 Hello everyone, welcome to the next lecture in the course remote sensing principles and applications. In the last lecture, we were discussing about the concepts related to imaging radar or active microwave remote sensing. Last class we discussed about the slant range nature of radar image acquisition like all the distances are measured in terms of like the slant range the line connecting the antenna and the ground point rather than talking in terms of horizontal distances. Also we started discussing about the resolution concepts of imaging radar especially the real aperture radar. So, in imaging radar the resolution has to be defined separately in two directions like the pixel size in range direction and azimuth direction. So, yesterday we discussed about the range direction like the resolution in how the resolution will be in range direction and that is determined by the pulse length of the radar system. So, here if you look at this picture, we were discussing concept related to how this pixel size is determined and this pixel size will vary in both the range direction and azimuth direction and we discussed about the variation of this resolution in the range direction. So, yesterday we noted that in range direction the pulse length or for what duration the this is determined by t the duration of our transmission of the microwave pulse. So, this will determine the range resolution. So, along the slant range if the slant range distance between them is greater than half of the pulse length two objects will be resolved independently. On the other hand if the slant range distance is less than half of the pulse length then those objects will not be resolved that is most likely those two objects will be imaged within the same pixel in the range direction. So, the slant length or the slant range distance is constant. However, the exact horizontal distance between the objects which determines the pixel size or spatial resolution for us in terms of the ground range distance will vary in with respect to the whether the objects are present in the near range or far range. Because the equation the equation to convert slant range resolution to ground range resolution is given by this whereas theta d is the depression angle. So, based on the depression angle the ground range resolution will vary. So, in general the pixels will have a larger dimension I will say coarser resolution in the near range and pixels will have finer resolution in the far range. So, we also saw an example in the last class that the length of the pixel here is 35.5 meters whereas here on the far range it is just almost 20 meters. So, two towers separated by a distance of 30 meters on horizontal ground distance will not be resolved in the near range whereas they will be resolved in the far range. So, the range resolution improves the range resolution improves in the far range. When you move from near range to far range the range resolution will be becoming finer and finer. So, as we noted the range resolution depends on the time duration for which the pulse is transmitted right tau. If we reduce this time of transmission like if the tau is reduced to a significant extent we can achieve a finer spatial resolution in the range direction. But that will reduce the total power transmitted because based on the frequency of the wavelength and the duration for which the wave is transmitted the power transmitted will be will depend upon. So, if we reduce the pulse length or the duration of the pulse transmission that will affect the power of the outgoing electromagnetic signal which in turn will affect the power that will be received back because whatever the power transmitted only a fraction of it will be received back right. So, that fraction again will go down. So, the system will suffer from lower SNR ratio like system may not get enough power back in order to differentiate it from noise. So, there should be a balance or a tradeoff between the pulse length, the range resolution and the power that we want to receive with the signal. So, there are some limitations we cannot keep on decreasing the pulse length in order to achieve a finer resolution in the range direction. Next we are going to discuss the azimuth resolution that is a resolution in the azimuth direction that is along the direction of flight. This depends on antenna beam width. So, what exactly antenna beam width is simply put when we discussed about the passive microwave radiometry I briefly told you or showed you this kind of antenna pattern right. That is an antenna is a highly directional element. So, which will basically transmit or receive radiation from one particular direction. So, there will be a primary direction in which almost all the power will coming in or the maximum power received by the antenna will be focused upon say this is the primary direction. Along this direction the antenna will be receiving its primary or maximum power capacity. So, the power received in this direction is the maximum. So, if you take the ratio P by P max you will get ratio of 1. When you move away from this primary direction the power either transmitted or received will be decreasing. So, there will be a point at where this power this ratio is 0.5 the power received to the maximum power that can be transmitted or received by the antenna will be 0.5. So, if you join this and if you measure the angle between them that will define the beam width. So, essentially the direction which is like covered by the antenna in order to like transmit or receive back half of the power like this is very similar to the concept of like full width at half maximum. Say the angle subtended by the antenna at which the power transmitted or received back is at least half of its maximum capacity. So, that will determine the