 So, we have discussed so far in a rather simplistic manner how to follow dynamics in femtosecond time regime using pump probe spectroscopy. Now let us think of a little slower time scale, 100s of picosecond to nanosecond but the technique that we are going to discuss is actually little more complicated. So it might be easier if we start thinking from slower time scale and then we will understand why we have to do this. Let us say I want to follow the dynamics in some time scale. So the easiest way of doing it is to excite by a pulse and either use a probe or look at fluorescence coming out from the sample, look at emission coming out from the sample and see how it changes with time. Now if this phenomenon happens in microsecond time scale then there is no problem because you can see it directly on an oscilloscope. We might have occasion later on in this course to discuss very briefly how an oscilloscope works but for now let us take a rain check on it. So an oscilloscope usually does not have enough time resolution or bandwidth to give you a reliable measure of times that are down to 100s of picosecond. Nowadays you do get oscilloscope but then there are issues with it. So you cannot do a direct measurement. When you go down to femtosecond we solve the problem by using the power of light. As we have discussed in case of fumprope spectroscopy we give variable delays but you cannot use that technique if you are talking about 100s of picosecond or nanosecond for a very simple reason. What kind of time delays do I have to give? Suppose I want to measure a process that is associated with a 10 nanosecond time constant. 10 nanosecond time constant means you should record at least up to 40 nanosecond. So 40 nanosecond time delay would be okay. The light goes and comes back so it amounts to effectively 20 feet. You need a 20 feet long transition stage. So two problems with that first of all you need a big lab. Secondly those who have done alignment of even a 1 foot long transition stage would know how difficult it is. So if you are going to align a 20 foot long delay then may God help you. It is not a good technique anymore. And also you record point by point it will take a long time. So for this intermediate time resolution where direct measurement is not going to work and this time delay optical technique is cumbersome there is no way other than taking the help of electronics. But then electronics has a problem that the response time associated with the electronic components that we are going to use is not in picosecond. It is in nanosecond or slower. So we will learn, we are going to learn this very elegant technique that uses electronics but uses a trick to circumvent the inherent poor time resolution associated with the electronic components involved to allow us measure hundreds of nanoseconds maybe tens of picosecond to hundreds of nanoseconds. This technique is called time correlated single photon counting or as it is commonly abbreviated TCSPC okay. What we see here on the slide are the different components that are used in TCSPC. This thing is a pulsed diode laser when we go to the lab we are not going to show you this will show you a femtosecond pulsed titanium sapphire laser but this is something that you can use and if you do not need too much of time resolution these are comparatively cheap and very easy to use solutions for light source and you can see the size this would be about 3 centimeter the width is about 1 centimeter compared to that you can see how small the sources are. Then you need a sample chamber inside the sample chamber you need to keep whatever it is whose fluorescence lifetime you want to record. And then of course you need a monochromator that is not shown in these diagrams then you need a detector. What you see here is a TBX04 detector from what is now Hori by Jobini one we bought it from some other company at that time which was the name of which was IBH. So this is a detector and some associated electronics and when you use this combination you end up getting the decays of fluorescence that look like what is shown in the lower most diagram. This Gaussian sort of thing is the laser pulse as the instrument sees it and this thing that is there is the fluorescence decay you might think that it does not look exponential it does not look exponential because we are showing rather small time window compared to the decay. So let us learn step by step how this technique time co-derated single photon counting works and it is important to learn this because this is now become a very commonly used ubiquitous kind of technique. And it is important that we know what to do and what not to do while recording the data and while analyzing it. So this is the basic principle of TCSPC even before going to TCSPC this is something we have discussed in the previous module in a little different way. What we are doing is we are exciting by a pulse and then we are looking at the decay. It looks like a straight line because we have assumed a single exponential decay and the y axis is logarithmic. So as we said earlier in the simplest case scenario decay of the excited state population is single exponential because it is a first order decay and fluorescence intensity at any given time f at time t is proportional to the excited state population n star at that same time t. So since n star at t follows this kind of an exponential variation we can write a similar exponential variation for fluorescence intensity as well. This is exactly what we studied in kinetics there is only one difference in