 Hello, and welcome to the third lecture of module 2. So, till now we have been learning about key terminology is used in synthetic aperture radar like the SWAT, what is NADR, what is azimuth resolution, range resolution etc. And we have also seen the basics of SAR image capture. So, today let us begin the lecture by trying to understand about aperture synthesis in synthetic aperture radar. So, till now our understanding about SAR says that a single small antenna is moved forward along a flight path and then SAR is transmitting coherent pulses in the microwave region. By coherent I mean having same initial amplitude and phase information coherent pulses. So, these pulses hit the target and the returning echoes are processed by using both the amplitude as well as the phase information. The net effect is similar to many antennas working together to synthesize a really large antenna up to many kilometers in length. Remember in the last lecture we understood the constraint the limitation of real aperture radar RAR. And by now slowly our understanding about synthetic aperture radar is becoming clearer and clearer. But then I still have a few doubts as in let us try to consider the imaging geometry of SAR in a little more detail. So, the schematic shown here represents a target as it moves through SAR beam. From some point say X on the axis to the center of the beam say X naught. So, what I am going to do is you may be already familiar with the diagram shown on the screen. I am going to represent the same diagram in this manner wherein the flight direction is shown and then the target as it moves through the SAR beam from some point on the X axis to the center of the beam X naught is shown here and R naught is the range distance. And now let us consider a point say X just before X naught. So, the same diagram is being represented here in a different manner so that we understand what is X naught, what is X, what is R naught and what is delta R. I will come to delta R. So, at X1 the distance of target from antenna is slightly longer. R naught is the distance of target at X naught from the antenna. Now when it comes to X1 the distance is slightly longer by a factor which we denote as delta R. Such that now I can write R equal to R naught plus delta R. R the whole range at X1 equal to R naught plus delta R. Say I can even write R square equal to R I can even square both sides is not it. But then I am going to write R naught square plus X square equal to R square can I write like this using Pythagoras theorem. So, if I put it together I can write R naught plus delta R square equal to R naught square plus X square. So, what did I do? I first wrote R as nothing but R naught plus delta R and then I squared both sides and then I have rewritten the same expression in this manner by replacing R with R naught plus delta R whole square. And we know that we have applied Pythagoras theorem that is why I have written the same as R naught square plus X square. Now if I rearrange a little bit I will get delta R equal to R naught square plus X square under a root minus R naught. And here the distance of the target from the center of the beam is assumed to be very, very small. I have just exaggerated X naught and X1 so that it is easy for us to continue with the derivation but actually the distance is very, very small. So, I can write that X very much less than R naught which means I can write the same expression in a different manner R naught square plus X square under a root equals R naught 1 plus X square by R naught square under a root. And this again I can write it naught square and of course it goes on which is nearly equal to R naught plus X square by 2 R naught. So, what is this? This is R naught square plus X square I have used the binomial expansion to write this. So, what have I done? I have initially written R as R naught plus delta R. What is R and what is delta R? R is nothing but the range distance of the antenna from a target. The center of the beam axis is given as X naught and I am going to assume a small distance along the X axis which is X or X1. So, what happens is the range distance is going to be increased by very small factor. I am going to call it as delta R and then using Pythagoras theorem I have started the derivation. I have written R is equal to R naught plus delta R. I have squared both sides and then I have used the binomial expansion to finally get an expression like this that is R naught square plus X square raised to 1 by 2 nearly equal to R naught plus X square by 2 R naught. So, let me call it as 2. Now, if you remember we had initially got an expression of delta R equal to R naught square plus X square raised to half minus R naught. We had got this in the previous slide, is not it? By applying the Pythagoras theorem and by rearranging the terms. So, what I will do is I am going to substitute 2 in 1 because now I have the expression of R naught square plus X square under a root. So, I am going to substitute it here and then let us see what we will get. So, we have delta R equals R naught plus X square by 2 R naught minus R naught. I can get delta R nearly equal to X square by 2 R naught. This is what I am getting which means the slight distance, slight increase in the range denoted by delta R is nearly equal to X square that is the distance along the axis X axis by 2 R naught where R naught is the range distance from the antenna to the center of the target, center of the beam, okay. Now, if the transmitted pulse has to travel this additional distance of delta R then obviously it is going to cause a change in phase of the measured echo. Remember, we started the lecture by mentioning that the radar echoes that reach the antenna will be having differing amplitude and phase information and by some means the SAR image