Principles and Techniques of SAR interferometry by Dr. Hari Shankar

Added: 2026-05-14

[00:00:01]Okay, good afternoon. Uh, so this is the second lecture of the course. Uh, so title is principles and the techniques of the SAR interprot.

[00:00:14]So uh this uh interprot uh we are using uh microwave remote sensing data sets only. So synthetic object radar interpometry. So principles and techniques. So coming to the uh uh techniques part first especially for the land deformation studies. So there are number of techniques to measure the uh land deformation some traditional techniques are there and some uh remote sensing techniques are there. So we can start from let us say from photoggramometric methods where we we can use some aerial photographs and analyze them and uh can measure the land deformation uh signatures.

[00:00:59]Same way some groundbased conventional surveying techniques are there uh based on the triangulation or the labeling equipments or monitoring by the total station. Nowadays uh some robotic to total stations are also there which can be installed over the uh uh certain locations stable locations and from those locations you can measure uh the uh deformation around that particular point. So you can say the surveying techniques are the techniques for measuring the land deformation on the point basis. So you can say the point data you can collect from these techniques. Another techniques are the GNSS techniques, global navigation satellite systems uh which can provide you the continuous data sets uh of of the position and the time of a specific location where the wherever these GNS stations are installed. So these are again the point observations or point measurement techniques. So question is if you want to measure uh the land deformation over the large area in the continuous way. So in using these techniques you cannot measure the continuous uh land deformation. But yes if you have the you know uh sufficient point measurements then uh by means of interpolation or some other uh techniques you can uh generate the continuous deformation maps also. So point is uh first you are collecting the point observations and from point observations you are generating the continuous deformation maps.

[00:02:40]Another technique is like uh some geotechnical techniques based on certain equipments or instrumentation especially the sensors like the extensometers, includes tilt meter etc. So these devices are installed toward the areas where the chances of land deformation are there.

[00:03:05]So certain parameters uh can be uh measured from these uh sensors and based on those parameters you can have idea about the deformation means uh what is the pattern of the deformation and what is the scale or the rate of deformation over that particular area.

[00:03:24]Nowadays people are using the laser scanning techniques also where they are scanning the entire surface uh under the deformation and uh using uh that data set point again that is the point data set or here it is basically the point cloud where the density of point observation is very very large. So ledger scannings people are using for the land deformation studies and microgravity methods are there where the gravity measurements are done by different ways and uh those are basically the indicators of the land deformation and uh most popular one is the differential s interrometry. This is space especially the space-based uh SAR interpometry based on the remote sensing data set microwave remote sensing data set and from the differentials are interpometry one can measure the continuous map or continuous uh deformation maps over a particular area.

[00:04:28]So in general you can say uh uh from uh differences are interpometry you can measure the large area simultaneously or the deformation over the large area and the frequency of observation is also very high as you as you have here the satellite is continuously revolving around the earth. So after a certain uh interval of time it is giving you know a new data set. So by combining all the data sets a regular pattern of the deformation can be observed. with the help of the differential senropometry techniques. Okay. So the advantage of over this technique is uh the frequency of observation is very high and it provides the observations over the large area simultaneously. Okay. If uh somebody wants to analyze the know entire country or the continent they can do it because these remote sensing satellite data satellites are covering the entire globe.

[00:05:27]uh uh during a or with a specific interval of time. So you can say that very large scale deformation maps can be generated using the interpometry technique. But at the same time if you think for example you are using the surveying techniques.

[00:05:46]So surveying techniques are costly costly in the sense uh uh first of all you are basically measuring the point observations. So point observations means you are using certain equipments or instrumentation going to the field and installing the equipment and taking the reading for certain interval. Let us say continuously you are taking 3 hours reading 4 hours reading at the same point. So if you want to cover you know 100 points in a uh given area of interest so it will take lot of time. So uh and again uh these are only point observations means they they are not continuous observations. So it is taking lot of time means when you are going to the survey and installing the equipment taking observation 3 4 hours then shifting the equipment to the another position another location and then again taking the observation 3 4 hours. So in one day hardly three four points you are able to collect and if you are observing the same same thing you know uh continuously for 10 or 15 days then you are getting let us say uh 40 50 points of observation and uh when the point comes to the monitoring means deformation monitoring it means only one one observation is not sufficient means in these 15 days you have taken let us say 50 points so uh this this is only the observation at one time. One time means only uh single observations are there. So these are not sufficient to monitor the land deformation. Uh uh the moment that monitoring term is coming, it means you have to take such observations after a you know regular interval of time. So let us say in the starting of the January you have taken some observations and then you have to take again uh the observation in the February or March. Then again after certain interval you have to take these field surveys uh and then you can uh comment over the land deformation over that particular area. So it is time taken or you can say sometimes you are not able to reach to the field. It means you are not able to collect the data set. So frequency of observation is very very low compared to the uh satellite data sets and uh the this is costly affair also surveying techniques because so many things are involved. So every time you are spending money and uh the coverage of the observation is also very small means you cannot uh do the survey over the entire country in 10 or 15 days. Okay. So a small area you can cover it means your observation space is only very very small. But uh if you compare this uh small observation space with the observation space of the satellite so there is a huge difference.

