How to Determine the Goodness of Fit in Fluorescence Lifetime Measurements?

[Hanneman]

Hi, I am trying to measure fluorescence lifetimes. Typically, the excitation pulse is measured and convoluted with an exponential decay function. This result is compared with the measured fluorescence curve in order to adjust the parameters in the decay function. The process is repeated until the calculated and measured fluorescence curves match well.

During each convolution iteration, the reduced chi squared value is computed to determine the goodness of fit between the calculated and measured fluorescence curves. A value greater than 2 indicates a poor fit while a value less than 1.2 indicates a good fit. The formula is:

Chi^2 = (1/N) * Sum_over_i [ ( Measured(i) - Calculated(i) ) / Measured(i) ]

N is the number of data points.

This only applies for Poisson statistics, which is valid for photon counting. But, we are using a PMT and a scope with a 1GHz bandwidth (until the cost of new equipment can be justified), so the above equation does not apply.

I have searched through older journals and have not found a different way to determine the goodness of fit. Does anyone have any ideas? Thank you in advance.

 

[Hurkyl]

You could use the same scoring function, but figure out what it's actual distribution should be instead, either analytically, or through simulation.

 

[sir-pinski]

Thank you for your question about using the chi squared statistic in fluorescence lifetime measurements. It is important to consider the limitations and assumptions of this statistical test, especially in your specific experimental setup.

First, it is important to note that the chi squared statistic is commonly used in fitting models to data, as it provides a measure of the difference between the observed data and the expected values from the model. However, as you mentioned, this statistic is only valid for Poisson statistics, which assumes that the data is discrete and follows a specific distribution. In your case, using a PMT and scope with a 1GHz bandwidth may not meet this assumption, as the data may not follow a Poisson distribution.

In situations like this, it may be more appropriate to use a different statistical test, such as the Kolmogorov-Smirnov test or the Anderson-Darling test, which do not rely on the assumption of Poisson statistics. These tests can be used to assess the goodness of fit between your calculated and measured fluorescence curves.

Additionally, it may be helpful to consult with a statistician or an expert in fluorescence lifetime measurements to determine the most appropriate statistical test for your specific experimental setup. They may also be able to provide guidance on any adjustments or modifications that can be made to your methodology in order to use the chi squared statistic effectively.

Overall, it is important to carefully consider the assumptions and limitations of any statistical test used in your research, and to seek out expert advice when necessary. I hope this helps clarify the use of the chi squared statistic in fluorescence lifetime measurements. Best of luck with your research!