 welcome to today's lecture on the topic of radiometry. So, what exactly radiometry is? Radiometry is defined as the quantitative measurement of electromagnetic radiation. But in remote sensing, we will be interested in measuring the amount of energy coming in towards an object or going out from an object essentially. So, we will be measuring from satellites, what is the amount of energy that is being reflected or emitted by any object. So, for us to quantify the amount of energy coming out of an object, we need to know the various principles and the various terms associated with radiometry. So, radiometry essentially is quantitative measurement of EMR in various wavelengths. Before going into the concepts of radiometry, we will first revisit some basics that we learnt in our high school mathematics. One of the major important concepts to know is solid angle. So, we know what a plane angle is. A plane angle like when defined in like two dimensions, that is why we call it as a plane angle is defined as the ratio of the length of the arc l divided by the radius of the circle with the arc subtens at the center. Say if you have a circle and if you want to measure like any angle like this, let us say this is theta, let us label it as theta. So, this particular angle theta from the center point, it will subtend like one particular angle and the arc length that it subtends will have certain length. So, the length divided by the radius of the circle will give us the two-dimensional angle or the plane angle. Extension of plane angle into three dimensions is what we call the solid angle. In solid angle means we are going to do our angular measurements in the three-dimensional space where instead of a circle around a point, we are going to construct a sphere around a point. So, this particular sphere is going to again have a radius r. So, what we are going to calculate is if we take any surface area s on the surface of the sphere, what is the solid angle subtended by this surface area at the center of the sphere? So, you just take analogy with the plane angle. In plane angle, we are calculating the angle subtended by the length of this arc at the center for a circle with radius r. Similarly, in three-dimensional space, we are going to consider the solid angle subtended by the area like a small surface area on the surface of the sphere at the center of the sphere. So, the solid angle, it will be indicated either as omega. If two symbols will be used basically, different textbooks will use different symbols is defined as the area on the sphere divided by square of the radius. So, as per the definition, the solid angle any one notation you can use is given by s by r square. So, essentially a solid angle is a three-dimensional extension of a plane angle. In plane angle, we will be talking about circles and arcs. In solid angle, we will be talking about a sphere and the surface area of the small element that is there on the sphere which is subtending a given solid angle. In order to make it more clearer, now let us take two live examples. Normally, what we will do like during daytime or evening time, we will stand outside and try to observe the sun or the moon from with our eyes. So, when we see them, they will appear as like a disc to our eyes and that particular disc will actually subtend a solid angle in our eyes. So, when we see them, we perceive all objects in three dimensions. So, that particular sphere be it like a sun or moon, it will subtend a solid angle when we look up at them. So, what are we going to calculate now is we are going to calculate what is a solid angle subtended by sun or moon on our eyes when we stand on surface of earth and we observe them. So, now just look at this particular figure, assume we are standing at the point O. The point O is where the observer is standing and the observer is observing either the sun or the moon. It will appear as a disc to our eyes basically, we will see it as like a circle when we look up in the sky. So, what we essentially want to calculate is when we look up at those celestial objects, what is the solid angle subtended by them in our eyes. In order to know them, we need two quantities. One is the surface area of the disc that is visible to our eyes and the distance between that particular celestial object be a sun or moon and our point. So, if we know these two quantities, we will be able to calculate the solid angle subtended. First, let us start with the moon like here the question as this, calculate the solid angle subtended at earth by sun and the moon. The data is given is the mean distance of moon from earth quantity is given, radius of the moon is given to us and the mean distance of the sun from earth is given. Similarly, the radius of sun is given. So, first we will start with moon. So, we know the solid angle if we call it as like omega is given by the area of the disc divided by square of the distance the D is the distance. So, area of the disc essentially it will appear to our eyes as a circle. So, we all know that area of a circle is pi r square that is equal to pi into for moon the radius given is 1.74 into 10 power 3 kilometers. So, we are squaring it divided by the D given is the distance between earth and the moon is 3.84. So, this is like average distance if you stand on like different points on earth during different times in a year this distance will change, but this is the average distance all throughout the year we can assume. So, this distance squared. So, if we calculated we will get the value of 6.45 into 10 power of minus 5 stradian. The unit of solid angle is stradian whereas, the unit of plane angle is radians that also we know like for plane angle we call it as radians for solid angle the units are stradians. So, you essentially have to append your answer with the unit of s r stradian. So, what essentially it means moon when we look up into the sky it essentially subtends solid angle of around 6.4 into 10 power minus 5 stradian. It is actually like a very small quantity like if you take a point and put a sphere around it say you are standing if we place a sphere around you the total solid angle within that particular sphere is 4 pi stradians like just compare it with analogy of always like a circle. In circle if you draw a circle around a point we say the total angle within the circle is 2 pi radians. Similarly, when we consider a three-dimensional space for a solid angle the total solid