 today's lecture in the course remote sensing principles and applications. The last class we saw different ways in which EMR will interact with the terrain features. We saw information about like reflectance, transmittance, absorptance, we saw how reflectance will vary with respect to surface roughness, specular reflector, diffuse reflector and all. In this lecture what we are going to see is after interacting with the terrain features the energy from the feature should reach the sensor for us to collect and analyze later. So how that particular energy will be transformed and what energy will exactly reach the sensor that is what we are going to see in this particular lecture. First we will get an overview of the various paths in which energy will reach the remote sensing system. If you look at this particular slide, in this figure I have given 5 different paths, path 1, path 2, path 3, path 4 and path 5, 5 different paths in which the energy can reach a sensor or in which energy can interact. What are those 5 paths, first we will take path 1, path 1 is the direct interest to us that is the direct radiation from the sun interacting with the feature or interacting with terrain and reaching the sensor. So this is path 1 which is of interest to us that is the direct solar radiation that comes in, interacts with the terrain, collects information about the objects here, reaches the sensor. Path 2, path 2 is we also saw in addition to the direct solar radiation we also have what is known as a diffuse skylight that is the energy that remains scattered in the atmosphere will be present throughout right and a fraction of that particular energy will directly reach the sensor that is it will be going in all direction, the scattered energy will be going in all direction. So a part of the energy will directly reach the sensor that is component number 2. What we call it as path radiance and component number 3, again it is related to the diffuse skylight instead of directly going to the sensor another fraction of it will be directed towards the object of our interest. It will come down will again reflect with the object of our interest will reach the sensor that we write it as reflected diffuse skylight. Path 4, sunlight will not only fall on our object of interest. If you take one area over which a sensor is looking at let us say the sensor is looking from the top over this area and we have like a small house here, tree here, a small pond and everything. Let us say everything is covered within a single area which image is actually looking at. So we are going to get signals about all these features together, if you are interested in collecting data about this particular building how this looks, we may also collect data about the tree, we may also collect data about the pond, everything will interact because solar radiation will fall on it everything will send energy back to the sensor. Same thing is depicted here as path 4. So path 4 what we call as reflection from neighbouring features and finally path 5. Path 5 is say we are interested about collecting information about any one object. So energy from sun will come in will be irradiating our neighbouring pixel let us say now we want to collect information about this tree. So sunlight will come fall on the house which is next to tree and a fraction of it will again fall on the tree which will be reflected. So that is energy undergoing multiple reflections. Say for example you are standing here let us say you are standing close to a building sunlight is going to is falling on you directly it is also falling on the building. If this building fuzzard is covered with like glass a fraction of the light will be reflected by this mirrors it will reach you and you will receive energy from the sun from the atmosphere and also from this particular building that is reflecting energy on you. Same thing will happen for other earth surface features too. So energy which is undergoing multiple reflections energy will be coming in from objects that are closer to the object of our interest. So these are 5 parts and path 4 and path 5 everything will reach the sensor. So these are the 5 parts in which energy can energy from the sun will reach the sensor. If you look at this path 1, 3 and 5 essentially carries some information about our object of our interest not some that is the one which carries information about the object of our interest about object of interest. On the other hand path 2 which is directly scattered from the sky the diffuse skylight or path 4 which is the signal going on from the neighbouring features they are not actually of our interest because that is not the signals that we want we want signals from this among this 5 path we will be actually able to calculate path 1 like what is exactly coming in the from the sun we will be able to model it to some extent path 3 the reflected component of diffuse skylight we will be able to model it to some extent. And then path 5 which is energy undergoing multiple reflections it is extremely difficult to model it because we do not know how the terrain will interact or how the terrain is oriented what fraction of light is falling on from different features that is extremely difficult to model. In addition to this that particular component will be too low too low in the sense since energy from the sun is undergoing multiple reflections say like we will look at the example of this building and this man let us say the building glass has reflect reflectance of