 and this is the second lecture. So just a quick recap of what we discussed as part of a previous lecture. So previously we tried to understand in simple terms the basic image formation when it comes to synthetic aperture radar or SAR and then we had an understanding that SAR image are composed of complex numbers with a real part and an imaginary part. We learnt that when it comes to microwave systems or radar systems they need to be compared with ears and not with eyes. As in in optical remote sensing textbooks tend to compare images synonymously with vision of your eyes. When it comes to microwave systems we need to compare it more with ears and as we humans detect sound in a similar manner the microwave systems they collect the energy from a wide range of directions you know many directions they collect all the energy. Remember we are yet to discuss about the directionality or sensitivity of microwave systems or you know their sensitivity to certain directions or range of angles. We are yet to discuss that but in a nutshell we have some simple understanding about synthetic aperture radar image. So let us move forward again for an imaging radar we discussed that individual echoes from the targets are used to generate a number of image data points. Now these targets can be distributed targets or individual targets and by some means the return echoes from the targets they are being related to the spatial dimensions of the target. By some means we will get to that shortly or let us rephrase the sentence. A sequence or a series of echoes are being collected as the satellite moves in its orbital track and here by echo I am referring to measurement across the swath. Now shown here is a sample for you to understand how a SAR imagery looks like and this represents the image of Maharashtra region. So remember SAR image is not a photograph made with microwaves no it is not a photograph made with microwaves but then a radar image is a fundamental collection of data points, fundamental collection of data samples. It can be a power of amplitude or a phase or of both amplitude and phase at different polarizations. And the fundamental dimensions of a SAR image are range which is known as time delay and azimuth which is known as flight path distance. Again the range and azimuth they do not equate directly to the dimensions on the ground. We will see that in detail but for now this is a sample for you to understand how a synthetic aperture radar image looks like. So moving forward shown here are few bands in microwave remote sensing their applications and the satellites which have sensors using these bands or operating in these bands. So we have X band that is predominantly used in topographic mapping and in flood mapping riset 2B operates in X band. We have C band which has applications of ship detection or oil spill monitoring and a few satellites which have a C band system are riset 1A and we sat radar sat sentinel 1AB etc. Remember this is not the complete collection but just a few examples of satellites that carry radar systems operating in the specific frequencies. Like for example if we look at S band it is used predominantly for crop classification or for ship detection, oil spill detection and NISAR that is NASA ISRO synthetic aperture radar. NISAR has a sensor that is going to operate in S band. Similarly when we come to L band it has good penetration power as compared to C band and X band and hence it is predominantly used in hydrology, forestry, agriculture and so on. When it comes to P band it is used for biomass estimation because it has a very high penetration to detect the targets within camouflage. Now for us to move forward we need to be aware of a few terminologies that will be used throughout as part of this course you know few technical terms. So let us try to understand them one by one starting with SWAT and NADER. Now before I start explaining what you see here is the platform that is the aircraft it is carrying a SAR sensor. The SAR sensor has a side looking geometry so it is looking down side looking geometry. You see NADER point marked here by NADER I mean the direction that is directly beneath the platform the platform being the aircraft here okay NADER direction directly beneath the platform. You see something marked as SWAT here isn't it? The microwaves as I mentioned earlier they are being transmitted sideways to the direction of flight. So the flight direction is indicated here and this shows the direction in which microwaves are being transmitted that is they are not transmitted perpendicularly in the NADER direction but they are transmitted sideways to the direction of flight illuminating a SWAT. So what is SWAT? It is offset from a NADER SWAT is offset from a NADER. Remember when I say that microwaves are being transmitted sideways it can be either to the left side or to the right side but the whole idea is it is a side it has a side looking geometry. Again range is something we should be aware about that is we have a long track as well as a cross track direction. When it comes to range we call it as the across track direction range okay range of a radar system across track dimension that is perpendicular to the flight direction and the area that is near to the NADER direction is known as near range and the area that is farther away from the NADER is known as far range okay. Now all the SAR sensors you know they are side looking sensors as in they would not be transmitting microwave pulses vertically but they will be transmitting them sideways to the direction of movement of platform which means as I mentioned earlier either to the left side or to the right side here two angles are being shown in the slide in front of you one is theta i incidence angle another is theta l that is look angle okay. Now while looking at the diagram you will be able to understand the meaning of incidence angle and look angle. When it comes to look angle it is the angle from the NADER direction that is from the perpendicular direction to the platform from the NADER direction to the instrument line of sight okay from the NADER direction to the instrument line of sight that is the look angle theta l. Now local