 The next technique we would like to consider for water suppression is the so-called jump return, jump return sequence. The way it works is you have a 90 degree pulse, you put the carrier on water, okay. So the carrier is on water, wait for a time tau, then you apply a 19 pulse again but this time you apply 90 minus x. Earlier you applied a 90x, then you apply now a 90 minus x and then you collect a FID like this, okay. So how does this work? Okay, let us look at, let us draw the picture like this. So initially all the magnetization is here, okay. This is at point number 1, this is at 1 and here at 2, so apply a 90x, I will get, let us say a magnetization onto the y axis, it comes here, this is at 0.2. Now different components would process here now, okay, they will go with the different frequencies. Okay, water will go with its own frequency and sample signals will also go with their own frequencies. Now since I am sitting on the water, water does not move because there is zero frequency. Since I am sitting on water, the water does not move. Let me say my sample signal which is present here, green one, during the period tau, during the period tau, what happens? The water remains there only because it does not, I am sitting on the water therefore it is a zero frequency, zero frequency and I will wait for the time tau such that my sample signal has come exactly here onto this, sample signal has come exactly onto this and the water has remained there only. Water has not moved because it is at zero frequency, water is at zero frequency, carrier is on water means it has zero frequency, so that does not process whereas your other signals will process, okay. So this one signal may have come here, it is also possible that there is one more signal, okay, so let me draw the spectrum here, suppose I have a spectrum which is like this and this is my water and this is another signal here. So this one is positive and this is negative, with respect to the water this is zero, okay. And the blue one which I have drawn here that has come exactly to this point, okay. Now let me draw another color, take another one here, green one and where would that go? That would have moved to some other point let us say here, let us say this is my green and this is the blue, okay, I am using the same color that does not matter. So the blue one has come here and the green one has gone to this place. Now then what they do is I apply a next 90 minus x, 90 minus x, so what will be the result of this? The result of this will be water will come back here, water will go back because I am applying a 90 minus x, I am rotating it back to the z axis and the blue and the green components will some components will survive. So something will survive here, of course certain other component would have gone there and similarly some component of green also will survive, some component of green also will survive, other components which are orthogonality they would also have gone back to the z axis. Now if I do a Fourier transformation of this, what will I do, what will I get? I will get let us say the blue one which is here, I will get a positive signal like this and that the water I will get is 0 and then I will get a green one, I will get a negative the opposite side because it has gone to the other side, at time t is equal to 0 it is on the other side, if this is on the plus x axis that is on the minus x axis therefore the initial point it has a minus, it has a opposite phase therefore it is gone here. Because this is a very ideal picture, the lines of course will have various kinds of distorted line shapes will be there but this is the ideal picture. The water has gone back to z axis and therefore there will be no signal of the water, ideal. Typically this does not happen ideally, there will be some amount thing there will be various kinds of waste distortions will also happen. The ones which are close to the water what will be the problem here, some which are under the water if there is a signal which is under the water you will also lose that, that also will disappear because that also will go back to the z axis you will not see. Therefore what one does is you adjust your tau such that you get maximum signal for the region of your interest. Because this distance is something like about delta, let us say this is delta. So you adjust your tau such that this has moved by, this frequency has moved by 90 degrees. Let me call this as your signal which is required, w desired, let me call this as omega i and 2 pi omega i, how much is the rotation of this of the blue signal? The rotation of the blue signal here is 2 pi times omega i times tau. That is the rotation in angle, omega i times tau is in the radiance. So in terms of, if I want to multiply that by 2 pi then I get it in degrees. Now if I adjust this to pi by 2, pi by 2 that means I have made it rotate by 90 degree. Therefore what I have to do? Therefore I have to adjust tau to, this will go away, 1 by 4 w i. So by doing so I maximize my signal for the desired signal in my spectrum. I may lose other ones, it does not matter. So typically this is used in applications where you have very widely different frequencies. So you have the water here, let us say and then you have the various signals here, these are the amide protons, amide protons let us say. This is typically in proteins, this is what you will have. The water is at 4.8 ppm, these are from 7.5 to 10 ppm. Or if you are looking at DNA, so in DNA the water signal is here