chemical kinetics you would write exponential minus kt here instead of that we have written exponential minus t by tau. So this tau is called lifetime to put it very simply tau is the reciprocal of time constant but then why is it called the lifetime of all things it is called the lifetime because it is also the average time spent by a molecule in the excited state. Let us let that be a homework this is worked out in Lakovic's textbook and many other places. Please work it out yourselves and convince yourselves that tau is actually the average time spent by a molecule in the excited state that will involve solving an integral that is all working out an integral. Now as I said this is simplest case scenario more often than not the decay is not single exponential and when it is not single exponential the most commonly used model that is there is a multi exponential decay where you take a weighted sum of exponential terms. Now multi exponential decay would generally fit any decay that you are going to handle but it is important to not forget that it is not necessary that it is an appropriate decay model for everything you might require different decay models we are going to come back to this issue and show you a couple of examples where a multi exponential decay is not appropriate and you have to use something that is more complicated like distribution of lifetime or stretched exponential but let that be the story for another day. Now we come to the schematics of the time correlated single photon counting experiment and this is where we sort of deviate from comfort zone of an average chemist and start trying to look inside the black box that the instrument is but if you have to do this experiment properly it is very important that the instrument is not a black box for you. You need to know unfortunately the days are gone when you could actually see the components but at least you should know how it works and where the components are. So the schematics are based on our old diode laser based TCSPC spectrometer there we had a pulse laser DL is for diode laser you can think that it is just a pulse laser it sends out a short pulse when you use a diode laser the output is typically elliptically polarized which means it is a mixture of horizontal and vertical polarization not to the same level but then as we learn later for our purpose it is important that we work with linearly polarized light. So if you are going to use diode laser then it is important that you use a polarizer in the path of the light before it goes into the sample chamber and excites your sample. If you use a titanium sapphire laser like the one that we are going to show you later on output of titanium sapphire laser is already linearly polarized. So this polarizer component is not required there in fact if it is there then it can be a hindrance if it is not exactly aligned with the polarization of the light. Then the emission comes out and as we have discussed in steady state emission experiments once again you would want to record at right angles typically and again this emission light is made to go through a polarizer hold your thoughts on this one in one of the later modules we will learn why it has to go through a polarization for now let us just say that for lifetime measurement what we typically do is we keep the second polarizer the emission polarizer at 54.7 degrees compared to the polarization of the input polarizer. So when I say 54.7 degree I do not mean direction I mean polarization of the second emission polarizer is set at 54.7 degrees with respect to the polarization of the excitation light and then the emission goes into monochromator and into the detector right. So far it is almost like the arrangement that you have in your steady state flow meter. The difference comes after this what happens is from the detector the electronic signal that is generated goes into something called a constant fraction discriminator. The job of constant fraction discriminator is to help us get an accurate timing information we will come back to this issue a little later. For now let us just assume that the output of the CFD is a pulse which we can time very easily precisely that goes to the start module of a time to amplitude converter a time to a amplitude converter has at its heart a capacitor which starts getting charged the moment a signal arrives at start and keeps on getting charged until another signal appears at stop. And where does this signal come from? It comes from the power supply of the diode laser which sends out a synchronous trigger. Synchronous trigger means the power supply fires the laser and at that instant sends out and a pulse of electrons and electronic pulse that again goes to CFD and goes to stop. What does the synchronous trigger signify? It signifies firing of the laser. So if your laser operates at say 1 MHz repetition rate which means it gives out 10 to the power 6 pulses per second. And for each one of this 10 to the power 6 pulses per second an electrical signal will go out that is a synchronous trigger. So the synchronous trigger has the same repetition rate as a laser itself. That is made to go through some cables and all goes to CFD and stops. So now what happens? Laser that is there inside TAC is charged for the time duration between arrival of a signal at start and arrival of a signal at stop okay and the moment stop comes charging is stopped. Some charges accumulated. Now it is discharged across a resistance and the voltage across the resistance is measured okay. So if I can try to draw it a little