[00:08:33]Okay. So uh that way there are different advantages over the satellite based inter technique based uh land deformation measurement and the groundbased observations.

[00:08:48]Okay. and uh most important is uh uh uh these observations are uh uh you are not able to take after a regular interval.

[00:09:00]So the this is the basically drawback major drawback over the groundbased techniques. So nowadays people are using the differential sopometry. But yes, another point which is uh also important like the level of accuracy means if you are doing the surveying in the field and what level of accuracy you are uh achieving for the land deformation whether the same level of accuracy can be achieved by the space-based instruments or let us say satellite based data sets. So straightforward answer is no. But answer may convert into yes if you are having you know certain precautions during the measurement of the land deformation from the space data sets mean. So one point is uh the selection of data sets plus the techniques which you are uh applying for the measurement of the uh deformation. So certain advancements are happening day by day mean advanced algorithms are there. If you are using those algorithms and uh using you know regular interval uh S data sets then the level of accuracy may be comparable with the ground observations. Okay. So the only challenge or only major difference between the groundbased technique and the satellite based technique is the accuracy level. But yes, if if you are doing uh very carefully and applying you know uh advanced concept of the interpremetry then uh there also a highly accurate outputs you can achieve and the accuracy is more or less comparable with the ground truth data sets. If suppose initially it is not coming then you can validate with the uh ground observations. So in that way you can say uh you cannot uh remove the ground based observations because groundbased observations are equally important otherwise you cannot have idea whether the satellite based observations are giving the right information or not.

[00:11:04]So to check them you are basically validating from the ground truth data sets. So ground truth is basically coming from the surveying techniques or the GNSS techniques. Okay.

[00:11:18]So now coming to the some advancement of the differential S interprommetry.

[00:11:23]Initially people have started the uh SAR interpometry using two data sets only.

[00:11:30]Let us say one one data set is taken one data set is taken at time t1 another data set was taken at time t2. So they have compared basically these two data sets. So each data set yesterday I I told you every data set is having you know its own phase amplitude as well as the phase. So both so the B phase of both the signals can be compared.

[00:11:53]Basically the diff difference of both the phases is calculated and that phase difference is converted into path difference and that path difference is nothing but the displacement or you can say the uh deformation.

[00:12:06]So uh the initially people have started work using only two data sets and that technique is called the classical DNSR or classical differential interpometric R. So uh but there were lot of challenge uh or you can say everything was not perfect with the classical DNSR technique means uh I will explain in the subsequent slide because some other component has to be removed. So the removal of those component is not perfect or not uh up to the expectation in the classical DNSR technique.

[00:12:44]So but yes the the the basic principles uh if you are able to apply then you can generate certain outputs related to the land deformation.

[00:12:54]Then subsequently people have started you know the uh the continuous monitoring of the landformation where uh the series of data sets are required. So not only the two data sets series of data set means uh 100 data set or let us say two years of investigation period 3 years of investigation period then you have you know 100 to 100 data sets. So using 100 or 200 data sets you are doing the same deformation analysis. So that is called the time series analysis. So that cannot be easily done using the classical densar. So some advancement was done and those techniques are written in the subsequent uh uh sections. So one is called the interprogram stacking. This is again the temporal summation of the interprogram mean different interprograms were generated at uh time t1, t2, t3 and so on. And using those series of interprograms the deformation pattern can be generated.

