 to today's class. So till now as part of module 2, we have been trying to answer the question, imaging radars, how do I interpret and underlined are the topics which we have been covering over the course of last few lectures. So as part of this lecture, we shall try to cover about polarimetry, okay. So we are in the 12th lecture of the second module on to polarimetry. Just a quick recap of what we discussed about polarization. Polarization by that I mean the path of tip of electric field vector of an electromagnetic wave is what is known as polarization. And given here are the radar signals which can be polarized between H and V, between horizontal and vertical with VV denoting vertically transmit and vertical receive. When I say vertical, it is the direction of oscillation of electric field vector of an electromagnetic radiation which has both electric as well as magnetic field. So remember the concepts what we discussed in module 1, okay. So polarimetry is one of the most challenging aspects of microwave remote sensing. As in an ability to visualize three dimensions are required and then one also needs to conceptualize them changing in time. Generally, we say that it is a two dimensional property, 2D property. It is in a plane and the only requirement is that it is composed of two polarization states that are combined together to form the actual polarization and that these states must be orthogonal, okay. So now we know the x axis, we know the y axis because the x axis for convenience we denote horizontal axis is x axis and which is parallel to the surface of the earth that you know that we denote for the sake of convenience. And we denote that y axis is a vertical axis that is perpendicular to the surface of the earth. The further thing to consider is the definition of z axis which runs parallel to the direction of travel of wave. You know what should be the direction of z axis in the direction of travel or away from the direction of travel. So let me take this background to introduce to you something known as forward scattering alignment and backscatter alignment, okay. Optical based polarimetry when it uses the direction of travel of wave in the positive z direction we call it as forward scattering alignment. Let me reiterate when the direction of travel of wave is the positive z direction we call it as forward scattering alignment abbreviated as FSA. When making a microwave instrument we know that an antenna is used without worrying about where the wave is coming from or where it is going to that is either it is being received or being transmitted and this is known as backscatter alignment BSA. The x and y axis remain as before but the direction of z axis is chosen to be parallel to the direction of propagation of wave. Remember that the use of polarimetric information it is very important in both active as well as passive microwave remote sensing and through this short section let us learn about the properties of polarized waves and how to describe them mathematically. Now try to remember the example that we discussed in earlier parts of the lecture wherein two waves being of the same amplitude say A which are in phase are used. Now imagine what will happen when the electric field vector of both the waves are combined, okay. Remember I am talking about two waves having the same amplitude which are in phase and I am asking you to think what will happen when the electric field vector of both the waves are combined. Assume both these waves have an amplitude of say A which means both the waves shall reach the maximum amplitude at same time and both these waves shall cross the origin and reach their minimum at the same time. Visualize it. Visualize it using the small short videos that I was showing as part of earlier lectures and here I am specifically referring to just the electric field vector whenever I mentioned the horizontal and vertical polarization. Horizontal which means electric field vector is horizontal and vertical means electric field vector is vertically polarized. Let me show you this graphically, you know. Assume Ex and Ey are the components of the electric field vector and I have represented it this way. So the amplitude of the new linearly polarized wave is shown here as root of Ex square plus Ey square. This means that linearly polarized waves can be generated at any angle by changing the relative amplitude of both the waves, isn't it? Further we can also define the orientation angle using Tan inverse, isn't it? At this point, let me also make it a point to mention about elliptical and circular polarization. Here you see the same diagram but the pattern of polarization is shown here as elliptical. A relative phase difference between both the electric field components shall result in a very narrow ellipse as you see on the screen and as the magnitude of phase difference increases eventually the wave vector shall trace out a circle that is when we call it a circular polarization. So shown here are the result of changing phase difference between two linearly polarized waves when the phase difference between both waves are 180 degree, you can see what happens. So here red and green denote the orientation of electric field vector red in the vertical direction, green in the horizontal direction and the cyan color is the resultant wave that you get as a result of combining both the waves which are polarized in the horizontal and vertical direction. So shown here is whenever there is a phase difference of minus 180 degree what happens. Similarly if the phase difference between both waves are minus 90 degree have a look at how the output looks like. So I hope now you are getting the idea of an elliptical polarization and a circular polarization. Moving forward let me show you the output for phase difference of 0 and the output for phase difference of 90 degree. See some radar systems they transmit only one single polarization. For example we have radar SAT that is the Canadian remote sensing earth observation satellite program. The radar SAT it transmits and receives only horizontally polarized wave and when we talk about ASAR or advanced synthetic aperture radar which is on NV SAT which is an earth observation mission of European Space Agency. It can receive both horizontal and vertical polarization that is ASAR on NV SAT can receive both horizontal as well as vertical polarization and there is also something known as a quad pole radar system. The fully polarimetric or quad pole radar systems they transmit both horizontal and vertical and they receive both horizontal and vertical respectively, quad pole radar systems. The pulsar or LOs has quad pole modes. You will be learning how to download the LOs pulsar data and how to process them as part of the tutorials. Moving on, so in radar polarimetry the scattering matrix it offers an efficient means to characterize the data. The scattering matrix is shown here as S. Here each element that is S, V, V, S, H, V, S, H, H each element denotes complex numbers describing the phase and amplitude of the transmit and received wave. So, let me reiterate when I say polarimeter it is nothing but an instrument that can measure the polarization of an electromagnetic wave polarization polarimeter and radar polarimeters are instruments which measure the polarization of the returned echo as well as transmits the equivalent of full range of polarizations and a radar polarimeter will transmit in horizontal as well as vertical polarizations and if we know the phase and amplitude the information from two polarizations are actually enough for us to synthesize the response from all the possible combinations of transmit as well as receive polarizations. There are some systems which provide only partially polarimetric data and polarimetric data they are rich in information as they decipher the orientation of the scattering targets. Remember polarimetric data can be very well utilized to distinguish between different targets as well. See this is a very exciting research area but more mathematical details about polarimetric synthesis or polarimetric decomposition it is beyond the purview of this course. So, moving on I shall leave you with one more new technology that is polarimetric ratio. Polarimetric ratio can be considered both an active as well as passive polarimetry. Simply speaking if we take the ratio of horizontal and vertical polarizations we are focusing on the relative properties of different polarizations, isn't it? For example, when we take the ratio of vertical to horizontal signal it relates to the expression for reflectivity. You have already seen how a synthetic aperture radar image looks like. Black and white it is not as visually pleasing as a satellite image that is captured in the visible region of the electromagnetic spectrum. So, say you need to create an RGB a colorful image using synthetic aperture radar images bands. You can very well create an RGB composite using the ratio of HH and HV polarization which can be used as the third band such that HH is assigned to red channel, HV is assigned to green channel and HH by HV is assigned to blue channel as what you see in the screen you know RGB composites. We will cover details about these as part of our tutorials as well. As I mentioned earlier, this topic of radar polarimetry is vast and it is a very exciting area of research and this short section was to introduce polarimetry as a challenging aspect to microwave remote sensing. The covering of complete mathematical details of radar polarimetry is well beyond the purview of the scores and the aim of this section was just to introduce to you the concept of polarimetry. So, thank you for listening and I will see you in the next class.