 Hello everyone, welcome to this lecture on the topic interaction of electromagnetic radiation with terrain features. In the last lecture we discussed about how a surface can be classified based on how they reflect that is specular diffuse, near specular, near diffuse and so on. So, how to characterize whether a surface is specular or not, that is what we are going to see in this particular lecture, how to tell whether a surface will behave specularly or on a diffuse fashion. Essentially that depends on surface roughness like in last class I told you whenever a surface is rough that is whenever there is like some elements are present like sand grains, stones, surface is not even it has like ridges and small falls, pits and everything that surface will appear rough to our eyes that is what we call it as basically surface roughness. So, based on surface roughness each surface may appear smooth or rough based on how much is the deviation. So, what is the criteria to classify a surface into smooth or rough and that particular criteria we are going to see in this particular lecture. The criteria is known as Rayleigh criteria. So, based on Rayleigh criteria we will classify a surface as smooth or rough. What Rayleigh criteria is we will see now. Let us say there is like a really smooth surface two beam of radiation they are like let us assume they are in phase two beam of radiation parallel beam of radiation coming and falling it. Let us assume they are in phase if the surface is really smooth what will happen this will be reflected this will also be reflected they will obey Snell's law and the phase difference or in phase nature will be still maintained even after reflection because they travelled parallely they got reflected almost at the same instant the surface is really smooth not much of difference would have occurred they would have still continued parallely without any change in phase. Let us say there is like a rough surface one beam of radiation is coming here one beam of radiation is coming here. Just because of the presence of this roughness now they will be reflected in different direction this will may go off like this this may go off like this first thing and since each one the distance they travelled is slightly different like here it is this particular wave stopped here itself this wave travelled little farther to reach this down point. So, the distance they travelled varied hence the parallelism will be changed and when they are now reflected therefore there will be a some sort of phase difference got introduced after reflection that is if a surface is not extremely smooth then there will be some sort of like phase difference introduced between the waves that got that came in and after it reflected within the first two rays between rays 1 and 2 even though when they came in phase after reflection there will be a small phase difference between them. So, the Rayleigh criteria was based on this particular phase difference what Rayleigh said is if the phase difference of between like different waves reflecting at different different points on that particular terrain feature if the phase difference is less than say pi by 2 then he said that particular surface can be classified as smooth. On the other hand if the phase difference between the two waves is more than pi by 2 he classified the surface as rough. So, how this thing came up the term pi by 2 is actually like a thumb rule he said pi by 2 and most of the people used it that is fine but how to calculate the phase difference for calculating the phase difference we will do a small derivation. Say here there is a rough surface given here. So, this particular line is the mean height line that is if you take average of heights in this surface this is like the mean height. So, there is like two different points we are taking let us say one here on some surface here let us say there is one more reflection happening at this particular height and this should be actually marked on a terrain but this is marked here just because for clarity. So, let us say reflection is occurring at height of mean height and another reflection is occurring from the surface slightly above this at a height of delta h above mean height. So, there are two points on terrain one with height of h and h plus delta h okay. Two waves are coming one is getting reflected from the point with height h one is getting reflected from the point at height h plus delta h let us assume both of them are in phase. So, now this is reflected from this point going like this this is reflected from this point still going like this but still there will be some phase difference introduced between them. Why this phase difference is getting introduced? This phase difference is getting introduced because of this additional path that this wave traveled to reach this point. When I discussed about coherence I told you like as long as two waves are exactly parallel they will be maintaining their phase relationship but when the path difference changes when they move away from parallel sea there will be what to say or when the path length changes they will lose their phase relationship the phase relationship will change they will lose their coherency. Same thing is applied here due to the difference in path length between two radiation there comes a small phase difference between them. How to calculate the path difference between the two points say this is two points so the wave two let us name this wave as wave one this is wave two the wave two has traveled this much distance more than wave one wave one got reflected from here to here whereas wave two has traveled an additional path a path difference is there when it traveled. So, how to calculate it if you take this as like kind of like a straight line this is also theta naught this is 90 degree this is perpendicular from this point I have drawn a perpendicular to the surface. So, this is 90 degree. So, we are interested in this particular let us call it as delta x. So, the phase difference the path difference we need is 2 delta x that is delta x is this side delta x this side first we need to calculate what is delta x. So, just look at that small triangle here this is theta naught this is the 90 degree line this is the delta x we need and this hypotenuse here is the delta h the height difference between them. So, cos theta naught is equal to delta x by delta h that implies delta x is equal to delta h cos theta naught. So, this is the half of the path difference. So, the path difference is delta h cos theta naught. So, we need 2 delta x because this is delta x this is delta x. So, multiply this by 2 we will be getting the path difference is equal to the total path difference is equal to delta h cos theta. So, now we know that for wave to complete one full cycle like for a distance travel between 0 to 1 full cycle lambda it has a phase of 2 pi here the path difference between 2 waves is 2 delta h cos theta. So, that is also a distance. So, what will be the path difference that would have come for this particular distance that is what we are going to calculate as a next step that is for a wave with wavelength lambda or distance for full wavelength lambda the phase is 2 pi for now our distance is 2 delta h cos theta it is actually a distance what is the phase we do not know because this is the phase difference between 2 waves. So, we