So as you all know, Ravens placed the franchise tag on one Matt Judon and then a few weeks ago he ended up finally signing it. And that led a lot of us to believe that Matt Judon will play this season on that franchise tag. A lot of other reasons that a lot of us believe that he'll play this season on the franchise tag, one because of the timing. Because had he signed the franchise tag before then there would have been a higher chance of him possibly being traded. Now teams are pretty much set. They spent most of their salary cap and then with everything looming with the possibility of the salary cap being even less next year, because of the possibility of either no fans or much less fans in the stadiums, we'll see what happens with that. But teams aren't going to really want to spend some crazy amount of money. But again, a lot is to be determined. So we'll just see how things go. But then my guy is Moteus. He brought out some good points and one of his questions from subscribers on why he felt like Matt Judon will definitely be a Raven, not only just for now, but for the long term as well. And one of the biggest reasons was the way that Eric DeCosta and company, they handle the franchise tag. Because as an outside linebacker, the franchise tag is supposed to be a little under 16 mil. The defensive end is supposed to be I believe around like 17 mil. But anyway, the Ravens and Matt Judon, instead of going back and forth and clashing and fighting over it, they just tagged him right in the middle of both. They tagged him right in the middle. So that kind of gave you reason to believe like Ravens really like may want to strike something with Matt Judon for the long term. And they at least at least this year alone, if they can't come to a long term agreement, and he would just play this year on the franchise tag. And Matt Judon has said both before and after he signed the franchise tag. He said this long ago, before he even signed it, he said that he's not going to hold out a football this year. He said that he's definitely going to be playing this year, whether he got a deal or a new deal or not. So he already put that out there. And again, this has been the most peaceful franchise tag process that there may have ever been in the history of franchise tags. Because as we know, franchise tag, it's a situation that can get very, very ugly, very, very ugly. I mean, we're seeing what happened with Jadevi and Clowney with the Texans. We saw what happened with what we're seeing, what's happening, what's been happening with Yannick and Godway and the Jaguars. And we've seen plenty of players over the years with the franchise tag. It can just be a very ugly situation. But Matt Judon had a press conference yesterday, and we're going to talk about some different things from that press conference, because Matt Judon, he just, he seems to be in very, very good spirits. He seems to be very, very just happy with his status, with the Ravens. And it seems like just he definitely wants to be here. So Judon talked about how they have 30 days. They got about 30 days to get a deal done because I believe the timeline is July 15th. If no long-term deal is announced between now and July 15th, then he will be playing on that franchise tag. But he said that he was actually happy with the franchise tag. And let's see exactly what he said. He said, I'm pleased to be tagged. I feel like only a few players get to go through this in their lifetime. As much as I want stability in the future, I'm proud of where I'm at. So what that's saying, at least to me, is that I'm just going piece by piece. I'm pleased to be tagged. Some people could be like, pleased to be tagged. Why would you be pleased to be tagged? You want a long-term deal of tags only for one year, man? But if you're even considered to be franchise tagged, that franchise, they value you. They really, they value you, and they are willing to put a big chunk of their money willing to invest a big chunk of their money. Even though it's a short-term investment, they're willing to invest a huge chunk of their money, all in you, all in you. They can make several other moves with all the money that's being allocated into you, but they take away that option when they franchise tag you. So I can understand him saying that he's pleased to be franchise tagged. I could understand that. Of course, he still wants a long-term deal for that financial security for the long haul, but still. And another reason why I think he's probably pleased to be franchise tagged is because, yeah, he was a fifth round pick. And with a fifth round pick, you're obviously making some money because you're in an NFL. You're on an active roster, you're making some money. But now he's going to be with the franchise tag. He's making in one year. He's making more money than he's ever made in the combination of all the years he's been playing. You put all the years that he's been playing in NFL, put them all together. Even multiply him a couple of times. It'll still, the franchise tag for this one year will still be more than all of those. So it sets him up pretty nice. I'm sure he was pretty happy to go take that check to the bank account. Oh, yeah, this is me. Fully guaranteed. Cash it, baby. So that's a beautiful thing. And another reason why I think that Matt Jude on will be pleased to be playing on the franchise tag is because the NFL stands for not for long. It stands for not for long. So with it being not for long, that means that things could change in the heartbeat. You be in a fifth round pick your, your, your expectancy rate, your life expectancy rate in the NFL is not long at all. The lower you're drafted and not saying that, I mean, just because somebody's drafted, though, they're a bad player because that doesn't mean that at all. But the lower you're drafted, the lower the expectation is for you to succeed in the NFL. Now, of course, when teams are picking in these later rounds, they hoping that a lot of these guys end up turning out to be better than where they projected to, but they still know. Okay. That's why the contracts are the way that they are. The lower that you're selected, the lower amount of money you'll get for your contract. So with Matt Jude on him being a former fifth round pick in the league, the NFL that stands for not for long and him making it to actually be the one player, the one because you can only dedicate the franchise tag to one player every season for him to be that selected player that the Ravens chose to designate this franchise tag to. That says a lot. And again, former fifth round pick. A lot of fifth round picks don't even make it to the second contract. So I'm sure that he's ecstatic about that. But anyway, continuing. I said, I'm pleased to be tagged. I feel like only a few players get to go through this in their lifetime. And again, that sort of goes back to what we said about the NFL being not for long because so many players come and go every year, every year. We've had so many conversations. Just, oh, what happened to that guy? Oh, what happened to him? Man, where'd he go? Because player and players can even be hot. They can even be hot for a certain amount of time. They can be like, oh, man, this player.  