angle within a full sphere is 4 pi stradians. So, here in this case if we look at the answer that we got for moon we can see the angle is very small 6.4 into 10 power minus 5. So, moon actually subtends a extremely small angle in our eyes when we see them. Now, next we will calculate what is the solid angle subtended by sun exactly the same thing solid angle subtended by sun at earth is equal to area of sun's disk divided by distance between sun and earth whole square. So, area of sun discuss again sun we will see it as a circle when we look up at it and the distance given is 6.96 into 10 power 5 kilometers whole square divided by the distance between sun and earth as given as 1.496 into 10 power 8 kilometers. So, we are squaring it if we calculate it we will get 6.79 into 10 power minus 5 stradians. So, if you compare the results or the answers of the solid angle subtended by sun and moon you can see both of them are quite similar with moon the solid angle subtended by moon is little bit smaller that is on an average days like when the earth and sun are its average distance the sun will appear bigger to our eyes because it is subtending like a biggest largest solid angle it will appear bigger to our eyes. Just imagine once in a year we heard about total solar eclipses right total solar eclipse are the days in which the moon will completely obscure the sun. We have seen such days like in news channels they will telecast how it is happening I think in the year 2018 or 2019 it happened over like US there are many people witnessed it lot of things happen it is like a important celestial event. So, what it will happen when we look up at it we would not see an object when something before it completely hides it essentially that is the idea. So, we all know what solar eclipses solar eclipses sun is behind moon is in front the moon completely abstract the sun that is what solar eclipses you look at the solid angle values given here the moon's solid angle is 6.45 into 10 power minus 5 radian sun's solid angle is 6.79 into 10 power minus 5 radian. So, sun naturally should appear larger to our eyes when we look at it. So, sun is larger moon is smaller but total solar eclipses also occur can you please think of it is in why please pass the video for a second and think and then you can play the video for the answer. The answer for the question is the distance that we have used here is the mean distance between earth and the sun. So, the distance between sun and earth and moon and earth will be keep on varying based on where the where those objects are where the earth sun and moon are with respect to their individual orbits each of them have their own orbits sometimes some earth goes closer to the sun in its orbit sometimes moon comes closer to the earth during its orbit. So, this distance that we have used is not constant it will vary with season or different days during total solar eclipses the moon comes very closer to us so the d square term in the denominator will go down and the solid angle will increase. So, that is because as the distance changes that radius of the moon is going to remain the same the moon disk or the solar disk area is going to remain the same that is not going to change but as the distance changes with different days moon will appear bigger to our eyes on certain days like full moon super moon and all we are seeing right. So, those days moon will come closer to us moon will appear much bigger actually. So, on those days what will happen moon will subtend the largest solid angle than sun that is why moon is able to obscure sun during total solar eclipses. So, solid angle is essentially what how much area and object covers in our vision when we look at it simply put. So, larger the solid angle larger the area an object will cover in our vision when we see if it is very small it will subtend a very small solid angle. So, as the object is growing bigger and bigger or as the object comes nearer to us it will appear larger to our eyes naturally and hence it will subtend a larger solid angle that is the concept how much area and object covers in our vision that is all. Now, we have seen the basics about plane angle and solid angle have solved a problem also. Now, we are going to get into the radiometric terms and its definitions. So, what are these radiometric terms or radiation quantities? In the earlier lectures I was repeatedly mentioning energy, radiation, radiant flux, radiant flux density all these terms. Those terms may appear similar when we hear them for the first time, but the way in which they are defined the way in which they are measured actually is very different. So, in this particular lecture we are going to talk in detail about the different quantification of this energy measurement. The first and basic quantity in energy measurement is energy itself. So, what energy is? Energy is the ability of ability to do some work say I am going to push some heavy object and move it. That means I am spending some energy from the body, I am transferring it through my hands to the object and I am moving it. So, energy is the capacity to do work. Similarly, for radiation also what is coming from the sun or what is emitted by earth, the radiation also has energy. So, the basic term is energy. So, unit of energy we all know joule. So, that is the basic quantity say whatever be the object, whatever be the time frame, what is the total energy content within it, we can like define or calculate using some extent. Now, let us say rather than energy we need to know what is the amount of energy coming in per unit time. That is I have some like what to say I have lit up a stove, I am keeping a pot of water filled over it. So, what I want to calculate what is the amount of heat energy being transferred from the stove to the pot of water I kept on top of it. If I switch on the gas stove, leave it for so much time and measure everything together, I would have calculated the total energy content. The heat energy supplied is this much. On the other hand, if I want to calculate the energy per unit time, so what I should do, I should measure the total energy transfer from the stove to the pot of water, somehow I should measure it. Simultaneously I should measure the time taken for this heat transfer say the water was cool and then I stopped the process when it started boiling, say it took some 10 minutes let us assume. So, what is the total amount of energy transfer