 Hello everyone, welcome to the next lecture in the topic of LIDAR remote sensing. In the last lecture we got introduced to what LIDAR remote sensing is and its basic working principle. This week we will sorry this lecture we will continue with that particular topic further. So in the last lecture I basically told you LIDAR is like a ranging tool which measures a distance between the transmitter and the target of interest. So essentially the heart of LIDAR remote sensing is ranging. How precisely or how accurately we range the distance between the transmitter and the receiver. This ranging can happen in two ways. One is the time of flight method and the other one is like the phase difference method. So time of flight method which is often used in remote sensing is like the simple way with that we know like this laser beam will be transmitted towards the target. It will be reflected off the target and it will come back. So this particular transmitter will measure the time taken for the beam to go and come back and using like simple principle of like B is equal to Ct by 2 where C is like the velocity of flight or electromagnetic radiation, T is the time taken for this entire two way flight and divided by 2 we do it because the beam has to go in the forward direction and again come back towards the receiver. So using the simple formula we can calculate it. This is the time of flight method and most often used in remote sensing. In some survey instruments we also use a phase difference method. Phase difference method means we send in continuous beam of laser. So here if we send a pulse like one pulse will be transmitted like for certain duration say 1 nanosecond 5 nanoseconds like that for like a very short time period a pulse will be transmitted towards the target which will go reflect and come back. After that we will send in another pulse like that. But in case of like continuous beam we will be continuously transmitting laser we will combine the laser wavelength with a carrier wave we will transmit it it will go and come back. So based on the distance between the transmitter and receiver we will the phase of the wave will vary like let us say at this point we are transmitting a wave we know the phase at which it is transmitted and based on the distance the phase will change. Say if the distance is integral multiple of wavelength the phase may not change let us say wavelength is for like simple example I am telling let us say the wavelength is 1 centimeter. Say the distance between the transmitter and receiver is 30 meters. So 30 meters is kind of like an integral multiple of this right say every meter has 100 centimeters. So this is like 3000 centimeters which is an integral multiple if the distance is exactly like this the phase will not change because whenever it travels a distance of one wavelength it will complete like one full cycle of phase 0 to 2 pi 0 pi by 2 pi 3 pi by 2 and 2 pi. So one full phase cycle is completed. So if the distance is integral number of like wavelength the phase will not vary. But if the distance is even slightly different than this integral multiple of this particular wavelength then the phase of the received signal and transmitter signal will vary and by come applying this phase relationship or by observing this phase relationship this is transmitted this is received what is the phase difference between them. By knowing this we can calculate the delta lambda or like the small difference in distance between them and by independent methods it is there to measure this n lambda. So the total distance is equal to n lambda plus delta lambda where n lambda is measured separately like that is like the integral multiple of wavelength plus the delta lambda. Let us say the distance is 30.2 meters ok. If the distance was 30 meters in our example of 1 centimeter it will be like n lambda only will be there this delta lambda will not be there. If the distance is 30 point let us say 30.2 meters or 2 to 5 meters which is not integral multiple of 1 centimeter this delta lambda has to be measured separately ok. So that separation will occur that measurement will occur separately and they will be added together. This is using like phase difference. But this is normally not being done for like a airborne or space bonded or lidar systems there we use the time of flight method we observe the time taken for the laser pulse to go and come back and use that. So essentially in the time of flight method the entire accuracy of the ranging system depends on the accuracy with which we measure like the time taken that is one thing we have to precisely measure the time like some of the space bond systems has like a precision of in the order of like picoseconds ok. So we can measure like even like very tiny fraction of time that is possible because light travels with like very huge velocity like 3 into 10 power 8 meter per second. So even like in 1 nanosecond difference means we will be like making errors in the distance measured. So that time should be measured very precisely and accurately. But also we need to know have like a clear knowledge about like the velocity of the laser beam. Like if it is like a short terrestrial application it is ok I am here the target is in front of me the distance can be the distance is short. So not much of atmospheric change will happen velocity I can consider it as constant. But let us say I am doing it from satellite from space. So when the laser beam travels through space there can be different mediums like we know the atmosphere is kind of like stratified it has different layers. So each layer has certain property the velocity of light will change when it passes through different medium. It has to pass through ionosphere troposphere mesosphere lot of different layers the velocity may change. So we need to know accurately how the velocity change and people will measure them or model them in order to get like an accurate distance measurement. So the major factors we need to keep in mind in the time of light method is the time the measurement of time it should be like precise and accurate and also the have a knowledge about the velocity of light as it travels through different medium. Say this light contains some basic formula for the time of light method. So pulsed lasers is what they use they send in like laser pulses it emits large number of pulses every second maybe some ground based systems will be like 10,000 40,000 pulses per second some satellite based system will be in the order of say 10,000 pulses per second and so on. And then the time is measured very simply using like the range formula that we are like already seen and also from an airborne platform point of