is representing the information about the target using the phase and amplitude of the return echo. And also remember, we discussed something about a chirped pulse in the last lecture. So, if the transmitted pulse has to travel this additional distance of say delta R then it is going to cause a change in phase of the measured echo as well which means now I can rewrite this expression of delta R as a corresponding phase shift for each X location. Let me write it down as a corresponding phase shift for each X location. So, we already know that phase is represented by phi. So, the phase shift phi for each X location phi of X I can write it as minus 2 delta R 2 pi by lambda. This again I can write it is equal to minus 2 pi X square by lambda R naught, okay. Same expression I have rewritten it by considering the phase shift at each X location. X is just representing an axis. Now, as the target is moving through the beam, remember we started the discussion by considering a footprint and then I mentioned that as the target is moving through the beam the phase will tend to change with the azimuth position X. By now, I am assuming that you are familiar with the terms of azimuth because we just discussed about azimuth resolution and range resolution in the last lecture. So, let me reiterate as a target is moving through the beam the phase tends to change with the azimuth position X. So, if the flight direction is something like this and the footprint the illuminated area on the ground at an instant when the platform is moving that is a footprint is something like this, then we already know that this is the azimuth direction this is the range direction along track direction and across track direction. So, as the target is moving through the beam the phase is tending to change with the azimuth position that is X. So, finally these echoes they result in something known as a phase history. Remember this is not a single echo that I am talking about as the target is moving the echoes are continuously getting reflected scattered from the target and they are trying to reach the antenna. So, these echoes they tend to create something known as a phase history which ultimately informs us where the target is located. So, the pattern of phase history now this is analogous to the chirped pulse that we discussed in the last lecture which is matched with the reference chirp. So, the pattern of phase history informs us the direction of target where exactly the target is located. So, let us try to estimate the azimuth resolution from this geometry that is shown that is from this geometry. So, we learn slowly as part of upcoming lectures that the maximum size of the artificially synthesized antenna of SAR is directly proportional to the wavelength. I will not go into details of this derivation now but it is worthwhile to discuss this. So, let me try to put it this way. Assume you have now assume you have a synthetic aperture radar which is having an artificially synthesized antenna of say dA say dA is the length of artificially synthesized antenna from SAR and of course, this is based on the distance that the antenna travels in the along crack direction as it is illuminating a target on the ground. So, please remember that the antenna in synthetic aperture radar is both transmitting a pulse as well as receiving an echo. So, it is doing both the functions and as we proceed through the course we will see that the best possible resolution that can be achieved by a synthetic aperture radar is when the azimuth resolution is one half the length of antenna. Let me try to repeat. The best possible resolution that can be achieved by a synthetic aperture radar is when the azimuth resolution azimuth resolution is one half the length of antenna, one half d by 2, one half the length of antenna. So, we will see the derivation shortly but for now I want you to understand the relationship between azimuth resolution and length of antenna. So, this was just to give you an overview of the synthesis of aperture in a synthetic aperture radar. So, with this understanding let us try to move forward and let us try to understand about the different SAR modes. By SAR mode I mean an operation by which synthetic aperture radar is collecting information. So, till now we were only familiar with the basic process of an illuminated area on the ground that is a footprint and the synthetic aperture radar that is moving and transmitting as well as receiving the echoes transmitting the pulse which is hitting the target, echoes are returning and then the antenna is receiving the echo as well. So, that was our basic understanding about synthetic aperture radar. Now, let me introduce you to the different modes in which a SAR can operate to collect information. The different SAR modes as written here. All right. Now, the first mode shown here is the scan SAR operation, scan SAR. Typically for regional to global scale monitoring we usually need wider swath, wide swath coverage is required and to get a wider swath of imagery it is necessary to acquire images simultaneously by transmitting pulses to image a small azimuth section of swath followed by imaging an immediate adjacent swath and then this operation is repeated. So, why are we doing this to get a wider swath of imagery? We are transmitting the pulses to a small azimuth section of swath followed by imaging an adjacent swath and this operation is getting repeated. So, the arrows shows the way in which scans are operation is carried out. The arrows shows the way in which scans are operation is carried out here. Adjacent areas are being repeatedly scanned and imaged and scan SAR mode as the name suggests, this is commonly used in advanced synthetic aperture radar ASAR. It is also used in radar SAT. So, SAR mode and scan SAR operation. Moving