And then all of a sudden, boom, they vanished in the thin air. I don't know every year. It happens out of nowhere out of nowhere. So that's just something to think about. And he said as much as I want stability in the future. I'm proud of where I'm at. So again, like we talked about, that's stability. That will be a long-term contract because the franchise tag, it does not give you anything for the future.  But anyway, the franchise tag, it is for right here, right now. It's one year only. That's it. So one year deal. That's it. Nothing beyond this year is guaranteed. Only this year is guaranteed. That's it. So that's why a lot of players get upset with it. That's why a lot of players have gripes with their teams about it. That's why a lot of players get into so many problems and arguments and debates and the back and forth with their teams about it because they don't want to be franchised. But Matt Judan is not complaining. This guy hasn't complained at all. And again, the way that the Ravens celebrated him being franchise tagged. It's like it's been weird because you just don't see that ever. You never see that. So that's been a beautiful thing. And again, he said, I'm proud of where I'm at. So that was nice. And then he also talked about how he's happy to be a Raven and he wants to stay stay here for as long as he can play. But then he said, unfortunately, we can't all stay on our rookie deals because they did talk to him about all those other players who have to get paid and and he knows the business. Matt Judan, he is very familiar with the business. He's seen it. He's seen it. And he said, but I understand that it's a business and they kind of have a bad good problem to have. We have a lot of young talent and it's true. We sure do. It's a lot of young talent that's coming up. It's so many deals. That's what I always talk about, man. Some hearts are going to be broken. Some feelings are going to be hurt because the Ravens they cannot keep everybody. They simply can't. They can't keep everybody and with them not being able to keep everybody. Some people got to go. Everybody's not going to be a Raven for life. And of course, it's nothing personal. It's business. It's business. Everybody can't stick around. But Matt Judan knows that he's seen it firsthand. So he knows that. But anyway, shout out to my guy, Justin Janigan. He said he was hyped because Matt Judan had actually liked one of his comments because he said, I hope that Matt Judan takes a team friendly deal. This could be a Patriots kind of franchise with the line not being too greedy and able to bring able to bring back all of our studs such as Matt Judan, Marlon Humphrey, etc. So he was he was hyped man and Matt Judan had liked that comment. Does that mean Matt Judan will be willing to take a team friendly deal? I don't know about all that. But you never know, man. But if he does, okay, cool. If he doesn't, okay, cool. Can't knock him for whatever. Can't knock him for whatever because that's his money and he trying to get the most of it. So we'll see what happens man with Matt Judan because he is a very interesting case because it's just like with the Raven with Matt Judan. I have just I haven't known which way this whole thing was going to turn. Haven't known which way this whole thing was going to go. Haven't had any inclination whatsoever about what direction it was headed in, even though with all the positivity from him, from the players, from the team. Seems like it's going to go in a long term direction. And then of course with the whole thing. Again, we will go back to what we said earlier with how they met in the middle with the amount that his franchise tag would be for that. That says a lot too. So but they also got Ronnie Stanley too.  And again, every time we think about this, oh man. I don't know, man. I just I don't know what's going to go down. But anyway, team keeping clean appreciate y'all. I love y'all. Shout out to Matt Judan because again, like I said, he has been. He has been extremely positive in this entire situation. And one of the best things about that is that there are like sometimes people don't know what type of impact they have on other people. They don't even realize it. There could be a kid. They could be an adult too. Who these players, they may have a bigger impact than they even realize because and they could be an adult having problems at his job where he wants to be paid a certain amount. He wants to raise. He feel like he deserves a raise. He been at the job for a couple years and feel like, hey, it's time. But his job, they may feel otherwise and they may not give him that raise what right away or they may not give him as much as he wants. He or she wants to get. And he's like, man, he may be wanting to go to work or just be angry and be upset and all that. But then he comes home just to watch some football. So to take a break from all that. And he sees everything going on with Matt Judon. He like, man, Matt Judon going through the same thing I'm going through. But then he listens to Matt Judon. He sees them and I'm not trying to make it deeper than what it is, but you just never know. You just really, you really never know. But he sees Matt Judon. He listens to Matt Judon speak about the Ravens about the organization and whatnot and he hears Matt Judon and how happy he seems and how positive he is.  Let me use some of that same positivity too. Cause there's some people who don't even have jobs right now. Whether it's before after the whole situation going on and some people that don't even have jobs, a lot of people that lost their jobs. And Matt Judon could be looking at it the same exact way. There's some football players whose careers are done now. There's some football players who can't even play no more. There's some football players who they ain't got no use for that pass anymore because their careers are done. Cause again, the NFL stands for not for long, but I do appreciate that Matt Judon is appreciating every second of this. So shout out to him for that man. Appreciate y'all team. Keep it clean. I love y'all and we out.