say 0.8 whatever energy is falling on it 80% of it only will be reflected towards you not even 80 if there is like if it can reflect in different different directions only a fraction of energy will be reflected towards you. So as the number of reflections grows the energy will go lower and lower and this will become too low. So path 5 it is difficult to measure or model but it is too low and hence we can safely neglect and also path 4 that is the signals from neighbouring features if it happens in remote sensing we cannot do anything about it like normally when we do our various applications our images if it contains signals from our neighbouring features, neighbouring pixels we have to use it judiciously. So that is kind of inbuilt within the system we cannot do much about it path 4. So we can say it is inbuilt in the system we can leave it. So essentially the path which we are really interested upon is path 1, path 2 and path 3 these 3 are the major things which we are interested upon. Path 4 and path 5 we are kind of neglecting path 5 is too low. So hence we can neglect it and path 4 once it is come once such sort of adjacent reflection adjacency effects comes in it is difficult to remove it. So we have to live with it. So we say like we think as if it is not present okay. So essentially the first 3 components the direct reflected skylight path radiance and diffuse skylight that is being reflected by object of interest is what we are really interested upon. So this is the primary energy that reaches the sensor which we will use for our various applications. If you look at some textbooks they may say path 2 and 4 as path radiance. So 4 is the adjacency effect and path 2 direct diffuse skylight component. Both of these can be clubbed together and called as path radiance. Paths 1, 3, 5 depicted in this particular slide can be treated as the ones which carries the signals of our interest. So now we will see little bit in more detail about how energy interacts, what energy will reach the sensor, how to calculate it and so on. First we will concentrate on shorter wavelengths that is visible NIR and SWIR wavelengths. We will first concentrate on that and then we will later move on to thermal infrared region. So this particular figure will actually tell us the different paths in which energy will reach the sensor for wavelengths typically less than 3 micrometers that is visible NIR and SWIR bands. As I said before it has only 3 paths depicted here, the direct path, path 1, path radiance, path 2 that is the diffuse skylight directly reaching the sensor and this is path 3, the reflected component of diffuse skylight. Path 4 and path 5 from the previous slide we are neglecting here. So these 3 paths will effectively contribute to the radiation that reaches the sensor and one more thing what we have to recall is the energy that reaches the sensor or which will be directed towards the sensor is actually the radiance from the target. This is we learnt what radiance is in the radiometry lectures. Radiance is the energy or power per unit square of projected area per unit solid angle. If we have like a unit area and the sensor is looking at it from an angle let us say this is the center line from an angle say let us theta. So what is the radiation leaving this particular area every meter square of area when the area is projected normal to the sensor. So now I am rotating the surface element such that it is appearing normal to the sensor then we calculate what is the area of the projected element. From this we calculate what is the energy leaving towards the sensor per meter square of projected area in a given unit solid angle. This is what is known as radiance and that is what essentially our remote sensing sensors are measuring measured by RS sensors. So we have to essentially calculate the radiance that is leaving the surface and reaching the sensor. And also one more thing you have to notice in remote sensing whenever we talk about this energy terms always remember they always have a spectral element attached to it. Spectral element attached to it means it has a wavelength dependency we will always talk about some certain bands of wavelength say red band, green band, blue band, visible band and so on. So the radiance to be more specific it is actually the spectral radiance, radiance leaving the object of our interest per unit meter square area that is projected area per unit solid angle in a given bandwidth per unit micrometer of wavelength. So the units of spectral radiance is what per meter square per stradian per micrometer of wavelength. So this is the unit of radiance which essentially leaves the target and reaches the sensor. So what we are going to do now is now we know the major three parts in which energy can reach the sensor. We are going to calculate or derive some basic equations to know how much radiance will reach the sensor. First we will discuss those equations in the shorter wavelengths. We will first look at what radiance reaches the sensor in shorter wavelengths. In shorter wavelengths we know sun is the primary source of energy, solar radiation is coming in, interacting with the object of our interest this is a sensor so this will reach. So this is path 1 and diffuse skylight component what is present here, path 2 and this diffuse skylight reaching the target going towards the sensor is path 3. So we are going to calculate these three parts now first we will talk about path number 1 that is the direct component of solar