[00:13:55]And then people have started you know the the last last one which is called the PSI persistent scatter and anthropometry. This is also time series technique also called the multi-temporal uh insert technique where uh huge number of uh data sets are used and what on which principle it is basically working uh the uh in this technique uh the phase difference between two images or you can say the the uh for generating one interprogram the phase difference is calculated only at the certain pixels means slowly Slowly we are coming back to the traditional techniques similar to the you know surveying techniques or the GNSS techniques because of the certain limitations of the classical DNSR because classical DNSR technique calculate uh the phase difference between the two images at each and every pixel. So if it is calculating the phase difference over each and every pixel it means most of the pixels are noisy in nature means some decorrelation effect is there because of that the phase difference whatever we are calculating that is not correct. If it is not correct it means lot of noise is involved. So noisy pixels cannot give no correct results. So uh in the subsequent advancement or in the advanced techniques it was decided that uh instead of calculating the phase difference over each and every pixel in the image let us calculate the phase difference only at the selected points or selected pixels where the phase difference calculation is correct because other pixels are noisy. So this PSI techniques works only on those pixels where the phase difference calculation is correct. Correct means uh the phase is stable. It is not fluctuating very frequently. So the phase stability uh should be maintained over certain pixels and those pixels are called basically the persistent scatterers and hence the name is persistent scatterer interparentry. So you can say PSI technique is only working with the uh persistent scatterers or you can say a specific type of the targets are there on the surface where where only the phase difference is uh is stable and those pixels are called the persistent scatter. So PSI technique is not calculating the phase difference over each and every pixel. it is only calculating the or only selecting the pixels where the phase is stable throughout the investigation period.

[00:16:37]Okay. So uh this tech so so PSI is using this particular concept and over the selected pixels the phase difference is calculated and that phase difference is converted into a path difference or you can say the displacement. Okay. And this phase difference is calculated between first and second image let us say first interprogram then first and sec third image that is sec another interprogram and then first uh to fourth first to fifth first to sixth and so on. So this way the whatever the phase difference is calculated and accordingly the path difference can be calculated displacement can be calculated. So you can say the series of displacement can be obtained very easily with the help of the PSI and this series of displacement is much more accurate because the calculation is not being done over each and every pixels or you can say the noisy pixels are avoided. So only the coherent pixels have been considered in this particular analysis and hence the accuracy level in PSI technique is very very good.

[00:17:49]Then again uh some limitations were also observed with the PSI technique. Uh the observ the the limitation major limitation with PSI technique was what will happen if suppose we are not getting sufficient PS points uh over your study area. As I mentioned now uh the phase difference is not calculated over each and every pixel. It means it is sele calculated over selected pixels only. And what happens if those selected pixels are very very less in number suppose sometimes in 1 kilometer square area only one point is there or two point is there whether it is sufficient to investigate the land deformation. So straightforward answer is no. This small amount of density measurement point density is very very less and not sufficient to investigate the deformation. So in that way you can say the PSI technique fails over that those areas or those area of interest.

[00:18:50]So what happens if density of measurement points or you can say density of PS point is very very less this technique fails.

[00:19:01]And where it can fail means if most of the pixels are noisy in your study area it means this this technique will not work. And where more chances of noisy pixels are there especially in the natural environment let us say forest patches hilly regions okay where uh every time the situation is changing or you can say whenever you have taken the first image the situation was different and if you are taking another image after some time that time the situation is different and both the signals are not coherent in nature it means the pixel becomes noisy and uh that cannot be considered as a PS and hence this particular technique fails.

[00:19:44]Another important uh aspect of the PSIA is another limitation basically suppose you have taken the investigation of period of 3 years. Let us say this is the zero time and this is the three end of the 3 years. So from this zero to 3 years you have series of uh images and then you have started making the pairs.

[00:20:05]pairs means as I mentioned uh for one investigation for one phase difference two images are required. So those two images basically called the pairs image pair or you can say the interfoggram. So suppose from here to here 100 images are there then how many pairs we can make.

[00:20:25]This is very simple concept just like uh out of from 100 you are taking pairs of two. So and uh the reference image is only and only one in the PSI technique.

[00:20:39]So suppose the PS the reference image is taken in the middle and then or let us say we are taking the reference image in the first one then we are started making the pairs between first and second first and third first and fourth first and fifth and so on. So the last pair between this first and 100th.

[00:20:59]So this is also pair first and 100th image. So the time gap is 300 uh 3 years. You can say time gap between the first image and 100th image is 3 years.

[00:21:12]So you can you think what was the situation at uh the time of the first first uh acquisition and what is the sit ground situation at the time of the 100th acquisition scenario may be totally different. It means these two signals means this one and the last one may not be coherent in nature. If they are not coherent in nature it means the coh coent means the correlation between these two signal is very very weak. that is called the coherence coherence okay so if coherence is very less it means that particular pair is not suitable for the interpiratory or you can say that is cannot be invited for the PSI analysis so what people have tried instead of considering the first image as a reference image then they have started making the pairs so don't consider the first image as a reference image let us consider the middle image somewhere here middle image as a reference image is and then start making the pairs. So the middle one then this side middle one then another this side another this side and middle one and the first one. Same way this side we can go middle one and the nearest uh of the middle then next next and the last one. So this way the whole temporal investigation of the three years can be divided into two parts by considering the uh middle image as a reference image. So the maximum time gap between the reference image and the last image and the reference image to the first image will be 1 and 1/2 year.

