In your Origin file, column A(X) is t, and column B(Y) is I(t). To calculate the average lifetime of your decay curve, I(t), all you have to do is:

1. Add new column C(Y) to the Book containing A(X) and B(Y). Right-click on the column C(Y) and choose "set column values". Type col(A)*col(B). You generated I(t)*t. Plot C(Y) as a function of column A(X). You plotted I(t)*t. Now you have to integrate this function (when the plot is active, click Analysis/Mathematics/Integrate). If you do this correctly you will get the value denoted as "area". It is the numerator in the equation for average lifetime: =Integrate[I(t)*t]/Integrate[I(t)].

2. Plot B(Y) as a function of A(X), integrate it. Again, you need the "area" value, which is now the denominator of our equation.

3. Divide area 1 by area 2. You calculated the average lifetime.

Before you do this calculations try to practice, e.g. generate in Origin a simple function, like I(t)=100*exp(-t/10). Try to calculate the average lifetime of this function with the above method. In this case you should obtain =10 for the average lifetime.

There is, however, one important issue and you should be aware of it. Namely, you have to know the "zero level" of your decay curve. In other words, your curve I(t) has to decay to zero. In real measurements the decay curve never decays to zero, due to the experimental background. This background level has to be subtracted from I(t) before calculating the average lifetime with the above method. So, when you measure a decay curve always make sure that you see the background level. Otherwise your I(t) curve is not complete, which makes calculations/fitting difficult. Another thing is that the average lifetime calculated for one sample only, does not tell you too much about physics (it is just a number). Nevertheless, if you have more samples, you can try to look for a tendency and suggest an interpretation. Good luck!

I don't think its right to control the parameters unless you have a reason to do so. The value of the lifetime will be the one you get after iteration to a best fit. Check the reliability of the fit using various means, for example, residuals. The number of components in your fit, one or more exponentials, should also be justified for instance, can you explain the existence of more than one lifetime in your sample.

You have to use the mono - bi- or tri- exponential decay function and fit your trace . Then you can extract from the fitting the tau1 or/and tau2 or/and tau3 depends on the function you are using , Also you can calculating the weighting of each component . If The fittinf is not good enough (you can check the x^2 to be more or less 1) and you get better fitting with quatromonoexponential decay , check the weight of the fourth component should be very low and usually we dont trust it so much .

I think, the global fitting is the best method...in this (http://www-ipcms.u-strasbg.fr/IMG/pdf/BRIAND_2009.pdf) thesis can you find more technical and mathematical data in the first step...

You could use the formula ‹τ› = ∑ αi *τi(power 2) / ∑ αi *τi,

I am not familiar with the program you use to fit your decay curves, but in analyzing luminescence decay, I used a hand-written program (Matlab, Fortran, etc.). Decays were fit by linearizing the fitting function according to the Marquardt Algorithm (Marquardt, 1963), which was used to fit the decay to one or more lifetime components. Satisfactory fits were judged by examination of the fitted decay, the weighted residuals, the autocorrelation of the residuals, and the reduced chi-square values. If the intensity of the decay curve is described by the function

I(t)= ∑ αi * exp ( -t/τi)

then the mean (intensity weighted) lifetime is given by the equation suggested by Tej Yenupuri earlier in this thread:

‹τ› = ∑ αi *τi(power 2) / ∑ αi *τi

During the fit, all αi and τi paramaters were not constrained, and were iteratively adjusted until convergence was achieved according to acceptably small changes in each parameter, again as judged by the weighted residuals, the autocorrelation of the residuals, and the reduced chi-square values.

You do not need to fit your data in order to calculate the average lifetime for a decay curve. All you have to do is to treat the measured decay curve I(t) as a probability density function. Then you can use the formula for average value (expected value) of a random variable, which is time in this case. Average lifetime can be calculated according to the equation: =Integrate[I(t)*t]/Integrate[I(t)], where the integration is over t and the denominator is introduced for normalization. In this way you can easily calculate the average lifetime for a given decay curve without making any assumptions about the model.

Which instrument are you using for doing experiment and collecting data?

