 So, we have been discussing about features which are exclusive to Fourier transform NMR. We talked about various important parts in that one. So, we will continue with that discussion with regard to the special features with our exclusive for FTNMR. In that one we now come to the 10th point which is phase correction. Typically we know that NMR signals are of two types. One we have a signal which is like this and this we call as absorptive signal or you may call this also as a spectrum with a zero phase or the other is the dispersive signal which goes like this and this is a dispersive signal and this we may call it as 90 degree phase. In the FTNMR we collect the data as let us say we collect the data is cosine omega i t and e to the minus lambda t, lambda i t suppose we have the signal which is like this. When you Fourier transform this it generates two components one is the real component and then you also have the imaginary component time domain function this is my FID. If FID is like this the real part will have a pure phase absorptive signal this is absorptive and the imaginary part will have the dispersive component. Now similarly if I have if my FID is of the type sin omega i t e to the minus lambda i t if I have this sort of a function FID this is my FID then after Fourier transformation I will get again a real part and an imaginary part. The real part will have the dispersive signal and the imaginary part will have the absorptive signal. So therefore we have to see what is it that we are going to get in FTNMR spectrum. Now often we find that the signal is not exactly dispersive or absorptive sometimes we get sometimes we get signals which are like this. So this is a mixture of absorptive and dispersive signals. So therefore this is known as phase error. So this is called as phase error and this has to be corrected. So now what is the source of the phase error? What causes the phase error? This we have to understand. Now as I explained to you suppose I have experiment done like this I have the initial magnetization here this is the M0 initial magnetization which is here if I apply a norm like 90 degree pulse along the x axis which is exactly correct 90 x then my magnetization will come along the let us say the y axis whether it is 90 x or minus x if it comes exactly along the y axis then my signal will be cosine omega it e to the minus lambda it this will be my signal if I collect the signal starting from the exactly magnetization aligned along the y axis. But often it so happens that this is not achieved and what happens is you get the magnetization which was initially a rotating to somewhere like this to some other position so then it will be oriented here in the transverse plane. If this is the case then you have the x, y and z so the signal which you are going to collect will have the contributions coming from this as well as from this. So if it is not 0 phase this is let us say this angle is theta then theta is the phase at time t is equal to 0. So in such a situation your signal will have real component which is the cosine component cosine omega it and also sine omega it so signal will have both the components. So if a Fourier transform this what I should get of course this will have a certain amplitude here this is the coefficient let us call this as a1 and call this as a2 there are two coefficients depending upon what is the error here theta error depending upon that the components along the y and the x axis will be different whatever is along the y axis will have a cosine omega it whatever is along the x axis will be the sine omega it. Now if I do a Fourier transformation of this sum together which is collected here I will have a mixture of in the real part it is also true in the imaginary part also this is the absorptive component and then I will also have a component which is coming from the x part which is the dispersive component this plus this will give me a signal which is like this. So this is because of the error in the initial pulse application the pulse is not applied exactly along the x axis but slightly deviated from the x axis. So RF phase is not exactly 0 but slightly away and that is a theta therefore when the 90 degree rotation happens it does not come exactly along the y axis but it comes somewhere in the xy plane and that if the angle is theta 0 the certain mixture of these two things will happen. So this is this is this has to be corrected okay and this is called as a 0 order phase 0 order phase error because this is not dependent on any frequency entire magnetization is rotated so at time t is equal to 0 all the magnetization components have the same angle at t is equal to 0 all the all the components the same phase error and in the this is in the real part the imaginary part similarly we will have a this portion will have pure dispersive component and and also a small absorptive component okay the trick in correcting the phase will be to mix these two appropriately so that the dispersive component from the absorptive signal will vanish and likewise the absorptive component from the imaginary part will vanish okay so that is the idea okay. Now there is another source of phase error and that is the following. Suppose my FID is supposed to be like this right and my data points my data points are should be like this here here here here here should be like this okay so therefore at time t is equal to 0 the magnetization is entirely along the y axis or whatever that is okay see in this case the magnetization is entirely along the y axis if I am collecting the y components but suppose I cause a small delay in the acquisition of the time so in this situation where will the magnetization be all the components of magnetization will be along here all the components so this will be all the components will be here in this case the normal case this is but instead suppose I do not start collecting the data from time t is equal to 0 this is at t is equal to 0 now if I collect the data this is my FID but I do not start collecting the data from the first point but I start