflected in the same direction as that of the receiver, because we know that that radar will have an antenna, it will transmit microwave radiation towards the object and whatever is reflected towards the antenna again alone will be collected. So, whatever reflection of scattering happens in direction anything other than this antenna direction will not be collected by this particular sensor. So, we call this as back scattering. So, essentially the radar antenna measures what is known as back scattering that is how much energy is being scattered back by the object towards the sensor itself. We call it as back scattering. So, normally when you look at like any scientific literature related to radar or retro radar remote sensing we will have this term back scattering commonly being referred to. Now, anyway like we are going to sense the power. So, the power received by the antenna depends upon the power transmitted multiplied by the gain of the antenna. So, here gain you can think it off like how well the antenna is focusing the power in a given direction. You can think it in terms of like that we are not going to elaborate on that. But you can think some sort of power is going to be transmitted from the antenna initially. So, how much is like kind of focused on a given direction. So, once this power is transmitted let us say this is the antenna. So, once this power is transmitted like a pulse is being released it will start spreading in all the three dimensions. It is not going to travel in kind of like a straight line microwave pulses they are going to spread across the power is going to spread across in all the directions. We know this because of this inverse square law whatever is the power that is transmitted it is going to spread across. So, this 1 by 4 by r square is to account for this spreading of power where this r is the distance between the radar antenna and the object antenna and object distance. So, that is if this is considered like antenna is kind of like a point source. So, this is like a target if p power is like transmitted from here it will slowly start spreading in the entire sphere surrounding it. So, we are going to use this inverse square law function in order to calculate what is the power received by this particular object with a given area. So, now these three terms will define the power reaching the object of interest from the radar antenna the initial power that was transmitted multiplied by the gain into accounting for the spreading loss. Now, whatever is the power reflected back will depend on the effective scattering area of the object or here we denote it as sigma where sigma is known as the radar cross-section. So, what radar cross-section is maybe like we will see it like little bit later, but consider it is terms of like it is kind of like reflectance think it similar to in terms of reflectance not actual reflectance I will describe it in later, but just for like simplicity sake for introducing this particular equation I am telling it like this. So, this is like think it radar cross-section think it in terms of like reflectance. So, some amount of power is reflected back by this particular object and it has to again travel back after reflection also it will start spreading again right from this particular small area it will start spreading all over again. So, this is to account for that spreading loss in the return direction this particular term 1 by 4 pi square and AR is the area of the antenna that is receiving the signal. So, if you look at this if you divide this particular equation into different components like sensor and object characteristics we can know that that power received depends on some sensor factors or sensor characteristics that is the term PT, GT, AR, area of the antenna are all sensor factors. The sigma what we referred as the radar cross-section actually defines the property of the object on the earth surface that controls this power that is reaching the sensor. So, essentially that single particular term sigma the radar cross-section will influence how much power will be returned back to the radar antenna and that is entirely controlled by the object of interest itself. Rest all the factors are all system properties. So, the power received if we think like ok system properties are all fixed once the system is launched if it is kind of fixed means then the only variable in the equation every time when an image is acquired is the sigma term the radar cross-section term also like distance anyway it is like a natural phenomena distance is always going to vary. So, the major factor that controls the signal received in the radar image or major factor of the object the earth surface feature is radar cross-section. What exactly radar cross-section is? So, here we would not I told you like think it in terms of like reflectance but it is not like it is not defined very anyway similar to reflectance at all. So, what radar cross-section is let us say there is some object now some power is falling on it some radar power is falling on it microwave signal. The object is sending back certain amount of that particular instant energy towards the radar antenna. So, that object can be anything in order to calculate the power that was like scattered back by the object of interest we take some reference that reference is known as like a perfect isotropic reflector or like a isotropic scatterer. What it means? We can think it in terms of like a polished spherical metallic surface which has good amount of scattering in the microwave wavelength and it will scatter the microwave wavelengths equally in all the directions like a spherical metallic surface we can think of. So, that is kind of taken as a reference. Why that is taken as a reference means say whatever be