Hello everyone, welcome to the next lecture in the course remote sensing principles and applications. In this lecture we are going to start a new topic known as passive microwave remote sensing or also known as passive microwave radiometry. So what passive microwave radiometry is, we know earth emits radiation because of its internal energy or its own temperature and that was the major physical reason behind us doing thermal infrared remote sensing. Say here we have this wavelength in x axis with the spectral radiant emittance or what is known as the radiant flux density in the y axis and the curve is plotted for a black body at 300 Kelvin. So this basically approximates earth surface ok. So this we have already seen before. If you look at this curve the radiation will be starting like here it has plotted something around like 1 micrometer. So typically the radiation will start emanating around like say 3 to 5 micrometer range radiation will begin to radiate it will increase and then there will be like a long tail. In thermal infrared remote sensing we use the wavelength range of 8 to 14 micrometers this particular range. So we used or we send satellite sensors to observe in this particular range, observe this radiance and calculate the temperature of earth surface features. But this curve will not stop abruptly earth surface will be keep on emitting radiation and if you have like a long tail which is extending all the way up to the microwave portion of the electromagnetic spectrum. So here even if you observe in millimeter range or centimeter range there is small amount of radiation that is constantly being emitted by earth surface. So this radiation is what we are going to make use of in passive microwave radiometry that is earth starting from short wave infrared or MWR mid wave infrared portion that 3 to 5 microwave range earth will be keep on radiating energy. This radiation will slowly increase and it will reach a peak in the long wave infrared portion around this 9.5 9 to 9 10 micrometer range. But if we since we call it as thermal infrared remote sensing but this radiation will not abruptly stop from earth surface and the radiation will be keep on emitting and earth surface will be emitting energy even in microwave wavelengths that is with wavelengths in the order of centimeters may be from 1 centimeter to 100 centimeters. If we observe this radiation from earth surface in these wavelengths in centimeter wavelength and use it for different applications we call that as passive microwave remote sensing or passive microwave radiometry. So naturally this is an extension of thermal infrared remote sensing. Extension means we are not producing any new form of energy whatever the earth itself is emitting we are observing it but in a different wavelength ok. So we are not observing any more in 8 to 14 micrometer wavelength but we are observing earth emitted energy in microwave wavelength in order of the wavelengths in order of centimeters. In those wavelengths also solar radiation is not going to play any role ok. Because we have already seen once we cross this 5 micrometer wavelength solar radiation reaching the earth surface almost goes to 0. So we can safely neglect any incoming solar radiation. So whether during daytime or night time whatever radiation we observe in microwave wavelengths essentially that energy will be due to emission from earth surface. Just study this in parallel with thermal remote sensing whatever even in the 8 to 14 micrometer wavelength whatever we observe is basically due to emission from earth surface. Same concept is applied here we are applying we are observing at a different wavelength but still whatever we are observing is due to earth surface own emission. So our wavelength only changed but the emission the source is earth surface and the various features present on the earth surface. So what exactly is the microwave portion of electromagnetic spectrum this also we have discussed in the earlier classes in the introductory classes. So in general the microwave portion of electromagnetic spectrum that we use for remote sensing of earth surface spans between the wavelength range of around 1 centimeter to 100 centimeters. So 1 centimeter to 1 meter. So we can classify it from say KA band, K band, KU band, X, C, S, L and P in the range of increasing wavelength. It starts maybe something around 1 centimeter wavelength to 1 meter wavelength. We have lot of divisions in between for our own understanding. This nomenclature this P, L, S, C, X these nomenclature have been developed in old and days as a secret codes during military applications like one of the earliest applications of microwave is in military like for different surveillance needs. So this sort of frequency the random names were given for frequencies in order to keep it secretly and that name prevailed even now. So these are all the common names we give it to the different portion of microwave portions. Like in visible band we call 0.4 to 0.5 as blue, 0.5 to 0.6 as green and all right. Same thing here microwave portion is a pretty long portion of electromagnetic spectrum. We have divided into certain classes and we use this for remote sensing. Whatever the portion we have seen from 1 centimeter to 1 meter from KA band to P band it is not essentially the full microwave portion of spectrum microwave is still really a very huge part of electromagnetic spectrum and it has its applications in various domains like in communications like our cell phones everything depends on microwave based communications. Microwave oven transmits microwaves for cooking of food. So microwave is there everywhere around us and we use it for several applications. Remote sensing is just one of the applications in which microwave wavelength of EMR is being used. Just imagine we have one some transmitter kind of thing emitting energy in one particular microwave frequency. There is a satellite a passive microwave sensor which observes the earth's surface in the same frequency. Just think what will happen whatever this transmitter is radiating is going to reach the satellite sensor and the satellite sensor is going to think something is coming from the earth's surface and as an end user when we take that image we will see what is there on the earth's surface. We will not know that there is some transmitter which is radiating energy maybe a cell phone tower what not. In order to avoid such confusions the microwave spectrum has been divided and for each application each portion of the spectrum has been allotted. So similarly for remote sensing a certain frequencies has been allotted okay only this frequencies has to be used for microwave remote sensing and only this frequency has to be used for communication purposes. If these frequencies clash say if a communication agency if some agency is using a particular frequency allotted for remote sensing if they have a radio if they have a microwave transmitter then that is going to interfere with what the satellite is going to observe. There is some artificial source that is emitting energy that is going to cast interference in satellite observations we call this as RFI radio frequency interference. These sort of