Modeling Photon Counting Experiments using Fuzzy Logic Controller

Abstract

The concept of point fractal is applied to analyze the time-scale variability of point processes resulting from photon counting experiments. A new algorithm – using a fuzzy logic controller – for estimating the fractal dimension is proposed to eliminate systematic and stochastic errors. It is shown that scale invariance exists in time and clustering will decrease in accordance with the increase of the threshold that corresponds to the inverse sensitivity of the detector. Under the variation of the threshold, it is verified that the maximum values of the homogenous scale invariant interval are the same. In addition, taking the probability scale law on different levels of threshold value, a relation is established between the saturation scale (return period) and the threshold (design experiment variable).