[00:22:48]So 1 and 1/2 year is time is also not very small.

[00:22:53]In 1 and 1/2 year also the situation may be different. It means initially we were thinking first image here taken as a reference and then taking the last image. So temporal gap is very large. So people the the images are not coherent and the coherence level is very low.

[00:23:10]Signals are not similar and not suitable for the interperatary situation has totally different. But this situation was slightly modified by considering the reference image in the middle is still some gap is there on both the sides and that gap gap means temporal gap.

[00:23:28]It's not uh one day or two day it is in years. if your investigation period is in years. Okay. So, uh in that uh time also the signals may not be coherent.

[00:23:41]So, point is if you're applying the PSI there are very tricky things to apply the PSI means we have to think whether sufficient points you are able to get or not. So in the first situation whatever I explained between the first and last there is you will not get any PS and now we are taking middle image as a reference image still one and a half year gap is there on both the sides there are likely more chances you will have more number of PS point but if you are applying this technique over the natural environment then again there are very very less chance of getting the PS points. So point is if you are investigating for 3 four years there are very very less chances to get the PS points over the natural environment. So this is the these are basically the limitations of the PSI technique. It means for a longer period of time if you are applying then uh and you are applying over the natural environment PSI technique generally fails. Then question is where it can uh pass means where where it is basically widely used. So over the urban areas you can apply and you will have uh some correlation between the first and the second image first and the last image also because in the urban areas whatever the buildings are there their structures are not changing very frequently. So those structures remains permanent or you can say the persistent and those uh buildings can be considered as a persistent scatterers. So you can say over the urban areas you can apply the PSI and you will have you know sufficient uh PS points and you can analyze and you can investigate the land deformation over the urban uh areas.

[00:25:31]Okay. But PSI is failing in the natural environment. Keep in mind just because of this gap temporal gap between the reference image and the secondary images.

[00:25:44]So another improvement was done. Can we can we reduce this temporal gap between the pair image pairs means uh reference image and the secondary image. So that was also tried and uh that technique was uh converted uh like the SW was the the third one uh small baseline subset analysis. So baseline is using temporal gap that is temporal baseline there are different types of the baselines uh spatial baselines temporal baseline Doppler baseline thermal baseline and so on. So uh uh the crackrux of this particular technique is suppose we are not getting sufficient PS points as in case of psi because their baseline is very very large. So can we reduce the baseline and then we can have more number of uh uh measurement points or we we can have more number of pixels where we can do some investigation because if baseline is small means temporal gap is small and the spatial gap is small then uh there are more chances of similarity between both the signals both the signal means both the phases then uh you will get you know sufficient measurement points. So this particular technique is again a time series technique but based on the concept of the small baseline means the crux is whatever the images you are selecting or whatever the interprograms you are making those interprogram should be governed by the small baseline not the large baseline because large baseline is the limitation major limitation in the PSI. So small baselines uh should be kept and more number of points can be invited for the measurement. So in that sense in terms of baseline you can say S was technique is based on the small small baselines and PSI is based on large as well as the small baseline because PSI is involving you know large baselines also and some smaller one are also there between the reference and the closest secondary uh reference and next closest. So those are small baselines but PSI is also having the large waist lines. So point here you have to understand the the role of small baseline in PSI technique is not that much significant because when the moment you are considering the large baseline and by considering the large baseline you are not getting the point and in a small baseline you are getting the point. So uh so in any of the pair if you are not getting the point that means the point cannot be considered. So point is if in the large baseline you are not getting point so there is no meaning of getting the points in the small baseline in case of psi because th those you cannot consider. Okay. So but in that sense you can say psi is a technique of the large baseline and as is the technique of the small baselines. Okay.

[00:28:48]Both are the temporal uh time series uh techniques or you can say multi-mporal insert techniques. Now let us uh move to the basic principles on which principle they are working and the name is no uh interferometry differentials are interferometry. So main word is the interferometry. So these are techniques working on the principle of the interference.

[00:29:13]So interference what is interference?

[00:29:16]Interference is working on the principle of superposition.

[00:29:20]So what is the superposition?

[00:29:21]Superposition is nothing but the combination of two waves. Let us say cinosidal waves uh because electromagnetic waves are cinosidal waves only. So suppose one uh signal is like this you can say uh this is the first signal and this signal is having phase let us say 51. Another signal is there let us say this signal and this signal is having phase 52. Okay. And both the signals are coherent in nature.