the microwave power that is falling over it that power will be scattered equally in all directions by that particular object like that spherical object. So, this is kind of taken as a reference. Now, let us say we have some object of interest that is scattering the energy back towards the antenna any feature cropland water body building whatever let the power that was like scattered back towards the antenna be X. So, now what we have to calculate is we have to estimate the area of this isotropic reflector that should be there in order to reflect back or scatter back the same power X towards the antenna under identical illumination conditions. I repeat it again for sake of clarity like let there be any object of interest on the earth's surface. Let us say it is scattering some power X towards the antenna in response to the incoming microwave signals. Radar cross section here means the area of a perfect isotropic scattering object like example I told you this metallic sphere right. So, the area like the surface area of the object that is required in order to scatter back the same amount of power X under identical illumination conditions by the microwave. So, here we are not calculating the reflectance of object, but here we are trying to calculate the area of the isotropic reflector that is required to produce the same amount of power that has been reflected back. So, it is kind of like may appear little bit confusing in the first go, but the concept is it is like very simple. Let us say there is like a very good reflector in the microwave band. Let us say take an example kind of like a very healthy crop plant or like a vegetation over like a standing water or something okay. So, what will happen is later we will see those kind of objects will produce like a very bright response like they will appear very bright in radar images. They will send back almost most of the energy that was transmitted from the radar. They have like very high scattering backscattering towards the radar itself. So, what it means in order to produce such a bright backscattering towards the antenna that particular object should be replaced by like a isotropic reflector with a bigger area. Let us say there is some other object which is like very poor which is a poor backscatter like a calm still water body. The backscattering will be kind of like really poor towards the antenna. Under that circumstances the area of the isotropic reflector to produce the same backscattering will be smaller. So, essentially based on the backscattering capacity of the actual terrain features we can calculate the surface area of the perfect isotropic reflector that will be needed to produce the same amount of power okay. So, this is known as radar backscattering. So, radar cross section. Here we are not calculating any ratios normally in optical remote sensing we will calculate the ratio right reflectance. We will calculate reflectance that reflectance is nothing but a ratio ratio of the energy that was reflected back to the energy that was incident. Here we are not doing that. Here we are trying to do some sort of like hypothetical calculations like where we try to calculate the area of the perfect isotropic reflector that is required to produce the same amount of backscattering produced by any natural feature. Higher the backscattering capacity of this natural feature larger will be the area of this particular isotropic reflector will be required. Hence, the radar backscattering will be larger. If the object has a lower backscattering capacity then even like a small area of this isotropic reflector can produce the same reflect same back scattering and hence the radar cross section will be smaller. So, the radar cross section essentially tells the backscattering capacity of the object. So, here we told like the radar cross section essentially determines the power that is reaching back the sensor. But this radar cross section has to be kind of normalized with respect to something like normalized with respect to something is what I mean is like normally a single pixel will have like many number of features like if you take like a 10 meter by 10 meter pixel it will have a large amount of features present and all. So, that can be many objects. So, we will get kind of like a combined radar cross section. But in order to normalize this in order to bring it to some sort of standard we will convert that to what is known as a radar backscattering coefficient. So, this is like denoted here as sigma naught the radar cross section is kind of normalized further to backscattering coefficient. So, what exactly this backscattering coefficient means? Now, we know this is like it has like ratio where in the numerator we have the radar cross section and in the denominator we have the area on the ground that produces or that requires this much radar cross section that is this is also an area sigma is nothing but a area area of the perfect isotropic backscatterer that is needed in order to produce the same backscattering received at the antenna under identical illumination conditions divided by area of the ground that actually produced that radar or that actually contained that radar cross section. So, here we are now dividing now we are converting into a ratio. Okay, this is the area of the object or this is the area of like the isotropic reflector that is required somehow we calculated once we calculated we normalize that with respect to the area of the ground that produced or that requires that much radar cross section. This is needed because like radar pixel size is not like a constant right we have seen that the pixel size of radar images will vary across the range direction and azimuth direction in case of real aperture radars. If that is the scenario as