things tend to happen but in order to minimize this or avoid this the microwave portion has been split up and several small portions has been created and each application has been allotted certain bands. Say for remote sensing purposes these are all some of the frequencies which we can use for earth observation or observation of atmosphere. You can see here there are two titles active and passive what exactly active and passive means passive is the passive microwave remote sensing that we have just got introduced to or what we are discussing right now that is whatever we are observing from space the energy is primarily due to earth zone emission. There is also an active mode of remote sensing what exactly active mode of remote sensing or active microwave remote sensing is we will have a sensor what is known as the radar this will transmit some electromagnetic radiation with a given frequency. This will interact with the earth surface features and this will be reflected back this will again reach the sensor and the sensor will observe it and use it for imaging purposes. So, this process where the sensor itself will transmit certain energy and receives it back we call it as active mode of remote sensing active remote sensing. So, in microwave it is possible to do active remote sensing we can send a radar to space that will transmit EMR in microwave wavelength get the reflected signals back. So, active remote sensing that is a topic we are going to see next after we finish passive microwave. So, that is possible in microwave. So, even in microwave spectrum for active and passive also the frequencies has been divided for example, let us take L band okay L band frequencies say typically these frequencies correspond to L band 1.2 to 1.3 and 1.4 range frequency gigahertz frequency. If you want to do active remote sensing you are supposed to use this 1.2 to 1.3 gigahertz. If you want to do passive remote sensing in L band you have to choose this 1.4 gigahertz frequency. There should not be any mix why an active remote sensing sensor and a passive remote sensing sensor if they work in same frequency then the active radar itself will became like an interference to the passive sensor. Let us imagine there is a satellite called SMAP soil moisture active passive which is like launched by NASA. So, it had both or it has both a radiometer passive microwave radiometer and also a radar. Both is there both is both will work in L band but the frequency in which the sensor will send in signals is different from the frequency in which the radiometer will observe. So, the radar will send a frequency a different frequency will observe a different frequency like say it will it will transmit in around 1.3 gigahertz receive the signal back in 1.3 gigahertz. Whereas this passive microwave radiometer will not transmit anything but will observe frequency one in 1.4 gigahertz. So, even within a same satellite even if you have active and passive mode of remote sensing mixer together the frequencies will be different because the active radar should not act as an interference to the passive. Imagine the active is also transmitting energy at 1.4 gigahertz what will happen 1.4 gigahertz will go get reflected the surface will come back and passive microwave radiometer will observe it thinking that it is coming only because of earth emission that itself is an interference. So, in order to avoid this interference there has been specific channels created to make sure or to minimize this radio frequency interference. So, for passive microwave remote sensing there are like specified channels or specified bands in which observations will be made. Before moving on to seeing the concepts of passive microwave radiometry we will look at the Planck's law one more time. Planck's law we have seen several times in the introductory classes as well as in thermal infrared remote sensing. Here also in passive microwave radiometry Planck's law plays a major role because essentially the radiation coming out of earth surfaces thermal in nature. The original form of Planck's law that is for the radiant flux density is given by 2 pi hc square lambda power 5 exponential of hc by lambda kt minus 1. So, this is the original form of Planck's law that we have seen earlier. So, this will be like the radiant flux density with units of watt per meter square per micrometer. So, for isotropic radiators of a lambertian surfaces we have seen that radiance is equal to radiant flux density divided by pi. So, by using this particular relationship we have derived this equation for radiance. So, this is the Planck's law for radiance, the only difference is this term pi will not be there. This also we have seen earlier.  So, essentially these equations are defined for black bodies whose emissivity is equal to 1 always in all the wavelengths. So, this particular equation the radiance equation will give us the radiance of a black body at a given temperature t that will be emitted at a particular wavelength lambda. So, if you look here there are like 2 independent variables t can vary independently and lambda can vary independently. If we assume the black body is at one particular temperature that is L of lambda at a given temperature t then this also will become a constant and this will be like the variable and hence this equation L lambda will tell us how radiance varies with wavelength radiance variation with wavelength. What I mean is this will be like the curve this will be lambda this will be the radiance. So, some sort of curve like this we will draw right say for t is equal to 300 Kelvin like this we will draw. So, if we fix the temperature of an object the equation given here will tell us at which wavelength what will be the radiance. So, essentially the equation given here will tell us what will be the variation in radiance for an with respect to wavelength for a black body at a given temperature t. So, mathematically this can be written as a partial derivative that is this L lambda is nothing but the variation of radiance with respect to wavelength dou L by dou lambda at a temperature t. So, here we are holding temperature as a constant that is why this partial derivative is coming with respect to lambda. In microwave parlance like whenever we enter the microwave domain of remote sensing most of the people like the engineers who develops the systems and everything the microwave antenna the sensor system everything they prefer dealing in terms of frequencies. But as remote sensing people we prefer talking in terms of wavelength. So, essentially that there is always need to convert between expressing something in terms of wavelength and expressing something in terms of frequency. So, it will be easy for us if we can convert this Planck's equation expressed in terms of frequency that is the variation of radiance for an object at a given