beam width. If the beam width is narrower if the antenna is like highly directional then the azimuth resolution will be better. On the other hand if the beam width is wider then the azimuth resolution will be poorer. So, the beam width depends on the basically the direction at which the microwave begins to propagate because the microwave once it starts spreading from the antenna it will be spreading in the all directions in the three dimensional in all direction in the three dimensions before it reaches the target. So, if you look at the slide the azimuth resolution depends on the slant range distance between the antenna and the object and lambda by L where this factor lambda by L comes in terms for beam width. Like the antenna beam width can be shown to be related to this lambda by L where lambda is the wavelength in which the antenna is operating the microwave wavelength chosen for our operation and L is the physical length of the antenna. So, this suggests that this number the range the azimuth resolution will become larger and larger or coarser or coarser whatever when the slant range distance increases that is the antenna beam will be spreading continuously when it is transmitting. So, whatever objects that fall within like one full beam they will be imaged as one single pixel say here the antenna beam width may be like this here it slightly spreading like this here it may spread like this. So, whatever objects that are present within the single beam width will be imaged as one single pixel. So, in the near range the azimuth resolution will be finer because of the less spreading of this antenna the microwave beam whereas it will be coarser in the far range. So, with slant range distance the resolution will become coarser also this depends on lambda by L. So, we should have like a shorter wavelength because lower this wavelength lower will be the number. So, lower will be the number finer will be the resolution that is the concept. So, short range distance sorry slant range distance should be shorter that is object should be near range lambda should be shorter wavelength and L should be very long. So, if these conditions are satisfied then essentially the this number the range resolution number will be finer or smaller leading to like a smaller pixel size. Okay. So, just look at this equation and then from which we can determine the azimuth resolution varies with slant range distance the wavelength used on the antenna length. But once the system is launched we cannot change the lambda and physical length of the antenna. So, the lambda by L should be fixed even before the system is launched and S anyway will vary based on whether it is slant range or sorry if it is like in a near range or if it is in a far range. Similar to the example that we saw for the range resolution we will also look at one more example to demonstrate the concept of azimuth resolution. So, just look at this particular slide here we have 2 towers 1 and 2 in the near range 3 and 4 in the far range these 2 towers have a horizontal distance of 200 meters between them. Okay. So, the slant range distance from the antenna to the towers in the near ranges 20 kilometers and the slant range distance to the towers in the far ranges 40 kilometers. And it is operating with the wavelength of 3 centimeters and the physical length of antenna is 500 centimeters. So, Ra is equal to S into lambda by L. So, if we work all the if we substitute all the values and work out then the near range azimuth resolution will work out to be 120 meters. In the far range the azimuth resolution works out to be 240 meters. So, it just doubles as the slant range distance doubled. So, this suggested the towers which are separated by horizontal distance of 200 meters will be resolved as 2 different things in the near range because the here the pixel size is just 120 meters. So, these 2 towers will be there in 2 pixels. Here just 1 pixel size it will be itself is 240 meters. So, these 2 towers both of them will be covered within 1 pixel and they may not be resolved properly. So, this suggests that as the slant range distance increases azimuth resolution will become coarser and coarser. In fact, real aperture radar systems what we just discussed cannot be used for space-borne satellites because the slant range distance will be like in the order of hundreds of kilometers right. Orbital height itself will be like around like few hundred of kilometers. So, the slant range distance will be very long. So, the slant range distances will be very large when we go to space-borne systems and real aperture radars cannot be used for space-borne systems if we want to achieve like a good spatial resolution. So, this is like a major limitation of real aperture radar to be used for space-borne systems. But the wavelength can be changed or the physical length of the antenna can be changed even before the system is launched. That parameter lies with the system designers. Wavelength anyway it is fixed on the application for which it has to be used like we all know the limitation of shorter wavelengths in microwave. They undergo like a very large attenuation in atmosphere their penetration capacity is low and all those things. So, for certain applications scientists will prefer to work in longer wavelength range. So, that depends on the application and the science which the scientists want to do. So, the parameter that can be changed freely is L the physical length of the antenna. Having a very long antenna will reduce that number or reduce the number of azimuth resolution say Ra is equal to s into lambda by L. So, larger the L lower will be this number and hence finer will be the resolution. So, increasing the antenna length is a possibility. But physically increasing it like having an antenna