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Averaging Correlation Times vs. Averaging Diffusion Coefficients

Table 1.
τD (ms) D x 10-8 cm2/sec
76.377.37
77.277.28
62.738.97
89.536.28
144.53.89
101.95.52
62.998.93
162.73.46
122.54.59
154.83.63

There is a small but important issue to keep in mind when averaging data from FCS measurements. Consider Table 1, to the right. In the first column we list a set of correlation times, τD, obtained for a sample with an FCS instrument. In the second column we have calculated the diffusion coefficients (D) based on a beam radius of 1.5 µm and using the equation:

Equation 1

If we average the column of correlation times we obtain (106 ± 38) ms. If we use this average correlation time to calculate an average diffusion coefficient, we obtain (5.4 ± 1.9) x 10-8 cm2/s. If we instead average the column of diffusion coefficients, we obtain D = (6.0 ± 2.1) x 10-8 cm2/s. The diffusion coefficient obtained from averaging the diffusion coefficients is 11% higher than that obtained from the average correlation time. This is because averaging correlation times favors large times, while averaging diffusion coefficients favors short times.

Which is the correct number to report? Here is the bad part, both are acceptable. What is important is that you specify how your measurements were done, and that, if you are comparing your results to someone else's, you need to know how they obtained their averages.