 Welcome to today's lecture on the course remote sensing principles and applications. In this class also we are going to continue with the topics of radiometry. Over last two classes we have been learning different concepts of radiometry such as plane angle and solid angle, different quantities of radiometry like radiant flux, radiant flux density, radiance and so on. All these terms we have defined. We have also learned the relationship between radiance and radiance flux density that is E is equal to pi times L which is applicable only for Lambertian surfaces. Then we also saw the inverse square relationship or inverse square reduction property of radiant flux density whereas radiance will remain constant within a given solid angle. So, these are all some of the properties about the radiometric quantities that we have seen. Today we are going to continue with what are like different directionality that is involved in remote sensing, what are different terms such as reflectance and albedo and so on. So, this is where we stopped in the last class. We have done a problem to demonstrate the inverse square law relationship. That is we use sun as an example. We calculated what is the amount of radiant flux density or exactly what is the radiant flux density that will be reaching the earth surface from sun. We have calculated a value of like 1368 watt per meter square and I also said we call this as the solar constant that is on an average this will be the radiant flux density from sun that will be reaching the earth surface. So, this uses the average distance between earth and sun please remember it but as I already mentioned the distance between sun and earth will vary with respect to like different days in a year but we have chosen an average distance here. So, the next important topic that we are going to see is the directionality of remote sensing measurements. Now, we would have come to like some basic understanding of how the energy is coming, how the energy is going out. So, how the energy coming in and going out is depend on the direction which we look is what we are going to see now. In this particular slide there are like different cases that have been mentioned which describes the the directions in which energy will come in and the direction in which energy will go out. Now, for the normal remote sensing purposes what will happen is let us assume like a sensor in space and there is like a land in here. So, each sensor will subtend like a small solid angle on the surface. So, this will be like kind of a cone we can imagine like a cone with an apex at the sensor and its base at the earth surface we can assume it like this. So, this suggests most of the measurements that we do with respect to like any remote sensing sensors essentially will have a form of like a conical reception. Conical reception the sensor will be collecting energy that is coming out from that particular cone that is that solid angle as we defined it is kind of like a cone. So, whatever the energy is there within the cone it will reach the sensor. So, that is explained in cases here like where the reflected energy is conical. So, this is most likely an example of remote sensing systems. But please remember in these diagrams what is a remote sensing sensor you have to like think as if it is present here. So, here the view geometry is like slightly changed where the view geometry is written from the point of land surface. But in remote sensing the same concept of conical will be there but from the sensor. On the other hand like on the other hand if we look at the incoming radiation we can consider incoming radiation either as like a direct like a single ray of radiation or we can integrate the radiation with an entire hemisphere etc. So, the different examples that I will tell say for example a bright sunny day. So, for a bright sunny day we can consider the incoming solar radiation as a single ray of directional radiation that is I already told you that the solid angle subtended by sun is extremely small and the distance between earth and sun is like quite large. So, what we can assume is the all the radiation coming in the sun comes from one particular direction as like a single ray of light we can consider like that because it is like the assumption it is an assumption but it is like a valid assumption that we can do considering the large distance between earth and the sun and also the very small angle subtended by the sun. So, we can consider if at all we are going to measure only the direct radiation from the sun we can consider that as like a the radiation coming in from only one particular direction. On the other hand I also told you that the radiation received at the earth surface is a mixture of direct sunlight and diffuse skylight that what is diffuse skylight means diffuse skylight is the energy that is present in the atmosphere due to scattering of the sunlight. So, for a normal land surface for any land surface or any feature on the earth surface will not only receive a direct radiation from the sun but also diffuse radiation from all directions surrounding it. So, this is like the major component of incoming energy the direct radiation from the sun whereas these things are all diffuse component of energy. So, any particular feature on the earth surface will receive both these. So, sometimes we may have to calculate the total energy that is coming in within the entire hemisphere surrounding the object of our interest that is an object say a small object is present this particular object is going to receive energy from the entire hemisphere surrounding it whereas the one particular component is a direct component from the sun and it receives diffuse skylight from all other directions. Similarly, most of the earth surface features will also have the tendency to reflect back energy in all directions that is take the example of the same object here in response to incoming energy the object will reflect a part of energy like it will be reflected scattered etc. The energy will be a part of incoming energy will be again like transferred into different direction into the sky itself. When this happens some objects may reflect in one particular direction whereas most objects have the tendency to reflect in many different directions surrounding it. Hence, if we want to calculate the