and you have the immunoprodons which are coming at 11 to 15 ppm. And your aliphatic ones will be here, aliphatic signals will be here. And same is true here, aliphatic signals. So if you adjust your, you keep your RF on the water and adjust your time to suit to this distance from here to here, then you will get, for these ones you will get positive signals on this side and then you will have reduction here and you will get negative signals here. For the aliphatic ones, because these are on the opposite sides of the water. So this sort of a water separation is also quite efficient and has been used for, quite extension, especially for DNA, this has been used very, very effectively. So this is so much for the special features of FTNMR. Now we go over to another concept which is called as spin echo. So what is a spin echo? I mean all of you know echo, what do you mean you stand in front of a hill and shout, you hear back your voice after some time. The sound goes, gets reflected from the hill and comes back to you, that is the echo, right. So when you shout, signal has decayed and then it is gone and when it gets reflected then it comes back to you, then it picks up, so that is the echo. In the same manner here also you can do a magnetization which is decaying and then you recover it so that you get an echo. So that is what is the principle here. This was discovered by Irwin Hahn in 1950 and this is one of the most important developments the discovery, very simple but very elegant and very important discovery which becomes a component of all multiples experiments, most multiples experiments in two dimension, three dimension, even in other one dimensional experiments as well. So what is the idea here? The idea is the following. So the pulse sequence goes like this. So you have a 90 degree pulse, 90X, let us say you have a time period tau here, you have a time period tau, then you apply 180 degree pulse, let us say I apply it along the Y axis, then you have the same time period tau, then after that what I get here. This is the echo, at this point I get the echo. I may collect the data afterwards but this is the echo. What happens during this period? Let us look at it from the single spin situation or we can do two spins also and let us do what happens. This is the time point 1, this is time point 2, time point 3 and time point 4 and this is time point 5. So consider one spin and let us assume that I have initial magnetization is here, this is at 1, time point 1, then I apply the 90 degree pulse, the magnetization has come here, this is time point 2 and then during the next period tau it has evolved with its characteristic frequency and now I will write only, let me write the full thing, it has rotated to some point here, this is my time point 3, now this was my X, Y and Z, X, Y and Z. Now what I am applying? I am applying a 180 degree Y pulse, so this is a 180 Y. So what happens to this magnetization, where does it go? It goes here, 180 degree rotation, so it goes out of the plane and comes back there. To understand it much more easily, you take the components along the X and the Y components and you see both the components will rotate. So the X component will go to the minus X axis, Y component will stay there only, therefore the net result will be along this axis here. The movement is happening here, here during the period tau with the characteristic frequency, its own frequency and how much it has moved, let us say it has moved by an angle theta, this angle theta. During that period it has moved by the angle theta because it has a characteristic frequency and this is equal to omega i times tau, it has moved by that much. Now this spin which has gone here now, this will continue to move in the same direction once again. So where it will come? After the next time period tau, this is my time point 4, where it will come? After that, then it will come back on to this axis. I drew only the transverse plane here. So if we have to drop the transverse plane here, this is in the transverse plane, so this will move down here to this point, it will move down to this point, the Z axis is up there. So whatever it has moved during the period tau, so this will again move, this angle is also theta, therefore it will move at the same angle theta in the next period at tau, so it will come back here. So therefore you see this is the refocusing, this is the echo. What was happening here during this period, during the period tau? You see the y component was progressively decreasing, right? If we were to look at the FID during this period tau, during the movement, during the period tau, what was happening? The magnetization was decaying, was moving, there is an FID. So this was decaying here, magnetization was decaying here and it was moving out of the y axis. Now when it comes back here, then it during the next period tau, it starts coming back onto the y axis, which means it is, it is increasing. So if we want to draw this here, magnetization is FID is decreasing during the period tau and this is my 180 degree and then it starts increasing again. So this is my echo. This is like a mountain, these 180 degrees is a mountain. This is the time it takes for the signal to go here when you shout and this is the time it takes. It comes back with the same speed, right? This is the sound with the same speed. It will come back here with the same speed therefore it will take the same time. So this is the echo. So now you see this is regardless of what the frequency