today what we will going to discuss is the time domain measurement of the lifetime
of the fluorescence lifetime and the last day what we are discussing about three
different methods for the time domain lifetime measurements the first one is time correlated
single photon counting method in one word this is known as t c s p c and the other method
which i will going to discuss maybe not today maybe on the next class is the fluorescence
up conversion method and i will not going to discuss this streak camera because probably
time will not permit me to do so ok so just let let us compare this time correlative
single photon counting setup and the fluorescence up conversion setup each setup has its own
benefit and also each setup has some limitation of it for example this time correlated single
photon counting method the time resolution right are the i r f is not very high depending
on system to system this can go to fifty picosecond to fifteen hundred picosecond also however
this fluorescence up conversion system as you can see this time resolution can go down
to zero point two to zero point four pico second right so in that sense the fluorescence
of conversion setup is superior to time correlated single photon counting setup however in the
t c s p c setup the advantage is that it has a very big time window right
time window is large right we can go to microsecond no problem but in this case the time window
is small typically one go to one to two nanosecond time window for this that means you cannot
measure the fluorescence intensity for a longer time period in this case although the time
resolution is high however in this case time resolution is like a fifty pico second
but we can measure for a longer time period right so time window is very large ok
let us start the t c s p c setup and as i said that for the time domain lifetime measurement
so that it is t c s p c or whether it is up conversion what we usually do we usually excite
the sample with an ultra short light pulse right so light is present for very short time
and ideally the light is present so short time that this light pulse is treated as a
delta pulse right so delta pulse excitation it means if i plot the intensity of excitation
light as a function of time then if this is the time axis so the light will come like
this way and then there is no light and this width is zero right so this is the my delta
pulse this is a ideal situation but in reality it depends on the quality of the laser
or the property of the laser because i want to generate the light pulse as short as we
can and that cannot be generated by normal light source thats what we have discussed
like a filament bulb or the general lamp or dodge ram lamp those things we have already
discussed so we need a special type of light source
to generate such kind of short light pulse right what is that special type of equipment
we need is a laser so special type of light source so we called this pulsed light source
and laser is very famous for that we will going to discuss the little bit about this
so once we excite this sample with this delta pulse light source as i have done here
so in no time in no time so this is my zero in no time the molecules will go to the excited
state on the other hand if you use a broad light
pulse for the excitation what will happen just just briefly i am drawing over here suppose
you are exciting a delta pulse for the excitation so this is my zero time so the population
so this is the excitation light pulse and this is the excited state molecule population
excited state population of those molecules you are exciting at the zero time the population
will be like this maximum and then this population will decay on the other hand if you use such
kind of light pulse in this case this is not a delta pulse right has some width delta t
so in this case this part of your light pulse will excite some molecule so the population
is something like this at time t equal to zero here the intensity is maximum so i will
get this maximum intensity so and at this time the intensity again small so i will get
the intensity small so the excitation right the excited state population will take such
kind of ship and each of them will decay each of them will decay and the decay will be distorted
that we are going to discuss later also ok so as you have understand that what i need
i need a very short light pulse like this short light pulse
and once you excite you got this excite state population whatever the population i have
just normalized to one right and then i will monitor how the population will decay right
how the population will decay like this and thats it if i know this then i will be able
to calculate the fluorescence lifetime because i know fluorescence lifetime we already
have seen that flow for fluorescence lifetime the dependence of this intensity i is the
function of t is equal to i zero which is initial intensity in this case is equal to
one for this particular case into e to the power minus t by tau right
so if i fit this measured fluorescence intensity as a function of time with such kind of equation
then simply i will get this value because this t is my variable t is over here t so
i will get this tau or i can say that when the population decay is about sixty three
percent a ce then i will get whatever the time i can denote it as my tau fluorescence
lifetime ok let us go to this t c s p c setup the set up by which we can determine this
lifetime as i said earlier that if the life time is very long long in the sense in hours
right then each second you can measure the fluorescence intensity by your normal flora
meter so no problem however the life time you know using the order of nanosecond that
we have discussed that means through lets say for such kind of nanosecond life time
if we start with intensity one then that intensity will going to be zero in about five into tau
right so five nanoseconds right so that simply we can calculate over here
for a lifetime of one nanosecond right so my equation is i equal to i zero e square
minus t by tau this tau is one nanosecond lets say i say that when i is equal to zero
point zero zero one times i zero then i said that intensity will completely decayed because
this is exponential function it will be zero where of the infinite time ideally mathematically
but for us when it is like just one percent i said that the intensity is zero right finished
so in this case what i can do i can do l n zero point l and zero pointy zero zero so
one percent i said na so let me write zero one