the pixel size changes like some pixel may have large number of objects some pixel may have the some pixel size itself may be small dimensions it may contain like very few objects that has like poor backscatter capacity all these things will happen and the radar cross section sigma itself will depend on the area actual ground area that is covered by the radar pulse. In order to avoid this we do this conversion we convert this radar cross section to radar backscattering coefficients so that the power received in the antenna will be normalized okay per unit meter of ground area say for a pixel what is the radar cross section per unit meter of ground area that is what we will calculate okay. Say let us say there is like a pixel size 10 meter by 10 meter. So, whatever be the radar cross section we will divide this by this 100 meter square in order to calculate this backscattering coefficient. So, essentially this is what we will calculate in radar image preprocessing. So, whenever like a radar image comes we will do some sort of like preprocessing steps before we use it for like further applications. So, one of the important step is to like convert the slant range distance to ground range distance, remove the distortions using what is known as terrain correction procedure after that like we will convert everything to radar backscattering coefficient. So, the backscattering coefficient will tell at each pixel what is the radar cross section required per unit meter square of area that will be there. So, again like I repeat for the purpose of clarity why we need to convert this radar cross section to backscattering coefficient just for deeper understanding okay. So, we will take like two examples one pixel 10 meter by 10 meter, another pixel let us say it is like 10 meter by 20 meter. It is natural that radar resolution will vary across the image in both the range direction Nazimut direction. If that is the case let us say both the pixels had like same radar cross section like it had like lot of bright objects this 10 meter by 10 pixel whereas this 10 meter by 20 meter pixel had like less number of objects kind of thing okay. Let us assume both of them has the same radar cross section but the same radar cross section has been produced by this pixels. One of the major factor that produced is the larger dimension of this pixel. So, has the dimension be uniform between these two pixels the radar cross section might have been different right in order to normalize that we convert this. So, sigma 0 of this pixel will be sigma by 100 meters whereas sigma 0 of this pixel will be whatever the sigma divided by 200 meters. So, essentially using the area on the ground will normalize the radar cross section for this variation in pixel size one of the important things that we should do okay. So, we calculate what is known as the sigma 0 and area we can define it in multiple ways normally the general convention that we use is the actual ground area of the pixel okay. What is the actual horizontal dimensions of the ground in the x direction and y direction calculate area out of it and use it that we call it as like sigma 0. We can also calculate the area of the ground in different directions say for example, a schematic is given here. If we use the actual horizontal ground area in order to normalize the radar cross section we get sigma 0 or if we use the slant range area itself like in the slant range let us say this is the and this is the ground like beam will be spreading like this. So, in two dimensions it will like spread and collect all the distance information power information. So, whatever like each pixel here it will have an area projected in the slant range direction right. So, the area of the ground which is used to define the pixel in the slant range direction itself if we define if we use that particular area for normalizing the radar cross section we call it as beta 0. On the other hand if we project this ground area in a direction that is normal to the radar beam or the radar antenna this is like normal that is the case this is like projected. So, that this area is now is normal to this radar beam then if we use that area to normalize this radar cross section we call it as gamma 0. So, the radar backscattering coefficient can be defined in three ways or the area itself can be defined in three ways the actual ground area the area of the pixel that produce the sigma the radar cross section in the slant range or the area of the ground projected in a direction normal to the radar antenna. So, we can defend in three ways but the general convention on the most often used factor is sigma 0, radar cross section sigma divided by the horizontal ground area okay. So, this will be one of the uh obtaining the sigma 0 for each pixel will be one of the important step in radar data processing. Once we get this sigma 0 we can use it for different applications. So, the sigma 0 essentially is the influence of the terrain features on the power that is reaching the radar antenna. So, higher the backscattering coefficient sigma 0 the pixel will have will appear bright like large amount of power would have been backscattered towards the antenna. Lower the sigma 0 the object would have like would not have backscattered same amount of like high amount of power it would have backscattered only like very less amount of power. So, the sigma 0 essentially tells us the characteristics of the object and its ability to backscatter microwave signal. Now, we are going to slowly discuss what all the factors of the terrain features that will influence this sigma 0 like when we discussed the optical remote sensing like visible NAR remote sensing and all we discussed what factors of vegetation controls its spectral reflectance curve what