is. No matter what the frequency of precision is, it will come back. So here I have drawn with one frequency. Suppose I took another frequency, this will also come back. So therefore this is frequency independent. The spin echo is said to refocus chemical shifts. So therefore this will refocus chemical shifts. So we are considering here a single spin and there it is completely refocusing. If it were two spins also it will refocus but only thing is there should be no coupling between them. These two spins are not coupled. If it is they are coupled then of course they do not refocus. And that is a little bit more tricky and we will try and go through it appropriately. Spin echo of coupled spins. Let us say I take two spins A and X, right? So the one dimensional spectrum of this will be the A will have two lines and X also will have two lines. The coupling constant between them will be the same. So this is my A spin and this is my X spin let us say. And this is the center of the A spin and let us say this frequency is nu A and this frequency is nu X and the separation is the coupling constant, okay? Let us draw the picture for the same. Now you remember here one more thing. How do these lines appear? How do these lines appear? If I want to draw the A lines little bit more elaborately here and also the X lines somewhat more separately here, properly separated and let if they call this transition as A1, call this as A2, okay? Call this as X1 and this as X2, okay? Now how does this transition A1 appear? You recall back what we did earlier. When the transition alpha spin is flipping, the A spin is flipping from alpha to beta. What is the polarization of the X spin? X spin this is in the beta state and it is in the alpha state. For the A2 transition, this for the A1 transition, X spin is in the beta state. For the A2 transition, X spin is in the alpha state, okay? So if you can recall that in a G-level diagram there, let us say this is alpha A, alpha X, alpha beta, alpha A, beta X, beta A, alpha X, beta A, beta X, okay? So this I have the transition here, one transition here, other transition here. These are my A1 and A2. Which one is my A1? This is my A1 transition, this is my A2 transition. In the A1 transition, alpha A is flipping to beta A and the X spin is in the beta polarization. For the A2 transition, alpha is flipping to beta and the X spin is in the alpha polarization. That is what I have written here. This is important to notice here, okay? Now let us look at what happens when you apply the spin echo. Let us look at the spin echo again here. The spin echo sequence, okay? This is tau, this is tau and now we sit on the, in the rotating frame of the A-spin. That means we sit in the center. That means I will want to focus only on the A-spin for the moment. Let us look at the moment of the A-spin. So at this point, at this point I will draw only the transverse plane. So this is my point, both the transitions are, both the transitions are here, right? At this point, this is my point 2. This is point 2. Now they will, during the next period tau, what will happen? These two transitions will go in opposite directions because I am sitting on the middle of the 2. If I am sitting on the middle of A, that means with respect to the new A, with respect to the center, A1 will go faster and A2 will go slower. So let me draw that here. Let us say A1 has gone here and A2 has gone here. This is going like this. This is going like this. When I apply the 180 degree Y, now these are my X and the Y axis or this is my X and this is my Y. Now if I apply Y pulse, let me also write which is A1, A2 because these are all very important things. So this is my, let us say A1 and this is my A2. During the next tau, now I apply 180 degree pulse, let us say on to A1 because this 180 pulse is on both, right? It is 180 pulse is on both. So what will happen during then, suppose 180 pulse on the A spin considering on the A spin. So this will come, so this is a rotation like this. The A2, A1 will come down, A2 will go here, A1 will come here. Now how was the A1 moving? A1 was moving like this, A2 was moving like this, right? So during the next period tau, they should come back and refocus. They should move with the same speed and they should come back and refocus. But now notice we are applying a pulse on the X spin as well. And this is the crucial point. This is the crucial point and that is what we will show here. So in the next, consider we break up this 180 pulse into 180A and 180X, 180X on the X spin. What does it do? 180X means X spin flips from beta to alpha. X spins flip from beta to alpha and alpha to beta. In other words, A1 will go to A2, A2 will go to A1. So I have these two transitions same here but now they will change their labels. This will become A1, this will become A2 and this will continue to go this way, this will continue to go this way, okay? So now you see there is a big difference. So during the next period tau, what will happen? They will continue to move in the same directions. They will continue to move in the same directions. This fellow would have gone there, this fellow would have gone there, okay? So therefore they have not refocused. Therefore at the end of the echo, this is the echo period, the two are not refocused, okay? So therefore the spin echo does not refocus coupling evolution, okay? So what are the conclusion we have here? One thing is, let me write that down explicitly in the separate one, the spin echo, two important