total amount of energy going out of an object then also we may be in a need to calculate over the or measure over the entire hemisphere surrounding the particular object. So, what I want to say is the incoming energy from sun and the direct radiation can be treated as a can be treated as coming in from one particular direction. So, we call that particular incoming energy as directional. So, that is where the incoming energy is directional but this is only an assumption the energy coming in from essentially comes in form of like a cone because that also is like a very small solid angle but still the particular energy from the sun comes in and falls on the earth surface through a conical means. But we can assume it is coming as like a from only one particular direction not within like a small cone. Whereas the energy going out from the earth surface can be treated whether as going in one particular direction as if a remote sensing sensor observes like already as I said sensors observe in form of like a cone or we will also be in a position to measure the energy going out of an object in the entire hemisphere surrounding it. So, now there are like three different directional property associated with remote sensing based measurements. One thing we will be interested in knowing the energy coming in or energy going out in one particular direction that is coming in one direction or going in one direction or we may be interested in energy coming in and going out of within one particular cone having a definite solid angle or we may also be interested in measuring either incoming or outgoing energy within the entire hemisphere surrounding an object of interest. So, three possible directionalities exist in remote sensing and if we combine if we take the two different directions of radiation direction means like one is incoming and one is outgoing. So, this single direction conical and hemispherical can be considered for both incoming and outgoing radiations. If we combine all of them we get this nine different possibilities given in this particular slide that is why that is what is given as nine different objects that is incoming energy treated as coming in from exactly one particular direction, outgoing energy also treated exactly as going in one particular direction. Similarly, I go to this case 5 incoming energy is considered as coming in form of like a cone, outgoing energy is also considered to be measured in form of like a within a cone and then come to case 9. In case 9 what are we doing we are considering the incoming energy within the entire hemisphere surrounding the object which has like a direct component and also like a diffuse component. Outgoing energy also we are considering the entire energy going out of an object within the full hemisphere surrounding it. So, what are like some examples for these directionalities in order to make it more clear normally as I said suns radiation or if we are using some highly collimated laser beam to illuminate some objects we can consider them to be directional that is coming in from only one particular direction. Say I have like a highly collimated source of laser beam I can use that to illuminate a target which will give me like a small point on the target of interest that we can assume it to be directional nothing is like really directional in the measurements that we do because we cannot directly go on to measure like a 1D one ray of light whatever we measure even if you use like a small collimated beam of light it will have like a small circle projected on the object of our interest. So, nothing is purely directional we are assuming those incoming radiation as directional measurements. So, what I want to say is some measurements or some radiation sources we can assume to be directional that is sunlight bright sunlight under like extremely clear sky days or like as I said highly collimated source of laser light these kind of incoming radiation we can assume it to be highly directional. But outgoing radiation cannot be directional truly objects sends energy back in different different directions. Then we will talk about like another example of the conical case. Conical cases let us say like we are using some sort like a bulb to eliminate an object of our interest we are in a dark room we are switching on a bulb. So, essentially a bulb is kind of like a small sphere which will radiate energy within like a small solid angle in form of like a cone basically if you imagine. So, using a bulb as a radiation source is a very good example of conical case of incoming radiation. Similarly, as I already said most of the remote sensing measurements with the sensors attached with it have like a conical form of collecting the incoming energy. So, that is we call it as biconical case where the incoming energy is also like considered within a cone outgoing energy also is considered whatever is coming within a cone. So, what is a very good example of like hemispherical measurements as I said if we consider the incoming energy in both diffuse and direct component then we are essentially measuring the energy over the entire hemisphere surrounding an object. So, considering all these cases normally in remote sensing we will be interested or we will be naturally doing what is known as this particular case will mostly we will be doing hemispherical or conical that is incoming radiation is hemispherical like taken together within the entire hemisphere surrounding an object but whatever measurements we do will be in one particular direction conical outwards. So, hemispherical here first refers to the direction of incoming energy, conical in the second term refers to the direction of outgoing energy. Similarly, if we construct both the cases if at all we are able to measure the energy within the entire hemisphere surrounding an object we call it as bihemispherical measurements. Incoming energy is also considered within the full hemisphere outgoing energy also is considered within the full hemisphere surrounding an object. This is like really important concept to know because we will see later based on the direction or based on where we are integrating over which surface we are integrating objects will look different. The next important concept to understand is the geometry between the energy source object and the sensor. The last slide I