[00:29:51]You cannot say the frequency of first signal is different, frequency of the second signal is different. No, both the signal are of the same frequency and both the signals are traveling with the same speed. The speed is also not changing. That was when you say the signal should be coariented mean they should be of the same frequency or the wavelength and the uh speed should also be same means they should travel in the same medium at a time.

[00:30:22]So what happens? Suppose this is the first signal. This is the second signal and both are meeting in the same phase.

[00:30:28]Means if you calculate the phase difference 51 minus 52 phase difference is zero. Phase difference is zero means the the behavior of this signal and this signal signal is exactly same. Means if this signal is going up here, this is also going up. Then coming down and this is also coming down at the same location. And if you draw a vertical line over here, so at the same time you will get the peaks and the uh uh bottoms. Okay. So this is basically called the uh phase difference between these two signals is zero. So you can say the 51 minus 52.

[00:31:07]Hello sir.

[00:31:15]So if you're combining these two signals let us say first signal second signal both are in the same phase the phase difference is zero and now they are superimposing with each other the intensity of the resultant signal will increase. So here you can see this is the resultant signal the overall amplitude is increasing because this is the strength this is made up of the both the signals. So the strength of the resultant signal is increasing. So the amplitude over here it is a smaller one but here you are observing the larger one. So the overall or the resultant signal have more intensity or the um amplitude. Okay.

[00:31:55]And on the other side just opposite side suppose these two signals are not in the same phase or you can say they are in the opposite phase or you can say the phase difference between this signal and this signal is 180°. 180° means if one is going up another one is going down.

[00:32:11]So same way this is coming down this is going up. So this way you can say both the signals are in the opposite phase.

[00:32:18]So phase difference is pi. And now if you they are superimposing with each other. So they will cancel out the uh the effect of uh each other effect of one another. Okay. So the resultant signal will be zero. Means if the signals are in opposite phase then you will get zero. If they are in the same phase, you will get the maximum intensity. But there are chances that the phase difference is neither zero nor pi. Means phase difference may be in between 0 and pi. Maybe 1°ree, 2°, 3°, 4° or let us say 179° and so on. So depending upon this variation between 0 and pi, the intensity of the signal will vary. Here you can say when the uh phase difference is pi intensity is zero. When the phase difference is zero then the intensity is maximum. So from here it is very clear if the phase difference is uh decreasing from 180° then the intensity will start increasing and when it approaching to zero the intensity is maximum. So here you can see a phase difference is pi let us say. So it is going up this is going down but it is not perfectly lower one lowest one. Okay this is maximum but this is not uh here minimum. So here it is in the middle. So if you are combining these two waves then you will not get zero you will not get maximum. Some intermediate situation you will get it. Okay. So if you are combining these two signals in these ways and B are infinite in number between 0 and pi. So you will get a particular type of the pattern a pattern of the intensity somewhere zero somewhere uh maximum and somewhere in between zero and maximum. Okay. So a gradual pattern of intensity you will receive if you are combining these two quant signals. Okay.

[00:34:18]So this is another representation.

[00:34:20]Suppose uh this blue one is uh first signal and this blue one is second signal. So the phase difference angle phase means angle from this to this.

[00:34:32]This is phase of first one is this one and the second one is also this one. So phase five phase difference is zero. So the resultant is maximum highlighted by the red color. And this situation one signal is this side another signal is just opposite of this side. So first phase is 51 which is 90° and uh another phase is 270°. So phase difference is 180° just opposite to each other. So uh they will cancel out the effect of each other and the intensity is zero and that is highlighted by this red color dot.

[00:35:07]Okay. The same situation is highlighted over here and suppose uh this is the first signal. This is another signal.

[00:35:13]This is pi 1. This is pi 2. So the phase difference is 90°. So the resultant we will get somewhere here. This is non zero but not maximum also. Okay. So this particular principle of superposition is used in the interpro intermetry and same principle is used in the s interrometry to generate the deformation maps. Okay.

[00:35:38]Now here you can see uh you might be aware about the Young's double slit experiment where one source of light is there then some slit is there then two holes are there and when the radiation is crossing the holes then both the signals are superimposing to each other then one pattern you are getting on the screen and that pattern is nothing but the intensity pattern and somewhere you know dark spot spot somewhere bright spot, dark bright spot, regular spots you will uh receive and that those spots basically a pattern basically called the fringes. So that is the fringe experiment in double select experiment and the same experiment you can understand from the satellite point of view. See one satellite is here and it is sending the signals and this way it is capturing the uh data. Okay. And if you are combining these two images, let us say one image from here, another image was taken from here. Now these two signals if you are combining then this pattern you are getting. See here bright then dark bright dark bright dark. This pattern is basically called the uh fringes. Okay.