temperature t with different frequencies that is it rather than having lambda and x axis now we are going to put frequency in the x axis that is what we need is we have to convert this dou L by dou lambda into dou L by dou f where f is the frequency we need to convert this into this. It may seem to be like a very straightforward operation just by replacing lambda with nu you know we know the relationship right c is equal to nu lambda using it we can replace but it is not as straightforward it is not a mere substitution of lambda with frequency it there needs a small mathematical operation in between. So, we will see how to do it. So, once we do it we will be in a position to calculate the radiance with a given frequency. So, what exactly we have to do just examine the equation once more. So, the radiance equation is a function of lambda and using this relationship lambda is a function of nu right if we can like take like c is equal to nu lambda that implies lambda is equal to c by nu. So, lambda varies with frequency where c is a constant like this we can imagine. So, essentially we need dou L by dou f or nu whatever. So, I write it as like f here so dou L by dou f what we have in our hand is dou L by dou lambda. So, essentially if we use the partial on the chain rule of partial differentiation we can write it as dou L by dou f is equal to dou L by dou lambda into dou lambda by dou f. So, if we do this we will be in a position to calculate what will be the change in radiance with respect to frequency. So, that is the thing we are going to do now. So, dou L by dou lambda we already have in our hand that is the Planck's equation given in the previous slide. So, this equation is nothing but the dou L by dou lambda. So, now we have to calculate dou lambda by dou f that is this one the variation of lambda with respect to frequency. So, c is equal to nu lambda or lambda is equal to c by nu just differentiated once dou lambda is equal to minus c by nu square dou nu. So, I am interchangeably using nu and f to represent frequency. So, dou lambda by dou nu is equal to minus c by nu square. So, this is done. This is actually a negative equation where the negative sign represents the direction in which lambda will change with change in frequency that is as frequency increases lambda will decrease and vice versa. So, this negative is an indication of direction. So, derivative is nothing but mathematically it is a slope right. So, normally we attach the concept of derivative with slope. So, in which direction this variable will change. So, as we increase frequency lambda will decrease and vice versa. For us for our particular application the direction is not important, but what we need is the magnitude. So, magnitude means I am just going to take the modulus of this particular function which means c by nu square the minus sign will go off. So, here we are going to calculate the variation of wavelength with respect to frequency. So, when we differentiate lambda like lambda with respect to frequency we get minus c by nu square where minus sign indicates the direction in which lambda will change. So, we are taking modulus in order to avoid direction. We are not interested in seeing in which direction the slope is going to go. So, we are taking modulus of it and we are getting a c by nu square. So, substitute everything there that is l lambda that particular equation you substituted to hc square divided by lambda power 5 exponential of hc by lambda kt minus 1 into this term will come in c by nu square. Now you replace now we have to replace all the lambda with respect to nu because this relationship is newly we found out between lambda and nu. Now we start substituting it now if you start substituting it l rather writing l lambda this is lf. lf is equal to 2 hc square into exponential of hc by c nu kt minus 1 into c by nu square this will come something like this. So, you cancel everything out and finally we will get this particular equation 2 h like c cube this will become c square and then this nu square will cancel this will become nu cube. So, numerator it will become 2 h frequency cube divided by c square exponential of this c will cancel out h nu by kt minus 1. So, this is the way in which we have to derive the Planck's equation to be expressed in terms of frequency. So, it is not a straightforward substitution for lambda and convert it into frequency we have we need we have a chain kind of relationship lambda like the radiance equation the Planck's equation is related to lambda and lambda is related to frequency. So, we have to combine them use the partial chain rule the partial rule chain rule of partial derivative using that we will derive this particular equation. So, this is nothing but the simple Planck's rule expressed in terms of frequency. So, now rather than telling you what is the radiance coming out of an object at a temperature of say 300 Kelvin at 1.4 gigahertz we can directly find it we need not convert frequency to wavelength and then substitute it. So, directly we can use and get the variation of radiance at a given frequency for an object at a temperature t. So, this is like a very simple conversion of one equation in given with respect to one variable into another variable that is all. Now, what we have seen till now is a generic form of Planck's equation and the original form without doing any modification. But in microwave wavelengths if you look at the Planck's curve it will be like the end portion like especially in the longer wavelengths we will have like a linear line. So, here everything is expressed in log scale even if you put everything in like a normal scale we will see it the tail portion can be approximated to be linear it need not be treated perfectly as a exponential curve the tail portion where the microwave emission comes essentially it is it can be approximated as a linear line rather than treating it as a exponential curve. So, we can do one approximation and this approximation is known as Rayleigh gene approximation for black bodies Rayleigh gene approximation of Planck's law to be more specific what this approximation says the Rayleigh gene approximation says that if this condition holds good that is hf by kt is less than much less than 1 or hc by lambda kt is much less than 1 then in this particular equation we can drop this exponential function and simply write it as Lf is equal to 2 hf cube divided by c square hf by kt that is all. So, we are dropping this exponential term this minus 1 this is applicable only when this term is much less than 1. So, if we do this then the frequency the Planck's law variation with respect to frequency will become something like this similarly the Planck's law with respect to wavelength also will become something like this. So, these two simplifications of the Planck's law is what is known as Rayleigh