detailed about the different ways of or different combinations of directions which can come into play when we do remote sensing measurements. Here in this particular slide what we are going to see is how a source object sensor geometry affects our measurement. Please look at this particular thing. This is like an object on the earth surface and object on the earth surface will be irradiated by sun. We call it as irradiation on the object because sun energy is coming and falling on it. As I said truly speaking sun's energy can be considered as should be considered as conical but under some circumstances we can consider it also has like a directional incoming radiation that is coming in from only one particular direction as a single streak of light. Whereas like outgoing radiation as I said if we have like a sensor I told you it will be integrating energy in form of like a cone coming towards it. So, this is with respect to the area over which we integrate the energy either are we integrating within a cone or are we integrating within a hemisphere something like that. But one more important thing to assume is even though we assume incoming energy and outgoing energy are coming in form of like a conical shapes we are integrating energy in form over a cone. Then the cone itself can be oriented in different different directions that is we can give two directions to it. What is the direction with respect to vertical it makes we call it as the zenith angle and what angle does it what horizontal angle it makes with respect to a single direction of measurement. Let us say I have a point here in three dimensional space if I want to give a coordinate to it I can give coordinate using what to say one elevation angle theta and if I assume this as like a reference direction x this is treated as the reference direction then I can measure the horizontal angle of this particular point and call it as the azimuth angle. So, this is I call the zenith angle that is the vertical angle this I call it as the azimuth angle and also if I know the radiation sorry radius R from this origin I will be able to precisely locate this particular point in three dimensional space. I need like two angles and one distance. But if we are really interested only in fixing the direction of that particular point where in which direction the point is located it is good enough for us to know only those two angles the angle with respect to vertical called the zenith angle and the angle with respect to one horizontal direction like horizontal angle with respect to one reference direction called the azimuth angle if we know those two angles we will be able to fix that particular fix the direction of that particular point in three dimensional space. Similarly sun's energy the incoming radiation and the outgoing radiation can have several directions that is let us imagine like a land surface. Let us assume sun is here sensor is here this can be one particular directional component where it will have like one zenith angle and one azimuth angle. Sometimes sun may be here sensor also may be here the same azimuth angle orientation sometimes sun may be directly overhead sensor may be lying somewhere here. So, these are all like different possibilities that can occur in remote sensing there are very few examples. But really speaking the direction of incoming radiation and outgoing radiation the direction in which we observe can have many different orientations many different combinations. Taking this directionality and combine this with the area over which we are observing are we observing in just only one direction which is almost I said impossible are we observing over like a small cones like a small solid angle or are we going to observe over like a entire hemisphere covering the object of our interest. All these things and this directionality properties come together and this makes remote sensing a little bit complex. Complex in the sense there may be like a same object on the earth surface. But based on the what to say the solid angle in which we are integrating and also the direction in which we are looking will make the object to look completely different when we get the remote sensing signals. Later we will see like what signals we will get how those signals will look and all. But here just understand that the same object will look different when we integrate over like different areas that is if you are integrating over a conical solid angle or are we integrating over entire hemisphere or from which direction we are doing it. All those things will always introduce some sort of uncertainties or some differences in the remote sensing measurements that we make and this is what we call it as the difference in the object properties due to variation in the illumination and viewing geometry. So, the direct illumination geometry refers to and the way in which the incoming radiation is coming. Viewing geometry refers to the way in which we are looking at the object and making our measurements. So, this illumination source and the sensor geometry is going to play a major role in all our measurements. Natural almost all natural objects will look totally different when we observe from different scenarios. That is even if you take an example of like measuring only in one particular direction over a cone or if you want to integrate the entire energy with an entire hemisphere objects the output we receive from the object will be different. At one thing the output we receive may be one number and the second case the output we receive may be completely a different number like a different output. So, this will definitely influence our remote sensing measurements and this we always have to keep in mind when we use remote sensing data for our applications. Now, we have come to a point of defining important properties or important definitions related to remote sensing measurements. That is called the reflectance and albedo. In remote sensing I already told you that the major interest that we measure is what is the amount of energy going out from an object. Say an object is here. So, what is the amount of energy going out from an object is what we are going to measure in remote sensing. This particular energy can be reflected sunlight that is sun will give us energy or radiation and a part of this incoming sunlight will be reflected