in terms of like hundreds of meters is not practical in airborne based systems like airborne based systems they can have few meters of antenna length. Even in space-borne the antenna length can be maybe tens of meters but not more than that. But we may need to have like hundreds of meters of antenna if you want to achieve like a very fine spatial resolution in the azimuth direction from space-borne systems. So, there are like practical limitations the antenna length has to be limited because it will increase the weight it may change the stability of the aircraft or the satellite whatever. So, we cannot keep on going on increasing the antenna length also. So, what is the way to overcome this? In order to limit this or in order to overcome this limitation synthetic aperture radar concept was developed. But before going on to the synthetic radar concept we will just quickly summarize the resolution concepts of this real aperture radar. So, in real aperture radar the pixel size will be coarser in the range direction in the near range finer in the azimuth direction in the near range. So, the pixel may be something like this this is the range direction and this is the azimuth direction. So, in near range this will be like this in far range range resolution will become finer this will become coarser the azimuth resolution will become coarser. So, the pixel may look something like this. So, there will be like a large scale distortion in the radar image say especially for the real aperture radar system say see how the pixel is oriented here like with longer pixel size in the range direction and shorter pixel size in azimuth direction and exact opposite in the far range. So, the pixel dimensions and the look of pixel and everything will change and there will be like a scale distortion across the image in the real aperture radar system. So, this is like another limitation of real aperture radar the resolution or the pixel size will be keep on varying based on the whether the objects are in near range or in far range. So, this is how like a radar image will basically be acquired. Now, we will go to the concept of synthetic aperture radar. So, as the name suggests synthetic aperture radar aperture indicates the length of the antenna ok. So, the antenna length is synthetically increased. Synthetically means artificially increased or people will call it as synthesized antenna length is synthesized. So, what does it mean? We know that the radar systems will collect the power that is received back and also the polarization information also right. Similarly, the phase of the incoming wave can also be recorded. Say whenever like microwaves are transmitted they will be like coherent waves like fixed phase relationship between there between the different pulses that are like transmitted. So, microwaves are like when the radar system transmits those waves are coherent. So, the phase information will be there. Similarly, after getting scattered back by the objects on the ground they will be received back and the radar system will also record this phase information what is the phase of the signal that got recorded. So, based on the relative position of different features with respect to this particular antenna there will be like a Doppler shift in the frequency of the received microwave signal. Like we just briefly looked at like Doppler shift in the earlier classes. So, what it will mean like whenever there is a relative motion between the source of EMR and the target the frequency of electromagnetic radiation will be appearing to change. So, it is an apparent shift in frequency. Say when the source and receiver are moving towards each other the frequency will appear to increase when the source and object are moving away from each other the frequency will appear to decrease. So, this is like an apparent shift. Noting this apparent shift we will be able to calculate the Doppler velocity or the velocity between relative velocity between the source and the target. So, this principle will be used in the synthetic aperture radar data processing. So, here system everything is remain the same, but by recording the phase information people will be able to synthesize a very long length of antenna. So, just like a very conceptual example I will tell you. Say this is like the physical antenna length D. Let us say there is an object here. So, when the system is moving like this in this particular direction. So, this particular object present here will be seen by the antenna once the antenna is here itself. Because like whenever some object is at a far distance we need not come exactly perpendicular to the object to see it right. We can see the object from little further distance because the similar antenna the microwave signals also will be like spreading out as it moves. So, even object that is far will be sensed by one particular signal. Say the object is here the beam with maybe transmitter like this. So, as the distance increases the beam with may spread across and it may fall over this object. So, the actual position of radar will be here, but just due to the spreading of antenna beam with the this object signal will be received when the radar position is here itself. Slowly as the radar is moving like this from different different positions the same object will be imaged by this radar system. So, when the radar system becomes exactly perpendicular and it will be recorded and it will slowly move away from the picture. After certain distance this object cannot be seen by the radar system. So, after this this object will vanish from the radar system. So, essentially same object can be imaged by the radar system from different different positions. Say this is like the physical length of the antenna. But imagine if there is a way to