bit so what you have is this let us say this is stop and let us say this is start. This signals go into charging of a capacitor. The start and stop the charging of the capacitor right. When it is stopped after that the capacitor is discharged across this resistance. You measure the voltage across a resistance. So now see do you agree with me that the voltage that you see is going to be proportional to the charge that has accumulated on the capacitor. And will you also agree with me if I say that the charge that has accumulated on the capacitor is proportional to the time of charging yeah. So I can write it like this. This voltage is proportional to delta T where delta T is the difference in times of arrival at start and stop okay. Now it is important to understand what is going on here. So the reason why we do all this is that we cannot measure the decay directly. So we are resorting to a method that is actually probabilistic in nature. So this here let us say is the decay of fluorescence. So if you do the experiment many many times what will happen? When I say this is the decay of fluorescence what I mean is that if you take a large number of molecules and perform an ensemble measurement then population decay is like this. If I take one molecule and keep on exciting with the pulse and keep on recording delta T what will happen? Will I get the same delta T every time? No right? I will get different delta T's at different time. The basic principle of time correlated single photon counting is that we say that if you take a single photon and plot probability of getting a particular delta T okay against number of times it occurs basically we are talking about histogram now we are saying that this histogram has the same shape as the actual excited state decay of fluorescence decay okay. It is important to understand this if you understand this this is very simple. So what is the working principle of TCSPC is we are going to record this delta T's again and again. So it is not a one-shot experiment you keep doing the experiment many many times and you keep recording delta T's and what we are plotting essentially is number of occurrences of number of occurrences versus delta T okay so delta T is 0. If I get delta T is 0 once I strike it off here then I get delta T equal to 10 nanosecond I strike off here then again I get delta T equal to 1 nanosecond I put a dot here again I get delta T equal to 1 nanosecond I increase the dot by 1 unit okay. So after a while what will I get I will get a histogram is it something like this are we clear about this. So what we are saying is that if you join the tips of the histogram then you get the same curve as decay of the excited state population decay of fluorescence intensity okay so what is our job then our job then is to perform a large number of experiments and keep recording delta T's and keep track of how many times a particular delta T occurs are we clear. So why is this called time to amplitude converter because you are actually converting time to a voltage that is why it is called a time to amplitude converter. So from there it goes to computer with MCA MCA means multi-channel analyzer so it goes into a multi-channel analyzer what is a multi-channel analyzer multi-channel analyzer is sort of like a digital graph paper see what I discussed a little while ago that I want to measure the number of times a particular delta T arrives if I am to do that manually what will I do I will take a graph paper I will mark off the delta T on the x axis and keep putting dots right I get one kind of delta T one dot same delta T comes again I go up by one notch and so on and so forth I build the histogram computer does exactly the same thing it has a card nowadays MCA is no longer a standalone instrument MCA means multi-channel analyzer so multi-channel means each channel is a memory location you can think like that the digital equivalent of a graph paper on a graph paper all those cross lines right are a memory location you can think a digital graph paper. So multi-channel analyzer has all these channels each of which is a memory location and what you can do is you can record there how many times a particular delta T is coming so that is what we do and that is how we build the histogram which has the same shape of the decay right so that is how it works what does the CFD do how does the CFD work so this is how a CFD or constant fraction discrimination works but before that let us say why do we need CFD in the first place before we go to constant fraction discrimination let us talk about something that is called leading edge discrimination see the output of the detector is something like this where this is time x axis and y axis is voltage typically this pulse is minus 100 to minus 300 milli volt that is the maximum amplitude this kind of a pulse is called a NIM pulse what is the meaning of NIM nuclear instrumentation module NIM means nuclear instrumentation module the thing is you make many instruments if every instrument has one kind of has a different kind of signal then it will be very difficult to interface instruments and then only one person can use one instrument that is not a very happy situation so some typical patterns are used and NIM is one such kind of pulse nuclear instrumentation module it is sort of a Gaussian pulse minus 100 to minus 300 volt milli volt in amplitude another pulse that is very frequently used looks like this and this side is typically 5 volt can anybody tell me what this pulse is called it is a square pulse but it has a name it is used