gene approximation. So, what is the advantage of doing Rayleigh gene approximation from Rayleigh gene approximation what we can observe is the relationship between temperature of an object and the radiance coming out becomes linear that is like L lambda becomes 2 ktc by lambda power 4. So, the t is there in a linear relationship with respect to radiance and also all the computations becomes highly simplified highly simplified in the sense we need not take the exponential we do not divide one by other like the many number of like computation steps you need to calculate to perform the certain operations is much simplified the equation is very simple. So, in order to Rayleigh gene approximation first tells us the equation like the Planck's curve or the radiation that is emitted by a black body is kind of like becomes linear towards the end that is one thing and second thing is all the computations that we are going to do becomes much simpler. Till now we have seen the Planck's equation for a black bodies like even when we converted into frequency or even when we did the Rayleigh gene approximation everything was for a black body. But we know most of the earth surface features are non-black bodies they will have emissivity less than 1 and the emissivity will also vary with wavelength. So, for such non-black bodies how it will be? So, normally what we will do for non-black bodies the radiance will be given by emissivity times the Planck's law of the object at a given temperature T. So, this is the usual way we do right even when we did it in thermal infrared remote sensing we calculated this as something like this something like this we would have calculated we would have just multiplied the Planck's equation with respect to spectral emissivity. Same thing we will do here even in this particular wavelength we will multiply the Planck's equation with spectral emissivity. However, here we will use the Rayleigh gene approximation because in microwave wavelengths especially for features of earth surface when the object is at 300 Kelvin with average temperature of 300 Kelvin Rayleigh gene approximation will hold good roughly when the wavelength once crosses 50 micrometers. Even for this sort of micrometer wavelength Rayleigh gene approximation will hold good, but in microwave terms we are talking in terms of wavelength in the order of centimeters say 1 centimeter to 100 centimeters. So, normally at this very long wavelength Rayleigh gene approximation holds good and hence we can write radiation or sorry the radiance using the Rayleigh gene approximation. So, 2 Kc by lambda power 4 and just taking the t and spectral emissivity out together. Let us say a sensor is being sent to space it is going to operate in L band around like 1.4 Giga hertz ok. So, hence as soon as the sensor is designed and sent to space wavelength is also fixed it is going to observe only in this 1.4 Giga hertz frequency or roughly 24 centimeters wavelength. So, this thing is fixed now this entire term within the bracket becomes a constant for that particular sensor. So, the radiance observe or the radiance coming out of any non-black bodies is now a direct is now directly proportional to the product of temperature of the object multiplied by surface spectral emissivity. So, this signifies for a non-black bodies the radiance emitted is directly proportional to the product of temperature and spectral emissivity. So, here both temperature and emissivity has a equal say in defining what will be the radiance that is coming out of an object. So, you just look at the equation in TIR band. So, this is the equation for radiance in TIR band. This is kind of like highly non-linear emissivity is here and the temperature is here in the denominator within the exponential all these things. But if you look at after the Rayleigh gene approximation equation becomes much simpler and the radiance is a is directly proportional to the product of T and emissivity. So, here the weightage of T and emissivity is equal in defining the radiance both have equal say if temperature increases radiance increases to the same extent. If emissivity increases radiance increases to the same extent and vice versa. So, here the influence of emissivity and temperature both are equal in defining the radiance coming out whereas in TIR wavelength in the original form of Planck's law the change in temperature will have a more influence or a larger say in defining what will be the radiance coming out of an object rather than change in emissivity. Maybe like when we do some like numerical problems later we will try to understand how these things work. Here also one thing we have to remember the product of temperature and emissivity for any given object is commonly referred as brightness temperature in microwave parlance. When we defined brightness temperature in TIR remote sensing we defined it in a different way. We defined it as the temperature of black body will have in order to produce the same radiance as observed by the sensor. Here sometimes in most of the literature you can sense like brightness temperature is defined as the product of temperature and emissivity because people assume in microwave wavelength atmospheric fx is negligible we will see it later and hence whatever is observed by the sensor is almost effectively free of atmospheric effects and if you remove this sensor response function and all. So, whatever the radiance received by the sensor is just due to the mere effect of temperature and emissivity. So, this thing you please be clear in microwave parlance brightness temperature the word brightness temperature in several literature will refer to the product of temperature of an object and emissivity of the object. So, as a summary in this particular lecture we have discussed or we have got introduced to the concept of passive microwave radiometry. We have seen what all the spectral bands used to in passive microwave radiometry and also we have seen in detail about the conversion of Planck's law from with respect to wavelength to with respect to frequency. Also we have seen the Rayleigh gene approximation. The Rayleigh gene approximation will help us to simplify our calculations and also to understand the relationship between temperature and radiance on also emissivity and radiance. With this we end this particular lecture. Thank you very much.