Hej Nguyen,

just a few more things:

1.) Whenever you do a fitting with a fit function, you must have a model of the dynamics you want to fit. If you expect something like A --> B --> C this might be two exponentials ... unless of course you know that your process obeys a non-exponential decay as Förster energy transfer. In addition, make sure that you get a proper description of the convolution (experimental response function) which is a Gaussian in the simplest case.

2.) Depending on your method, it might be that you do not observe all processes in your data. Sometimes, there are processes that show different time constants in different regions. For example if you consider ground state cooling in transient absorption spectroscopy.

3.) If you have several traces, you should try a global fitting routine, but it always halps to also fit single traces.

4.) The method of Grzegorz is called maximum entropy analysis and is a method to estimate the number of processes in your data, it is a good method but not implemented in Origin.

5.) In Origin (your question), you can fix certain parameters to values you like and leave some parameters free running. Sometimes you have to do it to make the fit converge.

Thank all of you so much for considering my question.

The enclosed data is the time decay profile and my fitting results using tri- exponential decay function. The components of A and t go overload and it look imposible to calculate average lifetime. Please suggest what I have to do. I did anything wrong or the results were not good?

In your Origin file, column A(X) is t, and column B(Y) is I(t). To calculate the average lifetime of your decay curve, I(t), all you have to do is:

1. Add new column C(Y) to the Book containing A(X) and B(Y). Right-click on the column C(Y) and choose "set column values". Type col(A)*col(B). You generated I(t)*t. Plot C(Y) as a function of column A(X). You plotted I(t)*t. Now you have to integrate this function (when the plot is active, click Analysis/Mathematics/Integrate). If you do this correctly you will get the value denoted as "area". It is the numerator in the equation for average lifetime: =Integrate[I(t)*t]/Integrate[I(t)].

2. Plot B(Y) as a function of A(X), integrate it. Again, you need the "area" value, which is now the denominator of our equation.

3. Divide area 1 by area 2. You calculated the average lifetime.

Before you do this calculations try to practice, e.g. generate in Origin a simple function, like I(t)=100*exp(-t/10). Try to calculate the average lifetime of this function with the above method. In this case you should obtain =10 for the average lifetime.

There is, however, one important issue and you should be aware of it. Namely, you have to know the "zero level" of your decay curve. In other words, your curve I(t) has to decay to zero. In real measurements the decay curve never decays to zero, due to the experimental background. This background level has to be subtracted from I(t) before calculating the average lifetime with the above method. So, when you measure a decay curve always make sure that you see the background level. Otherwise your I(t) curve is not complete, which makes calculations/fitting difficult. Another thing is that the average lifetime calculated for one sample only, does not tell you too much about physics (it is just a number). Nevertheless, if you have more samples, you can try to look for a tendency and suggest an interpretation. Good luck!

The fit looks reasonable. Just adding a few comments to the one of Grzegorz:

1. Little can be said without more information about the process (do three time constants make sense? What is the meaning of these constants?)

2. I there an oscillation on the signal (it makes the impression as if there is)?

3. You probably need a second measurement to confirm your data.

4. You can test your fit by looking at the residuals, i.e. the difference between your fit and the data. If you see more than just noise, something else might go on.

Which instrument u have measured life time decay'

We used the FLS920 FLUORESCENCE LIFETIME SPECTROMETER (Edinburgh Photonics) to obtain the time decay profiles. We found the software to calculate the average lifetime from this site http://www.fluortools.com/home

Thank all of you for considering my question.

I also used this instrument to obtain lifetime..but data is not fitted with expoential curve..wat to to calculate the value of lifetime?

Hey just for the sake of information, if you use the logarithmic time scale it helps to better resolve the components and offers a better view of the transients. 

One of the most practical approach is plot the emitted photoflux phi(t) as a function of time t. If the there is more one time constant of the decay with the time constants are different from each other for example three time constants with small value , large value and medium value such that Tau1

Hello thank you for answering

Grzegorz Zatryb Could you please let me references in support of your explanation. Why multiplying using t?