further, we also have different other modes such as what you see on your screen is known as the spotlight mode, spotlight mode. So, in the previous lecture we learned that azimuth resolution of a synthetic aperture radar is dependent on the amount of time a target is remaining in the vicinity of a narrow beam of microwaves, amount of time for which a target is remaining in the vicinity of microwaves. So, here in the spotlight mode the steering capabilities of SAR is used to continuously point a narrow beam of microwaves on the same area or target as the instrument flies or moves with the platform. So, as a consequence we get very high resolution for one patch of the ground. For this patch of the ground we get a very high resolution whereas the other area has not paid much attention here. So, you are focusing on only one patch of the ground. So, it has both advantage as well as disadvantage. Advantage is for this patch of the ground on which the spotlight is fixed you will get a very high resolution but then certain other areas are neglected. Spotlight mode easy to remember. Spotlight mode. So, we discussed about scan SAR mode and then spotlight mode. Let me try to introduce one more new term known as strip map mode. A small diagram is shown here so that we understand what a strip map mode wherein an image is formed when the synthetic aperture radar is following the line, flight line of the platform strip map. One strip is being imaged. So, till now we have seen the different SAR modes. Now also worthwhile to discuss here is the different data formats. You know how do we get data from a synthetic aperture radar? You see the transformation of real and imaginary components of SAR image. You know the transformation of that into data is elaborate. You know it is not very straightforward and at this point of time we shall not delve too much into it but nevertheless it will be helpful for us to understand the different synthetic aperture data formats that is in what way is the image collected by the instrument and what are the different formats in which SAR data is being made available to us. Let us try to understand from the beginning that is from raw data. The first format to understand is the raw data. So, as the name suggests by raw data we mean the format of data that is collected by the SAR sensor wherein each line represents an echo of the radar signal which has been scattered to the sensor by the targets raw data. Now where are these targets in the along track position? So, in raw data each pixel shall be a complex number consisting of a real part as well as an imaginary part that represents the amplitude and phase of the wave corresponding to the resolution cell. Now remember that raw data format it is the basic format from which all the other high level data products are being produced. The sample image shown here shows the real part towards the left and the imaginary part towards the right. So, it is obvious that visually it is very difficult to interpret what you are seeing. Now moving further we have something known as an SLC data as well as a multi-look data. So, usually to process a raw data the SAR sensor that is the SAR data processor is required to process a raw data and in the absence of a processor generally people prefer using something known as the SLC data that is single look complex data set. So, the single look complex data set are something that which we will be using as part of the tutorials as well, but it will look extremely elongated long because of the rectangular resolution cell on the ground and typically they are used for quality assessment for calibration etc. So, even the SLC data will be represented by complex numbers and they do have some ambiguities due to which people generally prefer to work with something known as a multi-look data what you see on the screen, multi-look data. We shall see more in detail about the SLC data when we reach the module on radar interferometry. So, again coming back to multi-look data assume I ask you to find the average power that is being returned to the satellite average power. We can understand multi-looking as the process wherein the azimuth beam the azimuth beam is being split into say n number of sub beams and using the small regions of the full bandwidth we get to create a number of small apertures. We get to synthesize a number of small apertures and these small apertures are termed as looks and the resulting image we can call it as an n look image. Now, we already know that SAR images are comprised of complex numbers. So, for multi-looking what we are interested in is the average power that is being returned which is given by a square a being the amplitude. Say we do not know the number of looks of an image then there are means to estimate the equivalent number of looks and we shall learn about what exactly is multi-looking and what benefits it offers as part of an upcoming lecture, but for now I want you to be familiar with the term multi-look data. So, we have something known as MLD data format that is multi-look detected data format as well as we have the PRI format that is precision images precision images. Now, precision images as the name suggests precision precise. So, precision images are nothing but MLD images that have been re-sampled into square pixels and few other steps are also being carried out like rotation and warping, but again I do not want to get into details. I just want you to be familiar with the different data formats available for you to access and download. Now, moving on we have something known as a geocoded data. Now, geocoding or ortho rectification it is the process by which a SAR data can be transformed from slant range or azimuth to map projection geometry and we get to do terrain correction as well on this data. So, the