incidence angle is measured between the line of sight and the normal to the ground surface please remember. Again when the platform that is hosting the sensor that is where the sensor is placed whether it is an aircraft or a satellite we need to have some basic understanding about the topography or terrain. If the platform hosting the sensor is an aircraft we can assume a flat earth wherein look angle and incidence angle can be considered as same equal for any given line of sight but we know that earth is not flat and when the platform which is hosting the sensor is a satellite which is operating at a much higher altitude than the aircraft we need to consider the curvature of the earth you know earth curvature effects need to be considered it has to be taken into account okay. Now moving on to something known as resolution okay resolution. See understanding the concept of resolution is fundamental to interpreting remote sensing targets because resolution helps us to understand the separation distance between two targets resolution ability to resolve okay. So resolution it means the separation distance between two targets for us to resolve them differentiate between them. Now if you remember as part of an earlier lecture I showed you the slide and then I mentioned that the elliptical region you see here is nothing but the illuminated area on the ground. Now because radar sensors are side looking the radar resolution that is the ability to discriminate between features we can define it in the parallel and perpendicular direction okay to the flight line. So which means in a direction parallel to the flight line in a direction perpendicular to the flight line. So we need to understand this a bit more clearly because you know when we look at an image captured in the visible or infrared regions the resolution is more or less same as pixel spacing okay. You just have one resolution for an image that is captured in either the visible or infrared region that is optical images they tend to have a spatial resolution. Now here when it comes to microwave images they tend to have resolutions in two directions which is what we will discuss in detail now. So just to reiterate the direction in which a SAR sensor a synthetic aperture radar sensor is transmitting pulses is known as range direction okay. The direction in which a SAR sensor is transmitting pulses is known as range direction and the direction in which a SAR sensor travels or moves forward is known as azimuth direction or flight direction okay. And as I mentioned earlier because of the two directions that is range and azimuth there shall be two resolutions azimuth resolution and range resolution. Remember in optical remote sensing there are single spatial resolution which are many times equal to the pixel spacing only one resolution is available when it comes to optical remote sensing but here in microwave remote sensing there are two directions okay. Range direction and azimuth direction which is why there are two resolution azimuth resolution and range resolution okay. Now the SAR sensor is transmitting pulses in the range direction while it is moving in the azimuth direction. Let us try to think of it in technical terms okay. So if you ask me I can easily define an azimuth resolution now because it is the ability of a synthetic aperture radar sensor to differentiate between two closely spaced objects or targets in the azimuth direction. So remember whenever I say azimuth it is the direction of motion of sensor okay flight direction and when it comes to range resolution you can define it as the ability of a synthetic aperture radar sensor to differentiate between two closely spaced objects or targets that are available in the range direction. Remember for this to be possible their echoes should necessarily be received at different times okay. We will see that in detail shortly. Now this is just a schematic for you to understand what is azimuth direction and range direction again. The flight direction is shown here flight direction along track direction azimuth direction and then the direction that is perpendicular to the along track direction is the range direction okay. Again just to make things clear here the platform shown is a satellite and the movement of the platform scans terrain in the azimuth direction to build up a two-dimensional image. Once again the movement of the platform is going to scan the terrain in the azimuth direction to build up a two-dimensional image. So by now we have understood what is what and in this diagram the azimuth direction and range direction is clearly indicated. So now let us go a little bit deeper to understand more about range resolution range resolution. Before that we need to understand what is a pulse and duration of a pulse. See the accuracy with which distance from a satellite antenna to the target can be measured by a radar system. It indicates the quality of a radar. How finely can a radar system measure the distance between the sensor as well as the target that indicates the quality of a radar. So when it comes to range resolution it is the ability to distinguish between two point targets. So again how does a radar distinguish between two targets? By in turn distinguishing between their echoes is not it? Because as I mentioned earlier radar system which is having a side looking geometry like a synthetic aperture radar. It is going to transmit pulses with a certain duration which is going to travel hit the target. It is going to get scattered in all directions and the return echoes a part of it reach back to the satellite which is then getting registered to give you a synthetic aperture radar image as you saw earlier as part of this lecture. So again how does a radar correctly distinguish between the echoes that are coming from two different targets? That is by differentiating or distinguishing between their echoes you know. Let me try to redefine the range resolution. Shown here are two objects. I am going to call it as T1 and T2 two objects. Now assume what you see in red are the return echoes from these two objects T1 and T2 and they are shown far apart in the range direction which is why the return echoes are