Calibration of probe volume in fluorescence correlation spectroscopy

In fluorescence correlation spectroscopy (FCS), an accurate evaluation of the probe volume is the basis of correct interpretation of experimental data and solution of an appropriate diffusion model. Poor fitting convergence has been a problem in the determination of the dimensional parameters, the beam radius, omega, and the distance along the optical axis of the probe volume, l. In this work, the instability of fitting during the calibration process is investigated by examining the chi(2) surfaces. We demonstrate that the minimum of chi(2) in the omega dimension is well defined for both converging and diverging data. The difficulty of fitting comes from the l dimension. The uncertainty in l could be significantly larger than that in omega, as determined by F-statistics. A modified calibration process is recommended based on examining two data treatment methods, combining several short data sets into a single long run and averaging the correlation functions of several short data sets. It is found that by using the mean of several converging correlation functions from short data sets instead of a long time correlation, more stable and consistent dimensional parameters are extracted to define the probe volume.