points, one chemical shifts the refocused, refocused. This means field enormogenities are refocused, field enormogenities because field enormogenities contribute to variations in the frequencies of recession, right? There is equivalent to chemical shift, different chemical shifts, field enormogenities are refocused. Two, coupling evolution is not refocused. This is the most important part and you will see this is what is used in various other techniques in multiple experiments, okay? The third point is relaxation continues to happen. Which relaxation during the spin echo? Relaxation continues to happen and which relaxation is this? This is the transverse relaxation because the magnetization is in the transverse plane or T2 relaxation. So therefore this provides an ideal method for the measurement of transverse relaxation times because it is not clouded by the field enormogenity effects. Field enormogenity when it is there, they will cause defacing because of the different frequencies and therefore the signal will decay faster because the lines will become broader and the field enormogenities will sort of give a wrong impression about the T2 relaxation. Because T2 relaxation is related to line width, right? So this is related to line width. And if field enormogenities are there, they are contributing to your decay of the signal because of precessional frequencies then you measure a wrong line width and that cannot be taken as T2. Here the field enormogenity effects are cancelled out so you can use this method to obtain measure the transverse relaxation times very accurately. So this is the important application, immediate application of this and this happens at the rate minus 2 tau by T2. So this is the relaxation rate. Now there is one more point which I will take up and then we will stop. We can use this spin echo sequence for water suppression and that is water gate. Water gate for water suppression. The pulse sequence is like this. So you apply a 90 degree pulse, you keep on water, the carrier is on water and then you apply a selective pulse 90 let us say X 90 minus X then immediately you apply hard pulse 180X which is applied to all the spins and then you apply another soft pulse on water. This is again a 90 minus X again on water and this period tau, this period tau. But there is one more thing that happens here and that is called as the field gradients. We use here what are called as field gradients. So you apply a field gradient here, I will explain what that means, you apply field gradient here and you apply a field gradient here and you collect the signal from this point onwards. What does the field gradient do? These are field gradients. It is a linear field gradient. It can be explained like this. Suppose you have a sample, your sample is here, your magnetic field is in this direction. There are additional coils which will change the field along the Z axis. This is my Z axis. It will change the field along the Z axis, so in a particular manner. So field gradient will increase, this is the gradient field. That means the field at different points will be H0 plus some coefficient times Z. So this is the gradient and this is the Z, coordinate along the Z axis. Therefore this is the linear thing and G is the coefficient. Therefore at different points the field will be different. What is the meaning? All those things which are seeing this, they will deface. All the frequencies will become different. So the result will be that if I draw the transverse plane here. So all the frequencies will deface as a result of this gradient because of the gradient. Now if I apply 180 degree pulse to this and then apply the same gradient once more because these are all going in this way and this way. If I apply 180 degree pulse then they all would have come here. So this will go like this, this will go like this and then during the next period term they will all come back again, they will come back here. Therefore they are refocused. So when I apply 180 degree pulse but now this is so far as the sample signals are concerned. But I have done another trick here. What I have done is I have applied 180 x and 90 minus x and 90 minus x. The water sees how much flip angle. The water sees zero flip angle. 90 minus x and 90 minus x is 180 minus x, 180 minus x, 180 x is zero. Therefore the water does not see any angle at all, does not see any flip. The water has zero rotation. So which means after it has come down into the transverse plane, this is the water signals. They continue to go and after that at the end also they continue to go even more spread all over. The D phase more and more because they do not see the gradient effect. They do not see the 180 pulse is not seen. They see the gradient effect. They do not see the 180 pulse. They see zero, there is no inversion. They continue to D phase, water signal continues to D phase, continues to D phase. As a result it will all completely cancel out. So water will be zero and at the end of this tau you will only have signals coming from the sample because they all have been refocused. The refocusing is happening because of the 180 pulse on the sample signal and the water is seeing a zero pulse, zero rotation. However it will continue to D phase, both the gradients will contribute to the D phasing only and therefore the water signal will completely D phase and will be eliminated. And this is how you achieve water suppression in this particular scheme. So I think we can stop here. This is the time is up.