geocoded data I would call it as the most user friendly data type. Here georeferencing means we are attaching coordinate information to the data and after geocoding we get information about the coordinates. So, this is one data type that we will have access to and moving on we will also get something known as a polarimetric data. So, here we have already seen that imagery from polarimetric sensors we often get them in one of these formats or in all these formats where H stands for horizontal polarization. Remember by polarization I am always referring to the direction in which the electric field vector is oscillating. So, I can get an H H image horizontal transmit and horizontal received. I can get a V V image, H V image and a V H image. So, here V H means vertically transmit and horizontal received polarimetric data. Now, a few small sections also need to be introduced so that when you access a source such as a Copernicus hub you will be more aware of where to click and what to download. So, in that context let me try to introduce something known as a metadata. So, what you see here is a sample image that has been opened using SNAP toolbox and I have sort of highlighted what is shown as metadata of the file here and if you watch closely it is an SLC image single look complex image. So, metadata shall include all the important image acquisition parameters and some examples are details about acquisition date, range samples, azimuth looks, image format, range pixel spacing and so on and you will find different informations in the metadata. For example, in this file you can see the orbit state vectors, the Doppler centroid coefficients and so on. Metadata just to let you know that they contain important image as well as image acquisition parameters metadata of a file. Now, moving on let me try to show you a glimpse of Copernicus hub which you can access to get information about the data. So, we will see in the upcoming tutorial that we can access as well as download data from the Copernicus hub. So, here I am showing you this slide so that you get to understand the different product types that are made available as part of the drop down window. So, by now I think you must be familiar with the raw data and the SLC data. As well as we have something known as a sensor mode, sensor mode and these are the different sensor modes that have made available. So, whenever you access the Copernicus hub to download a specific data, there are certain additional filters that you are required to fill in, you know to specify what kind of data you want to download. So, these terminologies what we discussed today will be helpful as in what is a product type and what is the sensor mode and so on. Now, you know as during the upcoming tutorials we shall be accessing and working with ELOS Pulsar data sets. This is the right time to know a little bit about them. ELOS Pulsar, ELOS stands for Advanced Land Observing Satellite, ALOS, Advanced Land Observing Satellite and it is a satellite from JAXA that is Japan Aerospace Exploration Agency. It was launched in the year 2006 and coming to Pulsar that stands for Faced Array Type L-Band Synthetic Aperture Radar. You may be a little confused about what is Faced Array Type. No worries, we will cover it as part of an upcoming lecture but for now you are familiar that it uses L-band region and it is also a Synthetic Aperture Radar. You are also familiar with SAR by now. So, Pulsar was one of the instruments on board the ELOS whose aim was to map fields and to provide precise land coverage for disaster monitoring etc. And the L-band Synthetic Aperture Radar from Pulsar was collected with different polarization, different resolution and swath width etc. So, a table shown here gives you the technical details of Pulsar as in the mode, whether it is you know the mode of capture as in scansar, the polarization used in each mode, the incident angle which by now you will be familiar with theta i the incident angle and the range resolution r we have also discussed what is range resolution and the swath, swath width we have also discussed what is swath. So, now we are slowly getting familiar with the terminology is used in Synthetic Aperture Radar and remember this data you get it as an unprocessed or raw data as well as a georeferenced data of amplitude images as well as we get something known as a terrain corrected geocoded image and you get this data in different polarization as shown here. The fine mode and the scansar mode you get the data in different polarizations and shown here is how the data looks like and this is part of Maharashtra and you can see Mumbai here. So, you know it may not be as visually appealing as an optical image but it has a lot of information content and how to process the data from Synthetic Aperture Radar will slowly get into the details as part of the upcoming lectures. So, just to summarize in this section we tried to understand the synthesis of aperture in a synthetic aperture radar and then we started discussing about the different SAR modes spotlight scansar strip map and then we went on to discuss about the different data formats the different ways in which data is being made available from SAR the different data formats we discussed about raw and processed raw data and then single look complex images SLC data we also discussed about multi looked data MLD data precision images PRI geocoded data and there were some terminologies new to you like ortho rectification or terrain correction they will be slowly covered as the lecture progresses and towards the end we also discussed about Allos Pulsar and few technical specifications of Allos Pulsar data and how the data looks like. All right. So, let me hope that you enjoyed this part of the section and I will see you in the next class. Thank you.