radiation. So if you look at the direct component of solar radiation we have to first calculate what is the energy emitted by sun and what energy reaches the top of atmosphere and what energy reaches the terrain. Because solar radiation we all know as suns radiation travels through some distance the energy goes down we saw the inverse square law the radiant flux density decreases with increasing distance we have to calculate that. Then we will calculate what is the energy reaching the top of the earth's atmosphere. So earth's atmosphere has certain scattering and absorption properties so that energy will be further reduced that also we already studied. So what fraction goes down and what reaches the sensor we have to calculate each and every step. We have studied most of these things we will quickly recall them. The first component energy emitted by sun we can calculate it on in a simple fashion using the Planck's law that is what fraction like Planck's law we studied in earlier classes in the basic class class. So if you integrate Planck's law between whatever wavelength you are talking about say for example I am now interested about calculating the radiance reaching the sensor in red band let us assume ok. So red band essentially we can say it as 0.6 micrometer to 0.7 micrometers. So essentially what we have to do we have to first calculate what is the energy emitted by sun in this particular wavelength. So integrate Planck's law between your limits 0.6 to 0.7 micrometers integrated m lambda t. So sun's temperature you can assume it to be 5800 Kelvin. If you do this integration we will calculate what is the energy emitted by sun in the given wavelength we call it as red band. Then second apply the inverse square law that is this problem also we did in one of the earlier classes. This is the energy that is the radiant flux density per unit meter square area of sun because that is what Planck's law will give per unit meter square area. But sun we saw it is a big sphere. So we multiply this with area of sun and divided it by 4 pi d square. This also we have done and if you remember using this only we calculated what is known as the solar constant 1368 watt per meter square of radiant flux density. That is for entire bandwidth like total energy that reaches the sun in all bands in all energy bands all wavelengths. Here we are talking about one particular spectral band. So essentially you give you first apply Planck's law calculate the energy emitted by sun within that particular wavelength band. Then you apply this inverse square law whatever the problem we have done earlier which will give you the energy from the sun that reaches the top of our earth's atmosphere within that particular wavelength. So that also we have done. Third thing so now we have calculated. So this is earth, this is earth's atmosphere, this is sun. So what we have calculated is for our example we have calculated how much energy reaches earth's atmosphere within say in our example red band. Now we have to calculate what is the energy that reaches the earth's face. What reaches the earth's surface, how to calculate it rather than calculating each and every component we will take what is the total amount of energy lost in the atmosphere. So we represent that particular component as absorbed energy and what remaining is coming in. So that particular remaining energy coming in we are interested upon. So energy E reaching the earth's surface is equal to E top of atmosphere multiplied by transmissivity of atmosphere in red band. What transmissivity is what fraction of energy that reaches the earth's surface. So let us say 100 units of energy reaches the top of the atmosphere out of that 100 unit if 70 units of energy reaches the earth's surface then transmissivity is 0.7 that is transmissivity. So this will give us the energy from the sun reaching the earth's surface. So for the first path we have just calculated what energy will reach the earth's surface. So technically speaking this particular energy whatever I am talking as energy energy is actually radian flux density in actual radiometric units it will have a units of watt per meter square per micrometer wavelength. So this is actually the radian flux density or spectral radian flux density what we have studied in radiometric classes. So this is the power from sun that reaches the earth's surface okay. So it has 3 path we have calculated it in 3 steps. Next step is energy has come reach the surface it will be a portion of it will be reflected back a portion of it will be absorbed a portion of it will be transmitted that we know. But whatever remote sensing sensor will collect essentially the reflected energy. So we are now going to calculate that particular component. See this is the energy from the sun that reach the terrain. If the surface is flat and if the sun came in perpendicular to the surface no problem everything will be coming in together. But normally most of the earth's surface features are not flat and also not every time sun radiation will come directly from overhead perpendicular to the surface it will always most of the time it will be coming in at an angle. Let us say there is like a small slope and sun's radiation is coming in from a certain angle see like this like this. So essentially whatever the energy that is coming in from the sun will be modified for this solar geometry effect. Solar geometry effect means if the sun's radiation is directly falling perpendicular to the surface. See this