collecting from here okay here some delay for various practical reasons I do not collect this so this can be a small time also it can be few hundred nanoseconds that is it has nothing to do with the dwell time it has some hardware limitations so you may want to give a small delay here this is a small delay we may call it as t0 so your actually data's collection starts from t0 so therefore your signal here will be cosine omega i t plus t0 okay so what does that mean in if I were to represent this in the transverse plane like this the magnetization where it will be to start with to start with we are because the t0 is a delay during this period time the different components will have processed to different extents right so during the time t0 the various components would have processed although I applied a 90 degree pulse correctly that it came to the y-axis the magnetization came to the y-axis why I did not start collecting the magnetization from that point I started collecting when the different components are moved to different extents that is t0 so let us say one component has moved here and another component has moved here okay and the third component would have moved here okay these are different spins different lines in your spectrum they are corresponding to different spins so they all have moved to different extents let us call this as 1 2 3 and all of these now have different thetas right they all have different thetas compared to the previous one it was a 0 order phase now in this case because of the delay in the data acquisition the different frequency components in your magnetization have moved to different extents therefore the first line would have a mixture something like this okay let us recall this as 1 and the second one the second one may have had some more here and the third one would have even more third and so on so different ones will have different mixtures therefore this is what we call it as frequency dependent phase shift and this is what we are talking about these are all in the real part of the spectrum similar thing will happen in the imaginary part of the spectrum so in order to correct for this here as well as in the previous case the strategy is to mix the real and the imaginary components okay so therefore phase correction phase correction would imply mix the real and imaginary parts appropriately eliminate the admixture the computer does this there are various kinds of knobs over there so this you just keep moving the knobs and in real time actually you can monitor on the screen how the phases are changing so these are the algorithms are there this is the mathematics behind this all that is all programmed into the computer it is all programmed how to mix the real and the imaginary parts and what should be the coefficients for the mixing all that is then you can manually adjust it so this can be manually adjusted okay to obtain the phase correction then we will have after you have done that you get pure absorptive line for the real part and pure dispersive part for the imaginary part you generally do not use the imaginary part for other purposes in when you want to represent your spectrum you only plot the real part you only plot the absorptive spectrum right imaginary part stays there in the computer but you do not you do not really look at that however it is used for phase correction so that is the important part of the Fourier transform NMR and this does not exist in case of conventional spectroscopy okay so now move on to the next important concept and that is dynamic range so what is dynamic range let us say we have a small signal and a huge signal like this this may be a solvent this may be from your sample and you notice in Fourier terms of NMR we excite all of them together okay in FT NMR all these are excited together and signal is digitized so when I collect the data in the digitized form it will be superposition of the contributions from all of those okay suppose this signal has the intensity of 1 this signal has the intensity of 100 then what I will be collecting will be 101 if this is 5 and this is 200 or it will be collecting will be 205 okay so that is what will be representing in my in my FID so this is what happens in the FID the FID which you have this you have the various points at various places and in every point we will have this summation represented okay therefore in every point the data has to be represented correctly this sum has to be represented correctly how it is stored how it is stored in the data the data is digitized right as I told you data is digitized and there is this device which is called as analog to digital converter analog to digital converter also called as ADC okay this collects data in the binary form okay so it gets collect data in the binary form because that is what the computer understands right and let us say we have analog to digital converter which has the resolution of about let us say 4 so there are 4 bits there are 4 bits in the analog to digital converter what is what is this this will be 2 to the power 0 2 to the power 1 2 to the power 2 and 2 to the power 3 so what is the largest number that can be stored here 2 to the power 0 is 1 this is 2 this is 4 and this is 8 this is equal to 15 this is a 4 bit 4 bit digitizer each one of them is called as a bit the 4 bit digitizer the largest number is 15 that is 2 to the power 4 minus 1 this of course is the very small number typically our intensity ranges will not be so small they will be much larger than this we would like to as a large a range as possible okay so therefore typically one uses what are called as 12 bit digitizer 12 bit or 16 bit 16 bit digitizer so in out of these they also have to account for the sign 1 bit is kept for the sign plus or minus 1 bit is kept for the sign so therefore what will be the number in this a 12 bit digitizer okay in a 12 bit digitizer 1 plus 11 this is for the sign and 11 bits what it will give you 2 to the power 11 minus 1 2 to the power 11 is 2048 minus 1 that is equal to 2047 okay so this is the largest number that