whenever you use any kind of binary logic any kind of computer it is called a TTL pulse I do not know why it is getting written like a stair but anyway TTL is transistor logics so this is basically you know very well that computer does not understand anything other than 0 and 1 right that is why computer language is all in binary right everything is in 0 and 1 so essentially this is 0 this is 1 so sequence of TTL pulses there is a computer what you want to tell it but here typically we do not use TTL pulse you see there is a provision of TTL output in most of the instruments but most of the time we do not use TTL NIM is what is used because most of the instruments are actually mounted in NIM bins so it is more convenient to work with NIM pulses now the problem is minus 100 to minus 300 there is nobody has said that is going to be 300 milli volt all the time or minus 100 milli volt all the time there is always a fluctuation so how will I say so if you remember the diagram some signal comes to let us say start of tack this is very easy to say signal comes how will the instrument know that signal has come cannot see so all it can do is it can measure voltage so you can tell the instrument that when the value has reached say 50 milli volt then you consider that the pulses are right so let us say this is minus 50 milli volt okay this is called leading edge discrimination you discriminate like that that all this is considered to be 0 here that is 0 time that is when you start but there is a problem with this because as we said just now there is nobody has said this will be exactly 300 suppose it is not I will exaggerate a little bit and draw it like this for the same signal let us say I have got a pulse like that now what will happen at this time x axis time remember value is not 50 milli volt when at work time is value 50 milli volt this time so depending on whether I get this big pulse or this small pulse I will have an uncertainty in start time by delta t this is called timing jitter timing jitter is eliminated by taking by using constant fraction discrimination rather than leading edge discrimination how do you do that okay let us take a pulse like that right so first thing that happens inside CFD and it is very easy to understand is that you divide the pulse into 2 parts so you can think of this pulse as electric current right is it easy or is it difficult to divide in electric current into 2 parts easy if you have if you think in a very gross bulk way you have some copper wires twisted together right you un-twist them that will give you 2 channels in which electrons can flow and you can have say 20 strands on one side and you can have 5 strands on the other side what will happen resistance will be different between the 2 so more or less fraction will flow in class 11 12 with current electricity all of us have been bothered with problems like this how much current will flow in which direction and all that where I try to do anything like that everything becomes you know that is a different issue but here it does not so depending on the resistances of the 2 arms let us say in this arm I have a larger pulse in this arm I have a smaller pulse alright next what we do is let us say I invert this pulse inversion using transistors and all is very easy in electronics and let us say to this one I give some time delay which means I use a longer wire now what will happen on this arm on this arm will have a positive pulse on this arm we still have a negative pulse but now this lags in time okay now let us combine them is it easy or is it difficult to combine very easy again wind the strands together now if you combine what will happen you have to add up these 2 pulses that will give you the output what will the sum look like it look like something like this right it will be a 0 crossing pulse now see instead of this pulse if I have a huge pulse what will the output be something like this amplitudes will change but the 0 crossing point will not change now if you tell your instrument that wait until the signal becomes 0 the first time and then start counting then this timing jitter is eliminated this is the advantage of constant fraction discrimination it is called constant fraction discrimination because you are taking a pulse of a fraction of the pulse here and another fraction there 1- that fraction there so constant fraction discrimination eliminates timing jitter okay so what we have learnt then is that we can do time correlated single photon counting to record fluorescence decays in 100s of picosecond to nanosecond time regime we are not limited by the time response of the electronics here because we are not trying to actually measure the time we are trying to measure delta t that can be done without much hassle as I hope you have understood now and to measure delta t with precision without timing jitter it is important that we do constant fraction discrimination rather than leading edge discrimination once we do that then we are good okay then we can get a decay like this in the time scale that we want but this is not the decay we really want this decay is more complicated than what we do have liked it to be because we are not used a delta pulse for excitation we have used the pulse that has a finite width that complicates the scenario so in order to make any sense of this curve that we get experimentally we have to as we learn deconvolute and extract the actual decay from the observed decay in which you have strong signature from the instrument as well that is what we are going to do in the next module.