distinctly separated. Two objects far apart in range direction which is giving rise to distinct echoes. Now let me give you a reverse scenario wherein the two objects T1 and T2 are very close apart. So close apart that their echoes tend to overlap. Again what you see here is two objects T1 and T2 that are so close apart in the range direction such that their echoes tend to overlap. Now if the echoes overlap we cannot tell one apart from the other isn't it? That is a problem. So what to do? So range resolution or the ability to distinguish in time the return echoes from the two targets. It is dependent on the duration of microwave pulse transmitted by radar. Duration of microwave pulse transmitted by radar. Now let us try to understand this a bit further. Again we have the two targets T1 and T2 which are at range distances say R1 and R2. What is range distance? It is a distance of target from the sensor from the satellite which carries the sensor. So R1 and R2 are the range distances for T1 and T2 two targets. Now if you look at the diagram I have given you a pulse which is having a duration of C tau P and the range resolution limit, the limit of range resolution is when the front end of the echo from T2 when it reaches T1 just as the tail end of echo from T1 has left. So let me repeat. What you see here are pulses that are being transmitted from the satellite. It hits the target T1 and T2. Now I want to know what is the limit of range resolution? The range resolution limit because beyond a point when the two objects are close together the radar will not be able to differentiate between their echoes because their echoes are going to overlap. So I want to understand what is threshold? What is the range resolution limit? What is the maximum distance between the two targets that a radar can differentiate? To understand that I am showing you T1 and T2 two targets. Obviously the pulse that hits the target is going to be scattered in all direction with a small part of the return echo which is going to reach the satellite. So the range resolution limit is when the front end of echo from T2 reaches T1 just as the tail end of the echo from T1 has left. Just as the tail end of echo from T1 has left and then the separation between T1 and T2 is known as range resolution which is given by C tau P by 2. This brings us to a very important realization that the range resolution is dependent on the pulse length pulse length. See here denotes the speed of light which means a shorter the pulse length closer the two targets T1 and T2 can be before their echoes overlap and as a consequence better shall be the range resolution. But then let us think about it practically because in reality it is going to be a challenge to go for transmitters which are capable of generating very short pulses with a high peak power. Remember we need a high peak power also. The echo or the return pulse needs to have a high peak power as they have to be registered with the platforms say space bond platforms or airborne platforms which are at a high altitude from the surface of the earth. Just to understand the concept of range resolution let us discuss an example a small example shown here is a pulse with pulse length. See tau P is given as 600 meter because tau P is nothing but 2 mu second and assume this pulse is trying to detect two aircrafts let this be T1 and T2 two targets two aircrafts which are at a distance of say 200 meters. Now the distance I am measuring from the nose of one aircraft to the nose of the other aircraft. So the aircrafts are closed apart so that their distance is 200 meters and I have shown you a pulse wherein C tau P is 600 meters which means the range resolution is going to be C tau P by 2 that is 300 meters which means if the separation distance between the two targets that is the two aircrafts are 300 meters it will be detected by the radar which means for this case when the separation distance is 200 meters the radar which is sending out a pulse of this pulse duration it would not be able to differentiate between the echoes coming from the two targets very difficult. Now let me give you another case wherein C tau P remains the same 600 meters tau P is 2 mu second but then now I have the aircraft the distance between the aircraft is 400 meters which means the distance from the nose of one aircraft to the nose of the other aircraft it is 400 meters which is greater than the range resolution of 300 meters which means this radar system will be able to differentiate between the echoes that are coming from two targets which are placed at 400 meters range resolution. So let us try to understand what to do because you know we need short pulses for better range resolution at the same time we should have a high peak power. Now let us try to also recollect the example in one of the previous lectures wherein you heard three piano notes with echo and without echo and in that particular example even when there was echo you were able to identify the nodes because they followed some pattern. Similarly here also we need to keep the transmitted power high at the same time we need to have a very fine range resolution shown in front of you is a chirped pulse on the x axis we have the time tau p and on the y axis we have the amplitude. In the case of a chirped pulse as shown here we are sweeping the signal across a range of bandwidth such that the transmitted signals is encoded. Let me reiterate we are sweeping the signal across a range of bandwidth so that the transmitted signals get encoded and this makes it easy for distinguishing in time. This relies on frequency modulation which is you know also common among echo locating bats. See our ears are capable of identifying different nodes from different instruments and let me clarify with another related example. We will say imagine you are in a highly noisy environment say a traffic junction wherein you are straining to listen to random piano keys which are repeatedly being played random piano keys. So in this highly noisy environment you will find it very very hard to listen to the piano keys. Now instead of this assume that you are at the same traffic junctions there is the same noisy environment