process all the data such that all these different positions can be combined together that is all the signals that were received from this object from different different position of the antenna that can be combined. So, that all the antenna lengths can be added together to synthesize a very long antenna length. So, the concept is like this. Same object can be seen from different different positions in the horizontal sorry in the azimut direction as the flight is moving or the satellite is moving. When that happens the data processing system will try to collect all the signals that came from one particular object from different positions and add up all the using the phase information the antenna length will be keep on adding up. So, if the object is farther say if the object is very far what will happen we can see the object like this from a very farther distance right. So, till we move for a very long distance object that is bit far in this particular in the range direction can be seen. On the other hand if an object is very near to the range direction that object can be seen say if an object is here let us say this object cannot be seen from this particular antenna location maybe this will appear in the image from this location to this location. So, the antenna length so the for the distance for which this particular object is seen will naturally be lesser than the distance for which the object in far range is seen. So, as the object moves away and away in the range direction the total length for which the object can be seen by the radar system will be longer. So, just combine all these radar locations and based on the object's position in the range direction the antenna length will be keep on varying an object if is that is very far it will be seen by the antenna for a very long distance. So, combine everything to produce a very long antenna if the object is a near range it will be seen only for a shorter length of shorter distance. So, combine everything to produce like a another antenna length. So, essentially the antenna length is synthetically increased. So, the different the signals received from different positions of antenna from the same object are all combined together in order to produce like a very fine spatial resolution. This is the very simple conceptual explanation of SAR. We are not going to discuss in detail about how this is processed, but the way it is processed uses the Doppler frequency shift. So, as like as the antenna moves like this with respect to this object the frequency will be keep on changing like the frequency the Doppler frequency shift will be keep on increasing as the antenna is moving towards the object. Then when it is exactly perpendicular to the when the antenna is exactly perpendicular to the object Doppler frequency shift will be 0. As the antenna again moves away from this object Doppler frequency shift will again be beginning to appear and slowly it will the object itself will disappear from the radar's point of view. So, using this Doppler frequency shift concept each and every object in the range direction can be imaged from multiple locations and everything are processed together to synthesize a very long antenna length. So, this is the concept of synthetic aperture radar. So, theoretically it can be shown that the spatial resolution in the azimuth direction for synthetic aperture radar is L by 2 or not L by its in this example it is D by 2 half of the physical length of the antenna. So, if the antenna length is say 20 meters the physical length then the spatial resolution can be 10 meters theoretically. And this theoretical resolution is independent of the slam train distance object whether it is a near range or far range each object can each pixel size can have like a uniform spatial resolution. So, this is like a major advantage of SAR system. So, here that is an example. So, this is like a real aperture radar system. So, this is like a synthetic aperture radar system. So, for real aperture radar system range resolution will be keep on changing azimuth resolution also will be keep on changing. So, you can see here slowly the azimuth resolution is beginning to what to say becoming coarser and coarser whereas for in the SAR system the azimuth resolution becomes independent of the slant range distance and hence it is it will be treated more or less constant. So, azimuth resolution will be many orders better than the range resolution. Range resolution there will be no change it will be coarser in the near range finer in the far range there is no change in the range resolution the azimuth resolution improves drastically in SAR systems. So, normally for SAR systems the azimuth resolution will be much better than the resolution in the range direction. So, this is like the basic working principle of SAR a conceptual working principle I would say not like the real working principle and also one thing to keep in mind is the azimuth resolution has now become independent of the range like in the real aperture radar system the azimuth resolution will be keep on becoming coarser and coarser as the slant range distance increases. For SAR systems the azimuth resolution is almost independent of the slant end distance and it will be more or less constant even if the objects are at a very far range. So, almost all the space bond systems imaging radars are synthetic aperture radars then only we will get like a required fine spatial resolution for our applications. So, in this particular lecture we discussed the concept of spatial resolution of radar systems like the azimuth resolution range resolution and also the limitation of real aperture radar systems and we got introduced basically to the synthetic aperture radar systems. With this we end this lecture. Thank you very much.