[00:36:56]And uh uh this uh fringe basically uh is nothing but the pattern of the phase difference. Phase difference of these two signals means somewhere if they are meeting in the same phase means phase difference is zero then you will get the bright fringe here and if they are in the opposite phase then dark fringe and uh in between then the gradual change you will observe. So if you put here some screen on the screen you will get you know bright dark bright dark bright dark pattern. So that pattern is called the fringes. And suppose if this same things if I applying from the satellite that is satellite is somewhere in the space and if the same patterns we are uh generating so these fringes uh you can observe and where this fringe will form these fringes will be on this earth surface. So you can say earth surface will act as a screen and on the screen you are observing the fringes. It means on the earth surface you will observe such fringes and what the fringes are telling us uh these fringes are telling suppose here the phase difference is zero then from here to here the phase difference is of the 180° then from here to here again 180° so you can say from bright to bright the phase difference is of the 2 pi and the dark to dark again the phase difference is of the 2 pi okay so you can observe suppose this this is a earth surface So you can say here is the bright fringe here it is the dark fringe. So from here to here phase difference is pi. So now you can calculate the path difference.

[00:38:34]Okay from this phase difference. So path difference from here to here. Here it is dark here it is bright. So from here to here the displacement can be calculated.

[00:38:43]So you can say suppose one image was taken when the target was here and then target was shifted slowly like this and then another image was taken. So from here to here whatever the sift is there or you can say displacement is there. So this displacement can be calculated from this fringe phase difference. Okay. So this way this particular technique we are using for generating the deformation map. Deformation mapping nothing but the displacement map. Okay.

[00:39:16]And uh as I mentioned if you you are using the time series techniques it means a series of displacement you can have means displacement from here to here means about one image is here one image is here one image is here. One image is here. It means you will have the displacement from here to here. Then from here to here then from here to here from here to here and so on. It means a series of displacement you can observe from com by combining these two images at a time. So these two images then these two images then these two images then these two images and so on. So series of displacement you can calculate and that series of displacement is the rate of change of deformation.

[00:39:59]Okay. And from the series of displacement you can calculate the velocity. And if you have the series of velocity then you can calculate the acceleration also. So what are these uh quantities displacement velocity and the acceleration these are the chynatic variables.

[00:40:17]And now you can go back to the Newton's law of motion in which only the velocity acceleration and the displacements are involved.

[00:40:27]It means if you're using uh applying this interpometry generating the time series displacement then you can generate time series velocity and then you can generate the acceleration or you can apply the Newton's law of motion or chyntics you can generate means chic variables. So these are the chynatics. Okay. So you can understand the chynatics of a particular region on the earth surface means how the land is moving up and down or in the horizontal direction and the inclined direction that kind of movement you can uh find out with the help of the intermetry and the laws of motion.

[00:41:08]So uh the another representation is shown here more or less same thing. And now if you here this is the p pictorial uh view. Uh suppose one image is taken another image is taken. Now both have combined by means of superposition.

[00:41:24]Then see on the background you are able to find out the know topography on the earth surface. So topography itself is you know behaving like a uh displacement in a vertical direction not exactly uh displacement but it is the path difference between the lower pixel and the upper pixel that is a path difference. Okay and with the help of this path difference the elevation is calculated. So you can say by means of the principle of superposition in SAR signals we can generate the DEM also. So this is called the D insar based DM. So you can say insert techniques or interpromtric technique can be applied or can be used to generate the topography or the DEM or to analyze the land deformation and I will show you some other things also from these two uh these interpometric concept one can do the atmospheric modeling also means how much deviations or delay of the SAR signals is there through the atmosphere.

[00:42:36]So the density of the different layers of the atmosphere can also be analyzed with the help of the interparometric S.

[00:42:43]Okay.

[00:42:46]So these resolution I will come later and uh now uh this is a mathematical formulation very basic concept actually.

[00:42:56]So you might be aware about the uh electromagnetic signals which are there which having the electric field vector and the magnetic field vector and the direction of propagation all of them are perpendicular to each other. So when we are using these electromatic signals in the remote sensing then the magnetic field component is very very weak. So all the analysis we are concentrating over the electric field vector only.