factors of water controls its spectral reflectance curve and so on. Similarly, we will touch upon briefly how different features exhibit this or how different factors of the features on the earth surface controls this sigma 0. So, basically from the radar equation we have inferred that the power reaching the sensor depends both on sensor characteristics and the object characteristics object here I mean the feature present on the earth surface. Some of the important sensor characteristics that control this power reaching the sensor are the frequency in which the microwave signal is transmitted, the polarization of the signal that is transmitted and received and the instance angle at which the angle is incident upon the surface. These three are really important factors from the sensor side that will control the power that is received back by the sensor. So, whether frequency means here I mean whether it is C band, X band, radar, L band, radar and so on. Polarization means whether it is transmitting and horizontal and receiving and horizontal or HP or VV something like that. And incident angle is whether the object is closer to the radar antenna like whether it is near range or whether it is in far range and so on. So, these are all the instrumental parameters. But as I said before like except this instance angle once the system is launched these two are kind of like fixed right these two cannot or not going to vary this is going to instance angle anyway is going to vary based on whether the object is present in near range or far range. But what we are really interested upon is to understand what are all the terrain characteristics that influences this sigma 0. Some of the important terrain characteristics that influences microwave backscatching or the surface roughness that is how rough or how smooth the surface is. Surface geometry basically dealing with the orientation of the surface itself different features that are present on the surface and the dielectric constant of the surface primarily influenced by its moisture content. So, these three factors are like the key controlling factors from the object side or the terrain side that will control the microwave backscattering towards radar antenna. So, essentially by looking at the sigma 0 value we may get some information about any of these either surface roughness property or dielectric constant of the surface and so on. So, first we are going to discuss the importance of surface roughness in the radar backscattering. Actually we have seen this in the earlier classes also when we discuss the interaction of electromagnetic radiation with the terrain normally what we discussed the surface roughness whether a surface that will whether it will appear smooth or rough it depends on the wavelength that is incident on the surface and also the look angle the geometry between the sensor and this object itself that we have like seen here also in radar the same case. But in radar the surface roughness plays a major role that is whenever we get signals from the radar surface roughness will have like a larger influence like when you look like radar images from like a rough surface and smooth surface there can be like drastic variations also. So, surface roughness influence will be quite high. So, what will happen in case of surface roughness just we will do like a quick recall. Say if a surface is like really smooth like we have also defined what is known as like a modified Rayleigh criterion in earlier classes please recall them like if the RMSE height of the surface like say this is like the height variation let us say this is like a soil surface. So, this is like the mean height of this particular there this is the bounding area in which I am interested upon. So, this is like the mean height of the area. So, the variation of the surface measured with respect to mean height if you can calculate kind of like a deviation or like a difference we can land up what is known as the RMSE height this is what we are going to use. If this RMSE height is less than lambda by 25 sin gamma the surface will be smooth for this particular wavelength and that will act as like a specular reflector. So, this we know if a surface is smooth it will act as a specular reflector. If a surface is rough that is its lambda that is the RMSE height h is greater than lambda by 4.4 sin gamma it will act as a rough surface or if the RMSE height is varying between these two limits the surface will act as kind of like an intermediate. So, what exactly will happen for a smooth surface the reflection will be specular and it will be moving away from the radar antenna that is let us take water still calm water is a very good example for a specular reflector. See like this is like the standing water column let us assume microwave signal is instant on this particular radar column since it is like very smooth sorry water column microwave energy is instant on this water column. So, this is like very smooth surface. So, what will happen is radar will be instant on it radar energy and it will be reflected specularly. So, most of the energy is going in a direction away from the radar antenna. So, the radar antenna which is looking for the back scattering is not going to receive may any like a large chunk of energy a large chunk of energy is lost in the direction opposite to that of radar antenna. So, normally specular surfaces will appear dark in microwave or radar images. If the surface is rough like kind of like a let us say a dry agricultural field that is just being plowed ok. So, it is plowed it is left to be kind of like dried or it is watered whatever. So, for such surfaces it will appear rough to the microwave wavelengths. So, it will produce scattering in all directions normally rough surfaces