around but then instead of the random piano keys your favorite song is being played. Now here by your favorite song I am referring to a predefined sequence of nodes. Predefined sequence of nodes that is following a pattern. So now what happens that even if the background noise is very much existing you will be able to identify the signal the song as you are listening to a pattern instead of a single note. You are listening to a pattern instead of a random piano keys which means even if you hear bits and pieces portions of your favorite song that alone is sufficient for you to identify the tune, isn't it? Now try to think of that example when we are trying to understand about chopped pulse which is linear frequency modulated pulse. So now I am defining range resolution as a function of bandwidth of the signal, bandwidth of the signal. Remember as the range of frequencies increases the range resolution shall be better and better. So now you see an expression here for plant range resolution where B stands for the bandwidth, C is the speed of light. So now I am defining range resolution as a function of bandwidth of the signal. Remember as the range of frequencies increases the range resolution shall be better and better and please note that the range resolution is independent of the distance of satellite with target and it is also independent of the target which means no matter what target is being observed a radar system shall have a range resolution which is system limited. Let me re-igrate no matter what target is being observed a radar system shall have a range resolution which is system limited. Also range resolutions are defined using pulse bandwidth rather than distance and remember larger bandwidth give better range resolution. So with this background let us try to understand about two terminologies. One is known as ground range resolution and the other is known as slant range resolution. A schematic is shown here where assume the shaded region represents the ground surface theta i is marked we are already aware of what is an incidence angle and shown here are something known as ground range resolution as well as slant range resolution. Now ground range resolution is the ability to discriminate between earth surface features ground range resolution. Now if we have a knowledge about the local incidence angle that is theta i we can estimate the ground range resolution. Remember with the radar sending pulses sideways the resolution gets better and better as one moves farther away from the nadir. Okay in the same manner say you consider two platforms one is a satellite one is an aircraft we know at what altitude an aircraft operates and at what altitude a satellite operates aircrafts operating in troposphere and satellites in exosphere. So one thing to note here that is worthwhile is that the incidence angle that is theta i increases as the altitude decreases. Incidence angle increases as the altitude decreases and again when we are trying to image over complex terrains or mountainous terrain say the Himalayas where there is huge variation in topography the local slope is going to influence the incidence angle. We will discuss this in detail when we come to image distortions in radar images. So given here is the expression that ground range resolution what you see here is nothing but slant range resolution by sine theta i. Theta i is the incidence angle and just remember this diagram so that you understand how to calculate ground range resolution. So now we have understood about range resolution and then we understood about what is ground range resolution and what is slant range resolution. See real aperture radar was known as the original radar imaging system wherein the radar equipment is mounted on the platform which is moving at an altitude above the reference surface and the antenna points sideways to illuminate a swath and this illuminated region is known as a footprint. Now a radar system sends microwaves that travel at the speed of light we know that okay and the return echo or the received power is expressed as a function of time delay. Time delay using which we can obtain the range as well as azimuth resolution. So the figure here what you see it shows the geometry of a real aperture radar. Now please note that real aperture radars they are limited at higher altitudes to provide a larger antenna they are limited at higher altitudes and this is not very practical okay. Once we start solving numericals we will understand the limitation of real aperture radar and the advantage of synthetic aperture radar. But for now you have real aperture radar also known as side looking airborne radar SLAR okay alright and by now I think you are familiar with nadir, azimuth, ground range, swath isn't it okay. So just to complete our discussion what you see in front of you is the azimuth resolution of real aperture radar which is nothing but nearly equal to wavelength into range by length of antenna okay wavelength into range by length of antenna. Moving on the range resolution of rare we discussed it is independent of platform height isn't it. Now whether it is rare or SAR it will have a particular range resolution as well as azimuth resolution. So we already saw the azimuth resolution what you see here is the range resolution and the slant range that is c tau p by 2 c speed of light tau p pulse duration okay range resolution in the slant range. So just to summarize in this lecture we understood that the fundamental dimensions of a SAR image are range that is time delay and azimuth that is flight path distance and these do not directly equate to dimensions on the ground very important they do not directly equate to dimensions on the ground and then we discussed about a few terminologies used in radar remote sensing. Now what are they we discussed about range about swath about azimuth resolution about range resolution and we also briefly discussed about what is the difference between slant range resolution and ground range resolution. Then we discussed about real aperture radar or side-looking airborne radar okay. So let me hope that you found this lecture useful and I will meet you in the next class thank you.