[00:43:22]Okay. So that electric field vector of the signal can be expressed as like this E vector equal to E not or E 0 E ^ I. So E not is the amplitude and E to the power I is S is the phase of this signal. So you can say the electric field vector is complex in nature having the amplitude E not and the phase five and this uh S or the phase can be expressed as also K dot R minus omega T plus P. So k dot r is you know phi this is phase. So phase can be replaced by phase only. It means k dot r is phase omega t is also phase and phi is also phase.

[00:44:02]So this k dot k is the propagation constant. So k dot r is called the propagation phase or most popularly known as the geometrical phase. Omega t is t is a time temporal phase and phi is called the scattering phase. Okay. So you can say the phase of the signal is made up of the three major components.

[00:44:22]One is geometrical phase, temporal phase and the scattering phase. So this particular concept we can use in the remote sensing purpose. And uh for that uh let us uh discuss this particular graph uh figure. Suppose this is the earth surface where some target is there at location P or you can say this target P is there. That time one image was taken from satellite position A. So uh from satellite some signal was transmitted reached to the target after interaction it came back toward the satellite. Okay. So uh the signal has traveled the total distance from A then again from PA. So A is equal to PA. So you can say to total travel distance of the signal is 2 * a or 2 * pa whatever you can write. Okay.

[00:45:18]Then some deformation has happened over this particular target and the target has moved from its original position to another position let us say p prime. So the distance from p to p prime is let us say small d. This is not only you cannot say this is only the one dimensional distance. It may be ludian distance or pythagorian distance. Okay. Or you can say this distance may be or uh we should not use basically the term distance.

[00:45:46]This is displacement. Displacement is a vector quantity. So the that vector may be one dimensional, two dimensional or three dimensional also. So you can say the distance may be three dimensional also. Okay. So after deformation there the target has reached to another position. when it reached to another position that time we have taken another image from another satellite position let us say B. So another image was acquired so signal was propagated from here and reached to the target and coming back and observed by the satellite and converted in the form of one image. Okay, that image is having amplitude as well as the phase and the same thing uh is there with the uh first image. Okay. Now these two situations we can find out you know this distance displacement which is a small t. So by uh by this this situation you can understand by different ways also. Uh for example in this particular situation you can generate number of triangles like BP B A B this is one triangle or let us say uh uh A P prime P this is another triangle okay or P B A another triangle.

[00:47:00]So different triangles we can form but keep in mind when the satellite acquired the data set so this particular angle is known from this this is called the look angle. Yesterday we have already discussed. So this look angle is known.

[00:47:13]Same way from this triang uh c position some look angle is known. So now in this situation we can form number of triangles.

[00:47:23]So uh in triangle you know uh if you know something about the triangles let us say one angle and two sides you know then you can calculate the remaining sides and the angles of the triangle. It means if something is known to the triangle then other unknown things you can calculate. So what is known? The known is the gap from A to B. This is called the baseline. This is a special baseline. So a special baseline is known. These angles are known.

[00:47:52]Okay. So this angle is known. This angle is known. This baseline is known. And this distance from A is known. BP BP prime is known. So you see few sides are known means this side of the triangle is known this side of the triangle another triangle is known and this side of the another triangle is known few side may be common in few triangles. So some sides some triangle angles are known and then what we can do this particular side of the triangle is not known. So that this side can be calculated what is new in this. Okay.

[00:48:31]So uh this this way you can understand and another way of understanding is we can uh concentrate on this phase component. So let us say when we have acquired these two images that time some scattering was negligible or let us say first we are considering these observations are taken at time t0.

[00:48:52]So omega t is zero only k dot r and phi is there. So now we can write the phase of both the signals. So for signal a the phase is 5 a is equal to the geometric phase k dot r of a plus scattering phase of a. Same way we can write the phase of signal b which is geometrical phase of b k dot r plus scattering phase of b which is five omega t we are considering as a zero.

[00:49:19]Now if you're assuming the scattering component in both the signal is same we can assume it may not be equal but if suppose atmosphere conditions are same then the scattering is in the equal amount if it is in equal amount then if you're subtracting let us say 5 b minus pi a so the scattering phase of b will be canceled out by the scattering phase of a so now if suppose we are doing interpremetry suppose uh the first signal into complex conjugate of the second signal. So this will be like this amplitudes are getting multiplied but the phase are getting subtracted 5 B minus 5 A. Okay. So this 5B minus 5 A is delta FI and this delta FI is nothing but the interparametric phase and 5 B minus 5 A we can use from these expressions. So if you are doing like this delta ph in subscript we are writing in that is stands for the interprommetry. So delta 5 for interprometry or you can say the interprometric phase equal to 5b this one minus 5 a. So 5 b minus 5 a and then we are using these two expressions. So geometric scattering phase is canceled out only the geometric phase of b minus geometric phase of ph is there. Then geometric phase of B can be written as 4 pi upon lambda because phase difference equal to 4 pi upon lambda into path difference. So this is four uh 2 pi upon lambda into path difference. But here the travel distance is 2 * bp prime. So that that two factor is coming. So it becomes 4 pi upon lambda into path difference of signal b is bp prime. So bp prime is here. Then minus again this is uh 4 pi upon lambda into a. So 4 pi upon lambda is common. So BP prime minus AP is there. This can be modified like this. BP is subtracted and BP is added.