Live from Washington, D.C., it's theCUBE, covering .NEXT Conference, brought to you by Nutanix. Welcome back to Nutanix Next Conf, everybody. Hashtag Next Conf, this is theCUBE, the leader in live tech coverage. We go out to the events, we extract the signal from the noise. My name is Dave Vellante, and I'm here with Stu Miniman. Stephen Hadley is here, he's a former U.S. National Security Advisor, and currently with RSG, who is an advisor to Nutanix. He's an expert on national security and foreign policy, public policy. Stephen, thanks very much for coming on theCUBE. Nice to be here. So very important topic, one that you just can't talk about enough, so let's start. I mean, we're here at this sort of infrastructure show. We're up leveling it now to this very important topic of security. There's so many things that are going on. We interviewed Pat Gelsinger on theCUBE five or six years ago and asked him, is security a do-over? He had a one word answer. Yes, so where are we at? What's the state of cyber today? Well, let's talk it in a couple of respects. You know, one of the things that's been interesting to follow your industry, and I'm not a technical person, but interesting following your industry, a lot of what was done, social media and all the rest, started to be a fun. It was almost a toy. And what has happened is you now have become, this industry and the services provide are a international, global and national resource, and is at the center of how we do business today. And it's been interesting to watch the industry deal with that challenge. It started out, what do you do about child pornography that gets onto the various sites like? Then it got to be, what do you do about terrorism? Now it's, what do you do about false news? And it's been interesting to see the industry, and I think very effectively start to respond to what are the responsibilities they have to their users in these various troublesome areas. And what are the solutions, technologically and process wise? And I think the industry is taking the lead and I would encourage them to do so because I think the industry needs to define the solutions. If you wait to Washington to define the solutions, we'll get it wrong as we usually do in Washington. Well, so let's come back and talk about that. But I like to think of sort of three categories of cyber threats.  You've got criminals, organized crime, and then you've got state sponsored. Where do you feel the industry, that you just sort of said, the industry really has to lead? Where do you think the industry should put its focus? Should they think about the attacker? Should they think about more about the defense? Is that a right way to look at it, those sort of three categories of threats? I think those are three categories. They are different kinds of threats. I think the industry is going to have to deal with all of them. I think the principal focus is going to be on defense. There has been a discussion in the literature, should companies have the ability to go on offense and to respond to cyber attacks by trying to reach out and hurt the attacker? That's a tricky question. And I guess as a national security type, my instinct is the industry needs to lead on defense. The government needs to think about offensive responses. I think particularly since one of the problems you've got in this business is the attribution problem. If someone marches into your country, you know who is doing it. If you get a cyber attack, it's not clear who the enemy is and who the attack is coming from. And it makes the issue of response very difficult. Secondly, the problem of collateral damage, as we saw beginning with Stuthnack and in these latest attacks, you try to hit somebody over here offensively with cyber and turns out you're hitting users in 150 countries. So I think the industry's responsibility is to defend and to try to prevent their systems being used by various nefarious characters. The issue of how to respond to cyber attacks I think is much more a state function, a law enforcement function in terms of ordinary criminals and the like, a national security function in terms of nation-states. Well, Robert Gates on theCUBE last April said that even governments have to be very careful about using cyber as an offensive weapon. And you mentioned Stuthnack and we saw what happened. But there are no standards with cyber war. With conventional warfare, there's the Geneva Convention, there's standards that we can apply with cyber that's the Wild West. So what is industry's role in terms of creating those standards of cyber attacks? I think industry can inform it. I think it's going to be difficult for industry to take the lead. And I think one of the, so my response would be, one of the problems is cyber attacks, the attackers pay no penalty with cyber attacks. It's hard to find, it's hard to prove, and there's no responses. And there's a whole question of what is the right response? So for example, some years ago, over 10 years ago, Russia pretty clearly took down the Estonian government which was a real E government. Now NATO is, Estonia is in NATO. NATO, one of the pillars of NATO is an attack on one, is an attack on all. Was that an attack? Huge debate within NATO, was an attack, was not an attack. Nobody died, traditional measure of where you've been attacked. On the other hand, the government was almost paralyzed. What's the right response? Do you have to respond only in cyberspace? Would you think of responding conventionally through conventional military power to a cyber attack? None of that has been worked out. And as a consequence, nobody pays any price for cyber attacks. And my own view, particularly with respect to state-sponsored cyber attacks, is until the country pays a disproportionate attack in cyberspace for a cyber attack, you won't get them to stop. But as you just talked about rightly, it's very hard to respond in cyberspace because of the unintended consequences and cyber collateral damage, if you will. My hope, the way out of this, is, as you've seen in these last attacks over the last week or so, which were targeted, I think the most recent one was targeted on Ukraine and ended up affecting 150 countries. I would hope that some of these, at some point, are going to bring the international community to its senses. And people are going to basically say, look, we're all vulnerable. We're all at risk. The United States is more dependent probably than other countries, but China isn't too far behind. And for the United States and China to start leading an international conversation about developing the rules of the road, I think that would be good. I think, though, there needs to be a panel from industry that supports that effort. Or my worry is the governments will get it wrong and will impair the growth of the industry, which is bringing so much benefit to the global community. Really interesting point. A couple of years ago, we interviewed the president of ICANN, the organization that oversees higher internet, Fadi. And he was really concerned that companies like China and Germany were going to say, we're going to have our own internet. We're just going to wall things up. Kind of goes against what you're saying, is we need to work together. We see dissonance between private corporations and governments now. How do we get