Optimizing sampling time in single photon counting experiments

The so-called "point fractal" concept is applied in the paper for analyzing the time-scale variability of point processes that are recorded in photon counting experiments. A new algorithm (based on a fuzzy controller) for estimating the fractal dimension is applied to eliminate systematic as well as stochastic errors. It is shown that there exists a scale-invariant region in time, and clustering decreases in accordance with the increase of threshold that corresponds to the inverse sensitivity of the detector. Under threshold variation it is confirmed that the maxima of homogenous scale-invariant intervals are just the same. In addition, taking the probability scale law on different levels of threshold, a relationship is established between the saturation scale (return period) and the threshold value (design experiment variable).