I should calculate it and divided by 10 minutes in order for me to calculate the what is the amount of energy transferred per unit time that is every second what is the amount of unit energy transfer. And that particular term that is energy per unit time we call it as radiant flux. So, what is the amount of radiant energy per unit time? If you look at this with respect to like energy and power, power is equal to energy by time. These are all definitions we have learned in school physics. So, essentially radiant flux is nothing but the power of the radiation that is what is the amount of energy per unit time. So, for energy the unit is joule for power that is radiant flux the unit is joule per second or watt on the other hand. So, joule per second is defined as 1 watt that is what is the amount of energy spent per unit time. So, the symbol to denote is a capital letter phi. So, phi can be like written as like a small letter like this or like a capital letter in Greek letter. So, here we are using a capital letter this is the conventional symbol used to indicate radiant flux. Now what have we done we have calculated the amount per unit time. Now my interest is let us go back to the example of stow and water pot. Rather than calculating in sorry in addition to calculating the energy per unit time I also want to calculate what is the amount of energy per unit time per unit area of pot that is let us assume the pot is like quite big say it occupies an area of say like it has a radius of around like say 2 meters very big pot let us imagine a very huge pot as if I am going to cook for like a big function huge pot let us imagine a 2 meter radius of pot it will have like a certain area we all know that it will cover like a huge area. Per unit area of the surface of the pot what is the energy I spent per unit time how I will calculate it I will first measure the total energy content I supply I will measure the total time taken for it then I will also measure the area of the bottom of the vessel then I will divide the total energy by time and also by area. So, here I will be getting the energy I spent per unit time per unit area this quantity we call radian flux density that is what is the amount of energy per unit time per unit area. So, the units for this is joule per second per meter square or watt per meter square. So, conventionally we will write it as watt per meter square. In remote sensing terms we will be interested normally in remote sensing of earth surfaces what we will do we will be having lot of objects on the earth surface and that particular object will receive energy from the sun similarly that particular object will emit energy on its own or reflect energy from the sun that we know. So, for remote sensing purposes in this radiometric term the exact definition of radian flux density is something like this. Let us say we have a small area here on a flat horizontal surface a flat horizontal surface the area is a. So, I am going to construct a hemisphere surrounding it. So, this hemisphere is like this is like land. So, there is like no full sphere if I stand here I will be able to see only a hemisphere around me right. So, I will construct a hemisphere around it. So, what is the energy falling on it falling on this particular object from within the entire hemisphere. So, I will say I am going to use a symbol of E E is equal to the energy coming in. So, energy I am going to represent it by this is like yeah radian flux sorry this is not energy this is radian flux that is per unit time I am going to divide it by the area a. So, the definition of radian flux density is if we have a small elemental area on a flat horizontal surface and construct a hemisphere surrounding it whatever the energy falling on that particular area from the entire hemisphere per unit time we call it as radian flux density. So, radian flux density means amount of energy per unit time per unit area and the units we use it for this is watts per meter square. Now, there are two terms involved one is here in this particular study itself I have written two terms one is irradiance and another term is emittance. What is the difference between irradiance and emittance definition wise they are the same, but the direction in which they are moving will define whether it is irradiance or emittance. If the object A is receiving energy from space or receiving energy from some other source we call it as irradiance on object A or other hand we will also write it as irradiance received by object A. On the contrary if A is an object that is emitting energy now again a flat horizontal surface and here the object A is there with a defined area I am again going to construct a hemisphere around it now this object is emitting energy into this hemisphere surrounding it. So, I am measuring the energy emitted by it in the entire hemisphere I am calculating the time taken for it I have to know the surface area of this this is what I call it as emittance. What is the energy emitted? So, the symbol we use this m m is defined by again the phi, but here this is now this is emitted divided by the surface area of the object. So, whether any surface is receiving energy or whether a surface is emitting energy we call it as irradiance or emittance, but technically both of these irradiance and emittance we should call as radiant flux density that is the correct technical term that is radiant flux density, but based on the direction whether it is coming towards an object or whether going out of an object we will classify it as irradiance or emittance. So, here please note we have considered a flat horizontal surface and the energy we have taken is in the entire hemisphere surrounding it. So, essentially we are talking about like a 2 pi solid angle surrounding a given object say if I stand here the solid angle surrounding me is like I can put a full hemisphere covering myself. So, the solid angle around me is 2 pi irradiance. So, what is the energy falling on me from the other sources within this 2 pi irradiance is what is radiant flux density. Now, we go back to the previous slide to look at the next most important term. The next most important term I want all of you to like pay attention to is what is called radiance. So, what exactly radiance is we will move to further slides yes. So, this particular slide will tell us what radiance is. So, here let us say someone is standing here like let us go back to our example of