act more like a diffused reflector that we also we have seen. So, what a diffused reflector will do a diffused reflector will reflect the energy or scatter the energy in all possible directions. When that happens a good chunk of energy will be scattered towards the antenna itself like this is like demonstrated here this is a direction which radar energy is coming. So, since this is like kind of like a rough surface it will scatter a large chunk of energy towards the direction of antenna itself. So, a rough scatterer naturally will have higher sigma naught under smooth surface will have a lower sigma naught under the case of all other factors being held constant like if all the factors that controls backscattering remain the same then a rough surface tends to have a higher sigma naught than a smooth surface. See this particular slide demonstrates that the surface roughness is the function of the wavelength and also like the depression angle or instant angle whatever we call normally like depression angle and the look angle are kind of like complementary to each other. So, here we have used the notation of depression angle. So, a same surface may appear rough to one particular wavelength say same surface may appear rough to X X band radar around like 3 centimeter wavelength where that particular surface itself may appear smooth to L band radar with close to 24 centimeter wavelength. So, let us say here the surface height is the RMSE height of the surface is let us say 0.4 centimeters let us assume this is like the RMSE height. So, for this X band radar this surface will appear kind of like a rough surface or like an intermediate surface whereas for an L band radar this will appear kind of like a smooth surface producing difference in backscattering. So, the band in which we are looking upon that is the wavelength in which we are looking upon and the sensor instant angle are going to play a major role in controlling the backscattering from the object. One more thing what we want to know is this is like the general surface roughness characteristic roughness of the just the top surface be it like a bare soil be it like a dense forest where the roughness will be defined by the canopy. Like if we have like a large cluster of trees like the radar signal will be encountering these tree tops what we call the canopy and the roughness of this canopy like if you closely observe the canopy the canopy cover may not be smooth it may be something like this each tree that can be like small small leaves, trees everything what to say protruding out. So, this will project like kind of like a rough surface. So, this is generally the surface roughness characteristics, but what about like the overall orientation of this particular surface like let us assume there is like a dense forest that is present on a flat horizontal surface and the exactly the same dense forest if it is placed on a sloping surface how that will change the radar signals that kind of like a schematic we will see now. Like here we have kind of like a near perfect specular reflector say the major share of energy is transmitted in forward direction. So, we call it as like kind of like a near perfect specular reflector. Let us say this is present on like a flat horizontal surface this is like the direction in which radar energy is coming in. So, a major fraction of energy will be reflected in a forward direction away from the radar and like a smaller fraction of energy alone will be backscattered. Let us say the same object is present on a slope that is facing the radar antenna. Slope facing the radar antenna means what will happen due to this topography even though the object is reflecting a large fraction of energy in the forward direction because of the slope still a major fraction of energy backscattered energy oriented towards the radar antenna itself thereby increasing the radar cross section. So, the same near perfect specular reflector if it is present on a slope facing the radar antenna because of this terrain characteristic or the sloping nature a relatively higher fraction of energy will be transmitted towards radar antenna. On the other hand if this near perfect specular reflector if it is present on a slope facing away from the radar antenna the amount of energy backscattered towards radar will further decrease like large fraction is going away from the radar antenna because of this slope effect the slope is the slope is kind of like reflecting the energy further away from the radar antenna only it is still like a smaller fraction of energy is going towards the radar antenna. So, not only the surface roughness but the overall orientation of the surface we call it as like macroscopic effect or like the topographic effect. So, the overall topographic effect where the surface roughness element is present that will also play a major role. Say in the example that we have just seen this will have the lowest back sigma naught because large chunk of energy is transmitted away from the radar antenna this will have kind of like an intermediate sigma naught this will have like a high sigma naught relatively. So, everything is in a relative sense with respect to each one of these three things ok. So, as a summary in this lecture we have discussed the factors that will influence the power that is reaching the antenna like we discussed what radar cross section is what radar backscattering coefficient is and we just listed the different properties of the surface that will influence this radar backscattering coefficient and the major factor that influences radar backscattering coefficient is surface roughness and also we have seen how surface roughness will play a role in controlling sigma naught. With this we end this lecture. Thank you very much.