globally working on technology, working together rather than fragmenting more? And you make a very good point. It's working together on the basis of our principles. Look, our view is that a global internet, free access for everyone is a powerful political statement and can be empowering of individuals. So it is a small D, democratic institution. And it is enormous economic power. It would be a tragedy if individual countries start to balkanize the internet and start to make them national systems. Because you know the countries that will do it are countries that are authoritarian and will convert a device that actually empowers individuals to be a device by which the state controls individuals. Secondly, it will risk cutting them off from the global community, which will have economic consequences, much less social consequences. So I think it is important for us to try to take the lead and start that conversation and to do it while we're still talking about a global internet and really haven't lost that. So this conversation needs to start sooner rather than later. You're the chairman of the United States Institute of Peace. I have to believe that there's some parallels between the work you're doing there and what we were just discussing. They're trying to co-operation and, you know... There is in this sense, one of the things that USIP has found is, and when I was in government, I always used to think about what governments can do to resolve conflicts and wars and preserve peace. And that's sort of top-down government policy. What US Institute of Peace is doing is bottom-up, you know, facilitating groups, civil society, and peace builders and peacemakers in war-torn communities to begin to resolve the ethnic conflicts, the tribal conflicts, the religious conflicts that are really the kindling and the fuel for conflict. And through an affiliated organization of the USIP called Peace Tech Lab, technology people are coming together with civil society people and saying, what are the tools you need that we can put on an app and use on an internet platform that will allow you to do your bottom-up peace building work? And it's very powerful. So for example, election violence, always a big problem. There are civil society groups using technology that we're able to monitor through social media the first signs of electoral violence and bombard them with text messages and the like to try to bring down the temperature. So what we're seeing at USIP is there is a bottom-up component of peace building that can be technologically enabled to allow people to try to maintain peace in their communities. It is the new frontier in some sense for the work of the US Institute of Peace. So with Stuxnet, we saw that Malware had the potential to kill people. Maybe in and of itself that Malware didn't kill people. People died and that whole dynamic with two nuclear engineers in Iran. My question is, and Stuxnet is 15-year-old technology. I don't think if Stuxnet was responsible for anything. No, right, yeah, let's clarify that. There was a separate. And it was associated with that whole initiative. There was an effort to set back the Iran. But it wasn't the Malware itself, but the Malware was demonstrated to do damage and it could theoretically and probably in practice kill people. So here's, as I say, 15-year-old technology and just scratching the surface. So God knows where we are today. You may know, I don't. But you sort of put forth this notion that countries, states need to come together and sort of address this problem. My question is that does the, well, I'm inferring that the U.S. has a lead. And as the leader with the best weapon, what's the motivation for the United States and other countries or the haves to work with the have-nots and actually create these standards? Is it because we have more to lose? I wonder if you could comment. I think it's vulnerability. I mean, look, we're more dependent on the internet. We're more dependent on cyber systems.  They're going to start in hospitals and it's going to get worse. So what is the task? The first task is, and we've known about this problem of the vulnerability for critical interest structure since the 1990s that the first studies were written. Government has been slow. Quite frankly, industry has been slow. And I think that train is finally moving. Some sectors are farther ahead. The financial sector is much better and further along at hardening their infrastructure against cyber penetration. But we still are very vulnerable through control systems in our water system, electric grid, all the rest. And of course, the internet of things has only multiplied the portals through which people can get into these systems. So there's a huge task of defense and hardening that needs to go on. And that's a responsibility of industry and government working together. It can only be done if industry and government work together. That's the process we need within the country. Secondly, then can the US lead in a process to try to develop rules of the road that provide another layer of protection? But it's got to start with hardening our infrastructure here at home. I got to ask you about fake news. Fake news in Russia. Is Russia an adversary? Should they be perceived from a diplomacy standpoint? Should we be antagonistic? Or should we try to be more friendly as it relates to what's been going on with fake news? I wonder if you can tie those together and give us your thoughts. Well look, one of the things that's different about Russia today is what we've seen in the election. This effort through hacking, through disclosing emails, through probing our electoral infrastructure through a variety of things the Russians are doing, they intervened in our election process in a bigger way than we've ever seen before and they're doing the same thing in Europe. That is a new problem. We need to get to the bottom of it to know what happened, what happened. People do it from the standpoint of retaliating against Russia. I think the bigger problem is we need to harden our electoral infrastructure. Our electoral infrastructure turns out to be critical infrastructure that we have to harden just like our electric grid and our water supply systems.  Fool me twice, shame on me. If we don't harden our electoral infrastructure so this cannot happen again, next time it happens, it's our fault. So kind of a cyber Star Wars, is it, we don't know if it's technically feasible, that's not your area of expertise, that's industry's problem to figure out. Stephen, you are a fantastic guest. Thanks so much for coming on theCUBE. Really appreciate your insights. I'm delighted to be here. Thanks very much. All right, keep it right there, buddy, we'll be back with our next guest right after this short break. This is theCUBE, we're live from Nutanix.nextconf. We'll be right back.