Dear Saurabh,

it is not trivial to answer your question as you don't provide information about how you assess the quality of your decay (Chi2, residuals?). A decay curve that you can fit with a single exponential decay can also be fitted with a two-component exponential decay function but the lifetime parameters obtained do not necessarily reflect the fluorescence decay of your molecule. This is especially true when the second component has an amplitude such as the one you obtain (2-4%)

For fluorescein at low concentrations of fluorophore and salt and in aqueous solution at pH 13, I would definitely expect a single exponential decay with a lifetime between 4.1 and 4.5 ns (the range of values found in the litterature).

The long exponential decay time that you obtain is very little (2 to 4%).  It might be because: you fit the tail of your decay (the noise); your IRF has a tail that is not taken into account by the deconvolution software; the fluorescence cuvette is dirty or there is a problem with the optical path (scattering from somewhere?)... or from the system parameters.

Before anything I would evaluate whether the single exponential fit is acceptable or not. If it is then it is a mistake to consider a two component exponential fit even if it has a better Chi2.

Hope that helps,

Mathieu

I agree with Mathieu considerations. Fitting  a decay curve is most of the time an hill posed problem and you can't decide the number of exponentials from common quality-of-fit assessments.

A 2-4% amplitude for a second exponential is well below the sensitivity that you can reach. As Mathieu said, there are several possible experimental or mathematical explanations.

As a last remark, if your baseline (uncorrelated background) has an average value of ~10 or less you should use an MLE fit and not a least-squares.

See this ipython notebook for an example of MLE fit:

http://nbviewer.ipython.org/github/tritemio/notebooks/blob/master/Lifetime_decay_fit.ipynb

Thanks for your answer Mathieu!

I am using Chi square/residuals to assess the quality of my fit.

May I ask what do you mean by " would evaluate whether the single exponential fit is acceptable or not."? Since the lifetime is short (4.5 ns) as compared to TAC (50 ns), I don't see many photons arriving after 25 ns in my histogram. When I am fitting my decay profile (0-25 ns) to single exp. fit, chi square is somewhat like 6, and when I fit it to double exponential , the value reduces to 2 with 99% fraction corresponding to 4.3 ns and 1% corresponding to 25 ns. However, when I fit it to (0-50 ns), chi square for single exponential fit is around 22 and for double exponential fit, it again reduces to 3. However, this time a 4-5% component corresponds to 8 ns and it changes substantially as compared to 95-96%% component (--4.5 ns) if I change any criteria, for example tail fitting, noise background, irf background etc. 

Also could you please elaborate more on the problems that I could encounter with the optical path?

Thanks,

Saurabh

Dear Saurabh,

Although it is challenging for me to assist from here, I suspect that you are not selecting the appropriate range for fitting your decay. I would suggest that you use a fluorescence standard such as Rhodamine B in methanol (check this paper and the SI for lifetime standards: Fluorescence Lifetime Standards for Time and Frequency Domain Fluorescence Spectroscopy) and try to retrieve the given lifetime and a Chi2 close to 1.

You are fitting the decay curve from 0 ns but I imagine that the peak of the decay (the channel with the most counts) is a few ns after this? If you deconvolute, try to fit around the peak but do not start your fitting range much before that. Check some publications and look at the typical range that researchers have used to fit their curves.

What I mean with the optical path can be for example if your excitation source is clipping somewhere (e.g. entrance of the chamber) or the beam reflects on some surfaces after passing through your sample...

Cheers,

Mathieu

Dear Saurabh,

I have few basic questions to you to solve your problem. What is the emission you are monitoring for fluorescein dianion? I am sure you have observed the steady state emission spectrum of the dianion which wavelength you are exciting your sample.Does the emission pattern changes with different excitation wavelengths. If there is more than one species then you can run a quick check by varying the monitoring emission wavelength (TimeResolvedEmissionSpectrum is recommended). After fitting (keep chi sq. within 1, error limit of 0.1), you can see the contributions from each species. Depending upon the decay pattern your fitting criteria may change. Here I have attached one file to show how you may fit your decay. The residual should have a definite repeating pattern.

Hope this helps.

Best,

Debanjana

Hi

If I may, I would like to add some useful pointers to the discussion:

1. What do you mean by deconvolution? Does the software literally deconvolute the theoretical decay out of the experimental one or does it assume a form of a theoretical decay and iteratively convoloutes it with the IRF to match the experimental decay (reconvolution)? The second approach is the approach of choice. The first approach is usually numerically unstable.