the sun and an observer problem that we already solved to calculate the solid angle. Sun is here and observer is standing here. The observer is looking at the sun as I already said the sun is going to subtend a solid angle. So, this is solid angle omega. So, whatever the energy coming in from the sun is actually coming within this particular solid angle because the observer is looking at the sun and the sun subtends the solid angle of this and whatever the energy the observer receives is actually coming within this entire solid angle. Similarly, say if you are flying on an aeroplane say there is an aeroplane and an observer is like we have got a window seat someone is sitting on a window seat and trying to see whatever is there on the surface. So, what we will see we will be able to see something like kind of like a cone and whatever solid angle we can see we will be receiving all the energy coming within it and our eyes can see it. Same concept is what radiance is to a satellite or in remote sensing parlance. In remote sensing parlance say a satellite will have a sensor. So, there we will take from the example of a sensor. Let us say a sensor is placed here it is seeing something on the earth surface. The sensor is kind of like a small element like our human eyes it is like a small element. So, when it sees the earth surface based on its sensors orientation and properties it will have a small solid angle subtended within it. So, whatever the area is covered within the solid angle it will observe. So, whatever the energy coming in within that particular solid angle will reach the sensor. So, essentially the energy within that particular solid angle what is the energy coming in that particular direction is what we are interested upon and conceptually this is what is known as radiance. So, now we will go to the exact definition of a radiance what radiance is. We again like take like a small area on a flat horizontal surface. This is like an area the area of the surface is A. I am placing a sensor or something here or let us assume there is a observer here standing on a some energy sources there something is there measuring it. So, now we are looking at at an angle of theta from the surface angle. So, now the direction is like not in like perpendicular to the surface it is the direction in which we are looking is having a angle of theta with respect to the surface normal. So, if this is the case if I want to calculate what is the amount of energy that is going out from this particular area in this particular direction of theta at a given solid angle, given solid angle omega or phi whatever we can call is what is known as radiance. So, radiance is essentially what is the amount of energy that is amount of radiant flux going on per unit solid angle divided by the projected area of the surface. So, what the projected area of the surface means the area is now if I am like if I am looking at some of the direction inclined angle of theta the area will not appear like A, but it will be projected it will have an angle of A cos theta that is the area will appear different. What essentially I am doing is I am trying to project this area perpendicular to the direction of motion of radiation. So, I am projecting this particular area in a direction perpendicular to the motion of radiation and what is now this projected area is. Say we have learnt like projections and how surfaces will change when we look from different perspectives like some engineering students will be there taking this course and you would have learnt about like projections how the area will change. Like very similar example like if you take like kind of like a large circular object on the ground if you are like flying in an aeroplane if you see it from like different directions with different viewing angles the same circle may appear as an ellipse may appear like a smaller circle elongated ellipse and so on its shape will be keep on changing. So, essentially the area that you are seeing is projected in that particular plane same concept whatever the area was there on the flat horizontal surface you are actually projecting it as if it as if in a direction perpendicular to the direction in which you are seeing it. So, radiance is nothing but the radiant flux divided by what is the total salt angle divided by the projected area and where the area is projected in a direction perpendicular to the look angle. So, now we go back to the slides where I given the various definitions. So, here so I just left this term I we need not concentrate much on it. So, this is given as L radiance is denoted as symbol L is given as d phi that is radiant flux that is what that is energy per unit time divided by what is the total solid angle within which it is going divided by what is the projected area dA cos theta this is what is known as radiance. Just to give one more example I go back to our earth and the sun problem the earth and the sun problem whatever the energy coming in from the sun comes within this particular solid angle say we calculated it as roughly 6.75 to 10 power minus 5 radian. So, whatever the energy coming in from the sun is going to come from this particular radian only this particular solid angle only and solid angle. So, if I am like if my vision is perfectly perpendicular to the direction of motion of sun so what is going to happen what is the area of sun that is look I am looking at my eyes and what is the energy coming within this particular solid angle is what is what defined as the radiance. So, radiance is nothing but the energy or the radiation within one particular direction simply put if I look in this particular direction in a given solid angle what is the energy going out or coming in. So, it varies based on direction. So, just to summarize what we have learned in this particular lecture in this particular lecture we have learnt about plane angle and solid angle. We have also learnt about certain radiometric quantities that is we define what energy is then we define what radian fluxes that is energy per unit time then we define what radiant flux density is energy per unit time per unit area then we also define what radiance is. So, radiance is defined as radiant flux per unit solid angle per unit projected area. So, radiance is highly directional maybe in the next class we will go little bit deeper into this concepts and look more into it in order to understand it better. Thank you very much.