[00:51:13]So this this uh term is called the displacement phase and this term is called the topographic phase. Why?

[00:51:22]Because if you see BP minus AP see here BP minus AP it means you are observing target P from two different satellite positions. So this situation is sim similar to this one same target is observed by two different satellite positions. So this is the principle of the DM generation that's why we are saying it this one this red component is called the topographic phase. Okay. And what is this BP prime minus BP? BP prime minus BP. It means this is related to somehow with D and D is displacement.

[00:52:00]Displacement means deformation. So this particular uh term is called the displacement phase. So you can say interpometric phase is equal to the displacement phase plus topographic phase. So the interometric phase you are just calculating first phase minus second phase means by different difference of both the signals.

[00:52:22]So that is a different interpometric phase that you have already calculated.

[00:52:26]This displacement phase you want to calculate and this DM phase you can simulate by a given DM. So suppose one non DM is there. So from that DM you can calculate this phase. So now in this equation three terms are there. This one this one and this one. This you can get from the DM. This you can get from the phases of individual signals. So this can be calculated from this particular expression.

[00:52:53]So you can say the interparometric phase minus this topographic phase. This way if you're writing then it is equal to uh displacement phase. So this is the difference of two quantities. So the another term is used here delta fi dint that is called the differential interprot. So you can say differential interpometry a technique where we are subtracting the topographic phase from interparometric phase. If you're not subtracting then it is only called the interpometry.

[00:53:26]But if you are subtracting the topographic phase then it is called the differential interpar. Okay. So this is equivalent to the displacement phase and then displacement phase you can convert into 4 pi upon lambda into displacement.

[00:53:39]So this way from this displacement phase the displacement PP prime can be calculated and lambda is known because this is the wavelength of the signal.

[00:53:48]Okay. So from this particular thing you can understand how the interpometry is working.

[00:53:55]So now from this expression is very clear interpometric phase equal to displacement phase plus topographic phase in this particular uh way but we have assumed so many things in between.

[00:54:07]So here it seems very simple but in uh in reality it is not simple means interpomearometric phase is not only equal to the sum of displacement phase and the topographic phase it is more than that and what is more than that. So the exact expression is written somewhere here. So here you can see that interperometric phase is equal to the displacement phase this one plus topographic phase this one plus solid tide phase plus flat earth phase plus atmospheric phase plus orbital phase plus decorrelation noise plus phase unwrapping term. So now you see this is the actual equation and this one is the simplified one or you can say this particular principle we are applying in the classical DNS technique and this principle we are applying in the time series investigations where we can get you know accurate information. So you can say the output derived from this particular equation is comparable with the surveying techniques output.

[00:55:13]Okay. So but keep in mind if you are doing the um uh the deformation analysis it means for your interest this displacement is there it means the other contributions you should remove very very precisely and all the components cannot be removed in a single step mean step by step in in one step you have you can remove this one in another step you can remove this one in another step this one and so on. It means a series of steps are required for the interometry.

[00:55:45]So this is called the interpometric processing chain. So interrogative processing chain requires you know multiple steps and more than that the removal you can removal of acet solid tide phase is not just like you know one step job of one step it is very very complex because the comp the contribution of the solid tide you can remove from this expression if you have the solid tide data sets and the data set is provided somewhere someone else so you have to collect the data from those agencies or individuals or the instruments and then investigate okay what is the what is the contribution of the solid tides for this particular time period and that contribution you can remove from here so the removal of single step is not a easy task you understand so initially I told you uh number of steps are required but it is not only the matter of steps behind every step lot lot of things are required. So you can say the the DNS is not that much simple uh as you have seen in this basic equation of the interpromantry which is classical dens.

[00:57:01]Okay.

[00:57:03]So this is the extended version of the same expression and these things actually time is not there otherwise these are basic terms you can uh uh few things I already explained. Okay. So now if you have any questions techniques are uh there like these slides I will share and then you can understand also. Okay.

[00:57:28]So thank you. Now if you have any