you can store therefore in your FID the digital point should you when you add up the intensities of the small signal and the large signal it should be below 2047 or let us say if you scale it for some reason you have a possibility of scaling it down I multiply everything by scaling factor like 1 by 5 or 1 by 10 or some that is a scaling factor even so that scaled number should be less than this in other words the ratio of larger signal to small signal should be less than 2047 then the whole thing will be represented and this is where the problem comes let us consider that you are collecting a signal in water consider a sample sample in water and we are recording the proton spectrum proton spectrum what is the what is the concentration of proton here in water so this is approximately 110 molar water concept proton is 110 molar and if you have a sample which is 1 millimolar what is this concentration this is 10 to the minus 3 molar and therefore what is the ratio the ratio is equal to 110 divided by 10 to the minus 3 this is approximately 1.1 into 10 to the power 5. So therefore it is impossible to represent this number in this 12 bit digitizer and this is called as the dynamic range in such a situation the small signal gets lost only the big signal is represented and the small signal is not represented this is called as dynamic range problem this is the problem so what should we do to avoid this we have to devise techniques to suppress the strong signal most of the most often the strong signal is from your solvent it is not of much use for you to collect your water signals solvent signal therefore you can suppress that strong signal and so that you can observe the your actual signals and there are various strategies to do this so therefore you would come to the next topic which is called as the solvent suppression there are various strategies to do this I will take you some of the very simple ones there and of course there are very elegant procedures which are there we will see or use them the simplest thing is first the pre-saturation so what is the strategy here let me represent my FTNMR experiment in this manner this is my 90 degree pulse and I am actually collecting the signal here as a FID this is my FID so what I will do is before I apply the 90 degree pulse I apply a soft RF another RF I do not use the same RF which is here I will use the soft RF here on water on water that is the solvent signal that means it will excite only the water it will not excite anything else so this will saturate the water signal this will saturate the water and it won't affect anything else because it is soft so it is applied exclusively to the water signal therefore it will only saturate the water now before that water saturated water returns back to equilibrium before it comes back you apply 90 degree pulse here or whatever the flip angle you want to use and then you direct the signal you finish your experiment before the water comes back so therefore in this area the solvent contribution will be reduced so this is the simplest of the experiments and there are other methods what we will see what is called as the inversion recovery we will see the next experiment which is called as the inversion recovery let me call this as A okay then I will say B B is inversion recovery inversion recovery technique so what we do here is the it has actually uses more than one pulse here so the strategy will be like this you apply a 180 degree pulse a hard pulse you a time tau wait for a time tau and then you apply a 90 degree pulse or flip angle whatever flip angle you want to give and you collect the FID here how does this work let us try to understand this in a vectorial manner vectorial picture inversion recovery means 180 degree x plus meaning what the magnetization is rotated from here to here right initially magnetization was here and that gets rotated to this point when you have a 180 degree pulse so let me draw that as here now this magnetization contains contributions not only from the water but also from your other signals for my other samples as well let me represent them with a different color so let us say I have another one here for two is enough for purposes of understanding now both these will try to recover back to equilibrium okay now what you do is suppose my red is water and the green one is my sample okay so in that situation what I will do is I will adjust tau such that water has come here because it is recovering as it is recovering water has come here at 0 point and but the green one has come here okay so which means they have different relaxation times the red water and the sample water and the sample have different T1 values because this is T1 relaxation right this is a longitudinal magnetization longitudinal magnetization is what is happening here this is here what is happening here is T1 recovery during the time tau there is a T1 based recovery so the if the two have different T1 values I adjust the time tau in such a way that the red signal which has come down to 0 but the green one has gone up or go either down either way it is possible it may not have reached there or it has crossed that okay now after this if I apply a 90 X pulse I will not get any signal from the water ideally I will get only signal from the sample however in practice this does not happen some signal will always come because the recovery is not all that very very precise adjustment is not so precise so this is a strategy this of course requires that have distinctly different values things which are very distinctly different values only then you can suppress the water if they have similar relaxation times then this will not work okay because if the water has relaxed to 0 your sample also relaxed to 0 okay so then you may lose it and then of course if the difference is not very large in T1 is not very large then your sample also will get will get attenuated sample signal will also be attenuated okay so this is an important technique okay now then we will stop here and in the next one we will continue with this and take more