1. May 2, 2005

### 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.

2. May 2, 2005

### Hurkyl

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