need to calculate this. So, rearrange this delta 5 is equal to 2 pi into 2 delta h cos theta naught by lambda that is equal to that implies delta 5 is equal to 4 pi delta h cos theta naught by lambda. So, what we did here I am just telling it again for simplicity sake that is a wave of wavelength lambda will have a phase of 2 pi over its entire wavelength for us we are going to calculate the phase difference for a wave which has traveled this much distance 2 delta h cos theta. So, the small phase difference delta 5 is 4 pi delta h cos theta naught by lambda. So, what Rayleigh said this Rayleigh criteria first he said this if this delta 5 is less than pi by 2 that particular surface is smooth. So, that is what he said or if this delta 5 is more than pi by 2 that particular surface is rough that is what is given in this particular slide. So, what essentially will happen if you imply that condition for this equation that is pi by 2 less than pi by 2 or more than pi by 2 we can calculate delta h here. So, if we if the delta h is less than lambda by 8 cos theta naught that particular surface is smooth. If the delta h is more than lambda by 8 cos theta naught that particular surface is rough that is the original Rayleigh criterion developed by Lot Rayleigh. But later on people decided a surface need not be only smooth or rough there can be in between nature. So, then people decided we will modify the Rayleigh criteria based on smooth surface, intermediate surface, rough surface. So, now there is like a three class. So, for those three classes the conditions are given here sorry the conditions are given here for the three surfaces. If the phase difference delta 5 is less than 4 pi by 2 pi the surface is smooth. If it is between 4 pi by 25 to pi by 2 that surface is intermediate or if the delta 5 is greater than pi by 2 that surface is rough. So, this is Rayleigh criteria to characterize whether a surface is smooth or rough. One thing you have to note is the calculation of delta h that is how much height a point is above the mean height of the surface. Like if there is like a lot of roughness elements that terrain we can fix a mean height and we can fix how much the height of other points varies with respect to that mean basically right that is what this delta h. So, if that delta h when we are calculating it it depends on the wavelength and the angle of incidence with which EMR is coming and falling on the surface. So, a same surface can appear rough to one particular wavelength but appears smooth to another wavelength like I said example of a sandy beach with coarse sand grains. When we look at it our eyes will see only visible wavelength at visible wavelength like 0.4 to 0.7 micrometers the dimensions of big sand grains is much cozier delta h. So, the Rayleigh criterion for roughness will be satisfied and that particular surface will appear rough. So, that is why like coarse sandy beaches we appear to our eyes as rough. On the other hand if you take an image of the same beach at microwave wavelengths maybe like say 30 centimeter wavelength and so on that particular beach will appear smooth because of wavelength dependency on surface roughness. So, same roughness same surface may appear smooth at one wavelength or may appear rough at other wavelength this you have to remember. So, surface roughness is not fixed it depends on the wavelength and also it depends on the angle of incidence whether the angle is coming straight from the zenith like theta is 0 or whether like theta is coming at like larger angle and so on this particular surface roughness characteristics will vary this we should remember when we work with Rayleigh criterion. So, one more important feature about EMR interaction with surfaces I said in wavelength less than 3 micrometers we will be interested to study the concept of or study the reflectance properties of objects how objects will reflect back. Each object has a characteristic reflectance curve. What exactly a reflectance curve is a reflectance curve is say if you are able to measure reflectance of an object and different different wavelengths and plot it in form of a graph that is known as a spectral reflectance curve example for this is given in this particular slide. So, here we have plotted reflectance as I said reflectance will vary between 0 to 1 here in this case we are stopping at 0.6 this is with respect to wavelength. So, all the three properties I said of objects reflectance, transmittance, absorptance all are wavelength dependent they vary with wavelength hence here I am plotting how objects will reflect at different different wavelengths. So, this particular curve that I got is known as a spectral reflectance curve and if we get this spectral reflectance curve for various features on the earth surface like vegetation, waters, sand, urban materials, ice, snow, whatever we will be able to see that different class of features has a characteristic shape to curve like this the curve given in this particular slide here is actually for vegetation. So, vegetation curve will have this characteristic shape it will have like a small peak a valley a large peak there will be lot of small small valleys in between. Same thing if you look at some other features say here in this particular slide what is given here the spectral reflectance curve of different features is given. So, this small dotted line is for water this is for grass again a vegetation. So, this is for like concrete this is for red brick. So, different features has completely different spectral reflectance curve and they are almost unique for each feature say when we do remote sensing actually we will have lot of other interference we will see later. But if all the interferences are removed if you are only capturing the reflectance of objects in like a closed laboratory in perfectly controlled conditions then each different class of objects will have a characteristic reflectance curve. Using this characteristic reflectance curve we will be able to identify that particular object from remote sensing images and that is why we call these particular curves also as spectral signatures like each one of us will have a unique signature. By looking at the signature people in bank will identify okay this is this is like ish where a sign is matching with them fine I can pay him whatever money he asked for. Similarly each one of us has a unique signature same thing each object has its own unique spectral reflectance pattern and hence we call this spectral interference curve also as spectral signatures. Using the spectral signatures we will be able to classify all objects most of the objects at least from remote sensing images. So, in this particular lecture what we discussed is we discussed the Rayleigh criteria of roughness what is the criteria to classify a surface as smooth or rough and based on the Rayleigh criteria we also noted that the criteria is dependent on wavelength a same surface can appear rough or smooth based on the wavelength involved and also we got introduced to the concept of what is known as a spectral reflectance curve and what is spectral signature. In the later classes we will understand what happens to this particular curves what all the problems we will face when we try to do remote sensing to classify objects using this curves with this we end the lecture thank you very much.