view I am just discussing this. We have like an airborne platform with like a scanning mechanism attached to it it can scan certain angle of like theta. At that circumstances the footprint size of the laser beam can be calculated by this formula H into gamma divided by cos square theta instant. So footprint as I told it is kind of like the projection of laser beam onto the ground. Say whenever like a laser beam starts it will directly come in like that then it will heat the surface. So it is kind of like projection of the beam that originated from the transmitter. It has small amount of divergence so it will not be coming in perfectly parallel it will not be coming in like this parallely there will be some small divergence. So based on the divergence and the flying height the footprint size will vary essentially. So the footprint is basically depends on the flying height and the divergence of the beam. This is applicable if the beam is transmitted towards nadir. But if the aircraft has a scanning mechanism attached to it then as the scanning mechanism moves away from nadir then the circular footprint the footprint is more or less circular in nadir like the beam will be coming in kind of like a cylinder which will project a small circular area of the ground. So that may become ellipse based on the angle. It may become slightly elliptical and the footprint size will increase. In order to account for that change we are using this cos square theta instant where theta instant is the instantaneous scan angle. Let us say this is like the position at which the measurement was made. So this instant the scan angle at this particular instant at which this range R is measured that is theta instant. So there can be many different theta instances like each of the location in the scan position you will have 1 1 theta instant. By accounting for this we can measure it. So this is with respect to airborne platform. Normally the spaceborne platforms that are currently in operation they do not do any kind of like scanning. They just send in pulses at nadir. So this will not happen this cos square theta instant we may not take care of it. The laser pulse depends on the flying height and the divergence of the beam. Basically it produces like a circular footprint on the ground. And similarly like the swath width especially if your system is attached with like a scanning mechanism you can define like a swath width. Again it is very similar to what we have learnt already for our normal visc broom scanners. The swath width is given by 2h tan theta by 2 where here the theta is like the entire angle with which the system can scan. Theta instant is at that particular instant of range measurement that is theta instant. Whereas the entire theta is the total scan angle at which the system scan scan. The swath width can be defined like that. But normally again in satellite systems since scanning is not happening like whatever is currently there in space scanning may not happen but they will send in like multiple beams that are like oriented in different different distances. It will measure the range of those footprints that are separated by certain distance. And as the satellite moves in different different orbits it will cover like the entire ground like that it will measure. Then one more important thing we should see is the point spacing in both along track and across track direction. What is this point spacing? Laser beam is like a ranging device we know. So, for each point at which it hits the ground the laser beam we will measure the range and effectively we can calculate the coordinate x, y, z of that particular point. So, if we want to measure the terrain in a very precise way we need to have a large number of points. Let us say we have like a small hill like this. So, this is let us say the flight is coming in the plane that is going into this boat like the flight is flying into the direction of the board or your computer screen whatever. So, this is the across track direction. So, it is doing some sort of scanning. Let us say the point spacing happens once every 300 meters very close but just for explanation sake I am doing it. And let us say this hill has like a base distance of say 200 meters it is like a very small mount not like a very tall mount. So, let us say the spacing is 300 meters. So, what will happen is one point may be collected here another point may be collected here or may be somewhere at a distance or it can be like this it can be here and here. So, you will know the x, y, z of this particular point you will know the x, y, z of this particular point we are going to miss this small mount in between. So, when you have this x, y, z normally what we will do when we process this points we will normally get a points x, y, z points. Then we process that he will join them using some sort of like interpolation mechanism. So, then our interpolation mechanism is not going to reproduce the mount or the small hill in between it is going to interpolate it like this point A, point B the mount is missed. So, essentially for in a for us to get like a proper representation of the terrain it is normally we will look for a high point density. Let us say the point density is pretty high we are measuring like several points along the way or in the across track direction. Then if that is the case then we will be able to measure all the points like x, y, z of all the points and our interpolation mechanism will properly interpolate the surface like this we will be getting like a more accurate representation of the terrain. So, the points spacing basically defines how dense or how sparse we collect the ground based observations. So, this is also one of the important parameter we should keep in mind when doing like LIDA serving that is why like terrestrial systems will have like a very high point density. It will try to cover like the almost like with like lakhs and lakhs of points of like if you want to cover like a big building it will send in like enormous amount of pulses to get the signals back. So, the point density will determine how precisely we are able to track the surface and map the minor undulations present within it. So, this point spacing in the across track direction varies with pulse repetition frequency pulse repetition frequency is how frequently our system will transmit LIDA signal maybe like as I told you 10,000 pulses per second and so on. And then altitude of the platform at which height the aircraft is flying that is going to have like a major say. Then the instantaneous angle of standing speed at which speed we are scanning more the scanning speed we are going to have like a lower point density. Then instantaneous