so l n zero one is equal to minus t by tau t by tau so this is be equal to minus four
point six equal to minus t by tau so t will be equal to four point six time of tau that
means when the lifetime is about one nanosecond the time window declared to see the complete
decay is about four point six nanosecond and if this time window is four point six nanosecond
that is zero and here is four point six here is two point three here is one point one five
like that and if you want to see this complete intensity decay right you need to get several
points over here right several several points over here that means you need to measure the
intensity of fluorescence right at right every point one nanosecond or point zero one nanosecond
or point zero zero one nanosecond something like that which cannot be done right using
your standard flora meter it was ok if it is hour but it is in nanosecond right
so i need to measure the fluorescence intensity at every pico second also that means ten to
the power minus twelve second that cannot be done so easily so what we should do we
should use some setup like this way just i will briefly explain you this setup here
i use a laser over here as you can see here so the property of the laser is such that
it will generate the ultra short light pulse right so this is capable to generate
light pulse of short duration now how short there is the question mark right if the total
time window lets say for this one nanosecond the total time window is four point six nanosecond
and if your light pulse is ten nanosecond so obviously we will not be able to see anything
its simply like that using a meter scale you cannot measure a millimeter like if your wristwatch
does not have a second needle right you cannot measure one second or two second using your
wristwatch right very to that if your excitation light pulse is much broader than this time
window right then you will not be able to measure that so your excitation light pulse
has to be shorter than this right so for like a normal fluorescence lifetime
measurement right if the lifetime is about a nanosecond we usually use a light source
of either one nanosecond or less than that so the light pulse should be about nanosecond
one nanosecond or less right then i will be able to measure it right ok so these light
pulse so these are the pulse light so pulse light means please note that the light is
present for some time then for the rest of the time light is not present again light
is present for some time this width is the pulse width of the light and then light is
not present for some time again light is present again light is not present again light is
present then light is not present that means what i will going to get i will get a series
of such kind of pulses and that series of pulses can be defined by its reputation rate
right so for example if the time between these two
successive pulse is t r then and and this pulse width is t p right then by defining
these two quantity by defining this t r and this t p i will be able to characterize such
kind of light and another quantity also have to defined here that is a wavelength
of the light because you need a particular wavelength for the excitation and another
property is the wavelength lambda so for a laser what i say that i i will fix
what is the color of the laser color of the laser what is the pulse width and what
is the repetition rate of the laser repetition rate of the laser ok so these three property
i need to look at now lets see that this laser is coming out of this um laser these pulse
rates are coming out of this laser and eventually it will excite your sample your sample is
situated in the middle of the sample chamber and then this fluorescence will come out of
this right this then the fluorescence will come out of this so this fluorescence is not
a single wavelength so you need to choose your lambda emission your desired lambda emission
that will be done by this monochromator and that will be directed to the p m t to measure
is intensity right so these setup works in a way that when this
light this short pulses are going to excite the sample over here at the same time it will
send one signal to a device called t a c this t a c is time to amplitude converter so at
the time this laser will going to excite your sample at the same time the laser will send
another signal to this device t a c the details of the t a c i will discuss later but for
now lets take this t a c as a kind of stopwatch so once it will send the signal to the t a
c the start signal to the t a c it will start counting the time right and this stopwatch
is a very nice stopwatch it can count the time in the order of picoseconds right so
so this laser will send one signal to this t a c that means ok now i have excited my
sample so please start counting time so then this device will start counting the time
so this obviously at that same time the sample has been excited now once you excite
the sample several molecule will go from the ground state to the excited state it depends
on the how many photons are present in the each pulse and what is the concentration
of your sample and so on so you will get a handsome population in the excited state and
as i said the last day that this not all this excited state molecule will come back
to the ground state at a particular time but this is a random process some molecule will
come back from the excited state to the ground state at early time some molecule will come
back from the excited state to the ground state later time some molecule will come back
at the time t equal to tau right so the molecule will come back from the excited
state to the ground state and i can measure this emission right by this p m t the condition
is that in this case that when one photon from this sample position will reach the p
m t when one photon from this sample position will reach the p m t right then this pmt will
convert this photon to the electron and he will generate a electron pulse over here so
he will generate electron pulse over here that is the current pulse over here and that
these current pulse will come and it will stop this stopwatch
so now stopwatch will measure the time so what stopwatch will measure stopwatch will
measure my t a c hm here stopwatch means my t a c so this stopwatch will measure the time
delay between the start and the stop that means you have excited your sample and not
immediately the photon is coming out of it it may take some time and you will get a photon
following on the photocathode of this p m t and this was converted to the electron and