is the surface horizontal surface solar radiation coming and falling perpendicular to it the entire energy will be used to irradiate the surface. On the other hand if the surface is slightly sloped or if the sun is not overhead it is coming in at an angle then the incoming energy will be distributed over actually a larger area as the angle becomes if from the overhead as the angle becomes larger and larger the zenith angle a larger area in the ground will be irradiated by sun we have to correct for it ok. So this is like even when we studied about the radiant flux density in radiometric glasses we always assumed surface is flat put an hemisphere over it calculate all the energy coming within it right that is how we studied. If the surface is not flat then comes a cos theta term into picture where cos theta what is the theta the theta is how much is the angle between the surface normal and the solar incident angle let us say surface is like this sun is here this is normal to the surface or we will say it as like even vertical at what angle sun radiation is falling in. If this is not the case if surface is oriented like this then you have to again draw a normal like this if sun is here you have to calculate at what angle solar radiation is falling in. So this is what you call it as incident angle this is to account for at which angle suns energy is coming and falling on the surface if suns energy is coming directly perpendicular to the surface no issues all the energy from the sun will be directly irradiating that particular area but if it is coming in at an angle with respect to vertical to the surface or normal to the surface then we need to account for with what angle the sun radiation is inclined that angle is called inclination angle or sorry angle of incidence incident angle for a horizontal surface incident angle is just the solar zenith angle for a sloping surface you have to draw a surface normal at the point and then calculate it normally we will calculate it with different means I will explain it later when we talk about topographic correction I will tell briefly about this. So now you just know that if sun radiation is not exactly coming in perpendicular to the surface there comes a cos theta term that theta is the incident angle between surface normal and the incoming solar radiation we have to correct the incoming solar radiation for instance angle and that is given by E lambda cos theta naught. So E lambda is the energy that reach top of atmosphere cos theta is to correct for this and we have corrected it for tau s. So this is the actual energy that will be reaching the earth surface. Now after it reached the earth surface it will interact so this E lambda naught tau s term this is the energy from the sun multiply it with reflectance of the surface where rho is the reflectance of surface say if the surface reflects 30% of incoming energy so reflectance is 0.3. So say 100 units of energy came into the surface after correcting for all this tau s cos theta and all these things finally 100 units of energy reach the surface out of which 30% is reflected means multiply that 100 by 0.3 so 30 units of energy will be reflected. So now we multiply with this reflectance still now we are talking in terms of radiant flux density that is what per meter square sorry per micrometer. There is whenever like energy relieves the surface and reaches the sensor we need to calculate radiance the term we are interested upon is radiance. Assuming the surface is Lambertian so we also studied what Lambertian surface is again in previous classes. So for Lambertian surfaces E is equal to L pi E is the radiant flux density L is radiance pi is the relation between them so L is equal to E by pi. Assuming the surface as Lambertian the radiance reaching or going out of the surface is this entire term divided by pi. So the radiance reaching the sensor sorry the radiance leaving the earth surfaces whatever it came from sun multiplied by reflectance of that particular surface divided by pi assuming the surface as Lambertian. So now this particular energy has now interacted with object of interest it has to again go back to the atmosphere to reach the sensor. So once again we there comes another transmissivity term tau where this tau is to account for the transmissivity of atmosphere in this outgoing direction because whenever sun radiation come in a part of it will be absorbed here similarly whenever it goes out towards the sensor a part of it will be absorbed there also. So it is a two-way path. So the final reflected radiation reaching the sensor is energy coming in from the sun multiplied by tau s the tau in between sun and the earth tau v transmissivity between earth and the sensor reflective reflectance of the surface divided by pi. So this is the radiance from the target of interest that reaches the sensor. So essentially in today's class what we have saw is we first discussed what are the different ways in which energy can reach the sensor. These are three major paths the direct radiation reaching coming in from the sun reflecting with object reaching the sensor path radiance and then third path is the surface being irradiated by the diffuse skylight and that reaches the sensor. So essentially in today's class we have calculated what is the amount of energy from path 1. So remaining two paths we will calculate it in next class and also we will look at how to do this for longer wavelengths such as thermal infrared wavelengths. Thank you very much.