Uniqueness A Caveat

As has long been recognized it is extremely difficult to accurately fit experimental decay curves to sums of exponentials, especially for relatively close lifetimes ( factor of 2). 55,56,59,60) That is, one can get good fits but with parameters that are physically meaningless. The same is true of many different types of models. However, the point is so important as to justify repeating. Earlier we gave several examples. 55,56 We 

To further appreciate the indistinguishability of these functions, we show the error bounds of a, assuming that the data came from an SPC instrument. Clearly, Poisson noise always greatly exceeds the differences exceptfor D3. For 104peak counts in SPC data, differentiation between any of these functions is impossible except perhaps for D3. Noise hides the differences. While we have selected only a small set of possible exponentials, clearly there is a continuum of possible lifetimes and preexponential factors that would be similarly indistinguishable. 

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