then current pulse will stop it so the delay between excitation and emission
plus the path length required to excite and then the whole process required to reach to
this stop pulse right so this is the difference between the start and the stop so in this
case what you will going to get you will get a time which is start or stop minus start
and for that particular time you will get a count right we will get a count you remember
that you have excited several several molecules right in your sample chamber some of them
will emit early time some of them will emit at the later time right
in this case what i have to ensure that the first emitted photon is not necessarily be
the first detected photon by this p m t let me explain it in a better way suppose
this is my decay profile as i showed here so these are the probably the first emitted
photon is at this time short time it is not guaranteed that these photon will come along
this direction it is possible that this photon will go in that direction because these type
of emission is a spontaneous emission is a direction less so it can go to any any
direction right it can go to the upper side lower side left right and all these directions
right so when these particular time photon is along
this line then only it will be detected ok lets consider that you got this particular
time photon is emitted and it is along this particular line in this particular line and
you got a signal that this count is for time t one you got a count obviously after that
the photon of this one photon at this time photon at this time photon at this time photon
at this time all this time will be emitted until it will be reach the four point six
nanosecond in this particular case but for this setup we will not going to use all these
emitted photon so once i will detect one photon which actually
make the stopwatch stop we finish the experiment and we will wait for the second excitation
pulse to come and excite the sample so for one turn one light pulse comes in excite the
emitted photon is detected which emitted photon i dont know it could be this one it could
be this one it could be this one it could be that one but in this particular case i
said that this is the emitted photon at time t equal to t one and that photon has been
detected but this excited state molecules are much more right is not only one right
so other molecule will also emit at the different different times but i will not going to consider
those photons for this particular light pulse what i will going to do i will wait for all
the excited state to come back to the ground state so i have to give enough time for relaxation
that means all the excited sate molecule will come back to the ground state
then when the situation is like before excitation right so the situation is just
like the before excitation all the molecules are now in the ground state so now what i
will do i will use the next excitation pulse lets say the next one like here so this will
come and then again excite so again these light pulse will take all the molecules from
the ground state to the excited state and for in that cycle it is not necessarily that
these photon will be directed along this path is not necessarily it could be that these
photon this time these photon is directed along this path for the second cycle so that
this is for the second cycle these photon probably directed along this path of the p
m t and lets say this is the time t four right so for the first cycle i got a count at time
t equal to t one for the second cycle i got a count at time t equal to t four right then
again i wait wait how long i should wait i wait till all them excited state molecule
will come back in that to the ground state then i use the third pulse right that means
is my third cycle right this is the first this is the second pulse this is the third
pulse right like that so when the third one will come so that is going to be my third
cycle so lets say for the third cycle these photon
which is emitted at very later time so this is my third cycle this is t seven right or
maybe t seventeen ok so these photon which is emitted that very late that is the only
photon which is directed to this path which is directed to this path then in the third
cycle i will get a count that time t equal to t seventeen right now consider you are
repeating the same ten million times that means that same cycle cycle one cycle to cycle
three cycle n cycle million times cycle ten million times and so on
so there is always a possibility that in that histogram you will get the photon of all these
different times to be accumulated right so thats what i was showing over here so here
is the laser laser is sending one signal here to start the stopwatch and then this is the
pulse train it is exciting and then this photon is coming it is not necessarily that the first
emitted photon has to be first detected photon because the spontaneous emission is direction
less and we do something over here to reduce the detection ability of the photon
so most of the photon should be lost somewhere right that i will going to discuss later probably
so that a emitted photon one of the emitted photon will reach the detector over here and
this detector will send the stop signal as you can see here and it will measure the
time so as at different different cycles you will get a different different point at different
different time like and this different at different time you will get a count
so ultimately what you can do you can plot a histogram like that as shown here for the
period one probably none of the photon has been detected in period two one photon has
been detected here nothing here one photon at this particular time here one photon at
this time here nothing here nothing here nothing here one photon this time here nothing here
one photon at this time and if you sum it up right for ten million times then what you
will get you will get a such kind of histogram which is nothing but the dependence of fluorescence
intensity as a function of time right and now if you feed this using your that equation
i equal to i zero to e to the power minus t by tau then you will be able to get the
fluorescence lifetime of your sample ok well so let let me finish here because time is
up and on the next day what i will going to show you that the basic setup which i have
shown here will actually not going to work we have to do several modification on these
basic setups to actually get this time because of several problem in this system and those
things we will going to discuss on the next class
thank you