scan angle forward speed of the platform all these things are going to affect our point density. So, for like an airborne system the point spacing is given by the altitude of the platform cos square theta instant alpha instant alpha instant is the angular scanning speed instantaneous angular scanning speed and PRF is like the point repetition frequency or pulse repetition frequency. So, this is one of like the important parameter like where our points are spaced that is important to know. Till now we are discussing about the LIDAR transmission. How will LIDAR will receive the returns like I told you like laser beam will come in it will hit the target and it will go back. How the LIDAR beam will return and how the signals may be recorded that is what we are going to see. Within a footprint there need not be only one feature with uniform elevation there can be several features. Let us say you have like a background without any undulation. Then the single footprint of laser beam entire thing is going to hit this particular surface and it is going to go back. On the other hand let us say you are going to measure something over like a land surface covered with trees or vegetation. So, within a single beam of laser or like I just slightly exaggerated for easy representation there can be like small small leaves present within it like there can be like a tree standing next here and these are like branches of the trees. There can be like small plants standing on the ground and all these things. So, what will happen this is like the beam of the laser this is the terrain. So, this is the terrain. So, within this beam of laser there will be like light photons everywhere present continuously. So, this the photons are within the beam there are like many different scattering elements present say this leaf will reflect some portion back, this leaf will reflect some portion back and this plant may reflect something back. There can be some reflection happening from the ground. So, essentially the returns will be not a single return but it will be kind of like a continuous wave like what is represented here. So, with respect to the time it will vary. So, this is maybe like the top single leaf it can be like a large canopy then these can be like small small leaves then again this is the ground. So, there will be like multiple returns per pulse of laser light when there are like more number of scattering elements present within the beam arranged at different elevations. If that happens the laser return will be you can imagine it terms of like a continuous signal like there are like many different returns going back. Not all laser systems will be able to record all the returns that is coming back. This incoming returning signal can be recorded in two waves two waves one is called a discrete return and another is called a full wave form return. So, what exactly a discrete return is? A discrete return means the systems can store a certain number of return points per pulse say two returns per pulse, four returns per pulse and so on. There are some systems can store the entire signal that came back. Say if there are like 50 or 60 reflections happened within that small laser beam all the 50 or 60 can be stored by some system. So, the one with discrete thing will have or will store only like a selected portion of signal whereas like a full wave form LiDAR system can store like the almost like the entire return that came back. So, how the discrete system will work? Say let us say this is like the power of the signal that came back. So, first thing is with respect to time we will be able to note what elevation it came in like this is like the top maybe like a small single leaf this is like a group of leaves that is like define the canopy this is like the ground and so on. Based on the scattering happening there maybe there can be like a large cluster of leaves or the ground can be highly reflecting whatever. So, based on the scattering happening each portion will return a small fraction of the incoming power like a single leaf may produce like a very weak return. Say within this beam here it is encountering only like one leaf whereas here it is encountering like a bunch of leaves. So, naturally this bunch of leaves will produce like a higher return or the more power will be reflected back when you compare this with single leaf. So, with time with difference in arrangement of different scattering elements in the elevation in the z direction the power also will vary. So, when there is like large number of like scattering elements with high scattering capacity back scattering capacity high power will be returned back, but if there are like one or two leaves it may return only like very weak signal back. So, based on it you the signals incoming signals will have variation in the power of the returned wave also. So, the discrete systems will look at like certain high power returns and may store it. Let us say our system is capable of storing three returns. So, it will say this is one instant where there was like high power return. So, store the power and the time there. So, this range will be measured this power will be measured then the next power came in here somewhere. So, this range will be measured R2 this power will be measured then the third large signal came from the ground. So, this range again will be measured R3 and this power will be measured. So, basically it takes in okay it will look okay where are like the instances where multiple power came in within that entire return signal it will sample only those points okay where it got like multiple power returns. So, it may store 2 points, 3 points or 4 points based on the system. So, for each laser pulse we will have multiple ranges measured along with its power or intensity whatever we call. So, for that particular ground point say this is like the point the footprint of laser beam x comma y you will have 3 different points for that 1, 2, 3. This can be from the top of the tree, this can be from the in between maybe like small leaves or something is present this is from the ground. So, we have 3 different elevation measurement for that particular footprint. So, for that x y if you consider one x y as like one ground point you have 3 different measurements. Normally when you use this for large number of over like 2 dimensional area we will have what is known as kind of like a point cloud maybe I like tell it later okay. So, this is like the discrete way of measurement of LiDAR signal. This was like the earliest developments most of the systems worked in this discrete mode. But people realized for some of the applications especially for vegetation monitoring and all having or