by the object. So, that is what I call reflected sunlight or the skylight component also diffuse radiation also will be reflected. So, essentially it is a reflection or it can also be an emission from the object emission means we remove all these external energy sources. What is the energy just going out from an object due to its own internal energy content or due to its own temperature that is what we call emission. So, the energy we receive in remote sensing can either be reflected energy or emitted energy. If we observe or if we make measurements in wavelength range less than 3 micrometers typically whatever energy we are going to measure is essentially the reflected energy. This we will see in detail in the coming lectures, but the energy the measurements we make in less than 3 micrometer wavelength is essentially the reflected energy from the earth surface. So, based on this reflected energy and outgoing energy we can define certain energy quantities. What are they? One is reflectance another one is albedo. What are these things? So, the reflectance is defined as the ratio of incoming energy to outgoing energy. Basically the very simple definition is reflectance rho is equal to what to say E outgoing that is radiant flux density outgoing divided by radiant flux density incoming. This is what is known as reflectance radiant flux density incoming and outgoing. The definition wise it may look extremely simple, but look at the practical aspects of this. As I said before the direction of incoming energy and outgoing energy will vary and also the nature of integration of incoming energy whether it is coming over like a conical projected area or whether it is coming over like a entire hemisphere it depends on the measurements we make. So, based on the directionality of the measurements the quantity reflectance that we measure is going to vary. What is this? That is what is given here. The observed reflectance may either be directional or conical or hemispherical that is I just defined rho as E outgoing by E incoming. It can also be the E can be coming in exactly in one direction and outgoing in exactly one direction. So, this is E directional incoming by sorry this should be outgoing sorry by E directional incoming. Second case is let us say sun ray is coming we are going to consider both the diffuse radiation and direct radiation. In that case we have to make measurement of incoming energy in the entire hemisphere surrounding the object. So, here we are making a hemispherical case of incoming energy and let us say we are using a normal sensor in space which integrates energy over a cone over like a conical solid angle. So, that case rho will be defined as E outgoing over a conical integration area E incoming which is measured over a entire hemisphere. So, these are like different different possibilities which can come into play in which over which solid angle we are integrating the energy. This is going to make the reflectance values to differ especially for objects which are non-lambarsian, non-lambarsian in the sense I already told you if we change the direction of the way we look objects will look different. Look is not the visual look that we see, but in other wavelengths the signals coming out of an object will be different. So, the reflectance value we measure here is going to be different based on the solid angle over which we are making our measurements. Are we making measurements exactly over one line? Are we making measurements over an entire hemisphere? Are we making measurements over a conical surface? This is going to make matters very different. That is why we have defined two different properties reflectance and albedo. Normally the reflectance measurements we make will have some sort of directional component of measurements that is say a sensor may be located here it may be like observing the land surface within like a conical solid angle and what is the energy that went in the direction it would have measured and we would have calculated a reflectance. But for some applications especially like cryospheric land surface modeling and all we will be in a position to measure the total energy that came into an object and total energy that went out from an object that is in both incoming and outgoing cases we should be measuring the energy over the entire hemisphere surrounding an object. So, for natural measurements it is not possible our measurements from remote sensing are highly directional. So, using some mathematical functions we will be converting this directional measurement to an entire hemispherical measurement. So, if we are reporting this reflectance value over an entire hemisphere like a bio hemispherical nature then we call it that particular reflectance as albedo that is incoming energy can be directional or conical hemispherical whatever but the outgoing energy should be measured in a hemispherical way. Hemispherical way in the sense the outgoing energy must be measured over the entire hemisphere covering the object. So, I already told you remote sensing measurements direct measurement that is not possible from satellites we need to do some sort of like model based conversions to convert our directional measurement from a cone to hemispherical measurement. So, what is the reflectance this is? Reflectance this is the ratio of outgoing energy to incoming energy but it can have directional component like the sensor might have looked from many different directions over a cone conical solid angle and we would have got reflectance. But normally we define which for most applications we will be needing reflectance values where the outgoing energy is measured within the entire hemisphere that has covered the object of our interest and we call that as albedo. So, please remember this there is a difference between reflectance and albedo reflectance has directional component whereas albedo our measurement over the object of interest should cover the entire hemisphere surrounding that particular object this is with respect to the outgoing radiation. Okay. So, today is in today's lecture we discussed in detail about and the directionality of remote sensing measurements and also we defined quantities such as reflectance and albedo. Next lecture we will continue little bit about this in order to make ourselves more clearer. Thank you very much.