2. How do you record your IRF? Sometimes the shape of an IRF after the emission filter/monochromator is different than what it would be measured by a scattering solution. This is called color corrected IRF. You can record it by measuring the a fluorophore of choice in high KI concentrations, so it'll become so quenched, its lifetime will be shorter than your pulse width. Alexa488 in 6M KI worked fine for me for approximately the same emission bands you are measuring. That can be done of course if you pulsed are not too short but in the ps time domain. Sometimes these subtle effects can yield different IRF shapes that eventually lead to artifacts in IRF reconvolution

3. Baseline- you can either fit your data to an exponential function with a baseline to account for possible background effects; you can also choose not to fit the whole decay but include a portion of it in the fitting procedure, so that the background effect would be small; You can also measure the solution in which you dissolved fluorescein, in exactly the same conditions for the same period of time and then subtract this blank from a decay. This sometimes works.

4. Chi Square is not enough! especially if you get values as low as 2, which are very high. Use the reduced chi square, with the standard deviation evaluated as poisson weights. But, chi square is just a normalized squared summation of your residuals. A good fit would leave residuals that behave like white noise (mean of 0 and no autocorrelation). Therefore better check these two features for statistical estimation.

5. A bad fit of 1exp. does not necessarily mean that you can move on directly to the 2 exp. fit. Remember that, sum of 2 exponentials and monoexponential models are nested models - monoexponential model is a private case of the 2 exponent model. In statistical inference, when comparing nested models for their best fit characteristics test the general case (2 exp.) only after you have shown that the private case (1 exp.) has statistically significantly failed - a bad fit by some statistical significance test criterion relating to the fitting residuals).

6. Choose a range for the fitting procedure. I find it useful to fit my decays so that I include as much as possible the convoluted part, and up to counts which is 1% out of the maximal count.

Hi Eitan! thank you for your reply! 

1. I looked at the details of my software and it says that the software uses iterative reconvolution with a least squares analysis for fitting.

2. I record my IRF using water as a scattering solution. For IRF, my setup looks like: (please refer attachment) laser--cuvette--90 degree --collecting lens--collimated beam ---converging lens--polychromator--detector--routing electronics

I cover my setup with a temporary black box to avoid stray room light reaching the detector. However, when I put my samples in, I generally put a 470 nm longpass filter between 2 lenses so that I can shun scattered photons to reach the detector. That way, the detector doesn't saturate quickly and I can collect data for longer period of time to improve my S/N ration.

Though, I just realized that filters can also fluoresce and can affect the decay profile. I am going to test that hypothesis by removing the filter and operating polychromator in 500-700 nm region.

I generally operate the detector at 95% gain however I change laser gain(/intensity) depending upon the CFD count to insure that at max 1 photon per pulse is detected. Earlier I saw that changing laser gain does change IRF to some extent but it is almost invisible. I was thinking about putting a neutral density filter to manipulate intensity of excitation light.

Also, I just purchased 2 polarizers to set up magic angle detection. I was wondering if that could affect my decay profile.

3. I haven't tried the subtraction of blank yet. As I mentioned earlier, the log decay profile looks linear initially (0-25 ns) but then it flattens a little bit suggesting a longer lifetime component. Please refer fig.2.

Please reply whenever you get the chance.

Hi

Thanks for the details. First thing I see when looking on your system is that the system is open, after the cuvette holder. Try to close up the system, starting from the cuvette holder and ending after the detector. This will help a lot with stray light. Second thing - water is not really a good IRF measurement solution. If you insist on measuring your IRF at the wavelength of excitation, you can dissolve some scattering materials like scattering beads or glycogen, which yield strong scattering. If you measure fluorescence at a different wavelength range than the excitation wavelength (as is done usually), it would be better to record the IRF the same way. I do it by taking my dye of choice, that has the fluorescence at the right wavelength range, and reduce its lifetime by collisional quenching using high concentrations of Iodide (KI), until the lifetime of the free dye is so small it can be literally regarded as a delta function in comparison to the IRF width.

From convolution theory, a convolution of a function, f, with a delta function, gives the function f, hence you achieve the experimental IRF at the conditions of measurements. This way you also gain an IRF quickly with high S/N and with low background.

In respect to magic angle polarizers - it is always better using them, especially if you suspect differences in parallel and perpendicularly polarized fluorescence in slowly rotating systems.

In respect to the decays and their fits you show here, you can always simulate a perfect singly exponential decay, add poisson noise to it, convolute it with your experimental IRF and then try to fit it to a single exponential function and see whether you get a good fit with the same lifetime as the simulated one. Other than that, I suggest you try redoing fits to measurements after you took care all experimental considerations written above.