storing the full return is beneficial for several modeling applications and so on. So, some of the laser systems LiDAR systems now stores the entire signal that is coming back like it is it either stores in analog form or even in digital form with like a very high sampling frequency. So, it will try to store as much as high number of observations coming in within the beam say some systems may store 50 or 60 returns sometimes which will be enough to cover like almost like all normal layers 50 or 60 returns within each pulse that is possible. So, a full waveform LiDAR may produce a more or less continuous representation of the signals that is coming back like the entire waveform that got reflected can be stored in the LiDAR system. So, LiDAR system can be discrete or full waveform. So, a discrete return system will produce a 3D point cloud information that is for each X, Y you will have many number of Z points if you are talking in terms of like elevation measurement or here if I talk in terms of like say from a terrestrial perspective where you are measuring like horizontal distances say this is like a tree you have like large number of points that is being measured. So, each point is kind of like a scattering element which produced backscatter towards a target. So, this is looking this picture B is from looking from like added perspective. So, here basically we are getting kind of like a point cloud if you look in three dimensions say for each X, Y you will have many number of Z. It will appear kind of like a point cloud say you can classify all first returns separately like first return means whatever came in first from each pulse you can save it together first pulse return then you can store second return then you can store third return. So, if your system is capable of storing three returns per pulse you can store them separately as three different layers first returns second return and third return. And when you see them simultaneously you will get some kind of picture about the three-dimensional nature of the terrain say all the first returns say if you are like running the flight over like the forest all the first return might have come from like the canopy right. So, all the first return if you see them you will get a nature of like the canopy height maybe it may look something like this after like doing some sort of like interpolation. Then all the last returns if you put it can it can it could have come from ground. So, it may look something like this this is like the last return. This is not the point cloud this is if you have like n number of points in one particular line you can join them using some interpolation mechanism. So, using that I am imagining as if it is joined together. So, this is like the interpolated first return point this is like the interpolated last return point. So, the difference in height at any given point the difference in first return and the last return may give you like the height of the structure that is standing over the part. Say if it is a tree if the first return came from the top of the tree and if the last return came from the ground then last return minus first return is going to give you like the height of the tree. Imagine if you are able to do this over like entire 2D space, we are going to get a kind of like a three-dimensional representation of the topography. So, this is like the major advantage of using like a LiDAR system. Instant very quickly you will be able to generate like a point cloud. If you are able to like filter the point cloud properly, apply some processing algorithms to it, there are like highly specialized algorithms to it. We are not going to see them in detail. But just I am telling you, if you are able to process this, we can separate these layers, we can do some sort of like interpolation to it and get this is the topography of the terrain with all the features attached with it. Let us say I need to have like a flood model or I need to model how if at all there is a rain, how the flood water will recede. I want to generate a model for which surface topography is one of the very important information. If that is the case, then let us say I have like a small like urban settlement or something kind of it. So, these are like buildings here, there are like trees and so on. So, if I have all the first returns and last returns, then I can create like a elevation layer, what you call like a digital elevation model, which will tell me what is the elevation of my bare earth with respect to some datum or what is the elevation of my entire topography including the trees, buildings and so on. All these we will be all these information we will be able to get from by processing this point cloud. So, all the first returns might have come from the top surfaces, buildings or tree tops, all the last returns might have been from the background surfaces and so on. We will be able to model these, what is the elevation of the terrain, how the topography looks all these things. I will be able to model using this discrete return LiDAR system. But as I told you for some research purposes especially like for vegetation monitoring, carbon up, carbon cycle applications, vegetation biomass application and all, it is always recommended to store like the full return of the waveform that came back. So, full waveform LiDAR is preferred. Like whenever you want to measure like biomass of like a tree standing, a tree may have especially forested trees, they may have like large number of leaves which will produce like multiple returns. So, if you store all of them, we will be able to position or we will be able to come to some sort of idea how many returns came in. So, that many scattering elements that they are present within the tree, it can be many number of leaves. So, from this indirectly we can model the biomass, all these things is possible with full waveform LiDAR which is not possible from discrete return LiDAR. So, full waveform LiDAR also has received a lot of attention nowadays and people are using it for several applications. But one thing we have to remember is a full waveform LiDAR will store up lot of space in the computer memory. Like just imagine instead of like taking 4 samples per pulse, now we are taking 60 to 70 samples per pulse, which is like a tremendous increase right. So, which will have like a large strain on the system. So, normally like a full waveform LiDAR will use up lot of storage space. So, as a summary in this lecture, we discussed about like again like further basic principles of how LiDAR system works and also we discussed about like a full waveform LiDAR and a discrete return LiDAR. With this we end this lecture. Thank you very much.