Measurements of Second-Order Properties of Point Processes

International audienceThe second order statistical properties of point processes are described by the coincidence function which can be measured by a coincidence device but such measurements are long and complicated. We propose another method of measurement and we analyze its performances. The starting point is that the coincidence function can be deduced from the probability density functions of the life times (the distances between points) of the process. The idea is to transform the point process into a positive signal whose values are these distances. From an appropriate processing of this signal we deduce the coincidence function. For the validation of the method we use point processes for which the coincidence function is known. The agreement between theory and experiment is in general excellent. Finally the method is applied to measure the coincidence functions of some point processes for which no theoretical result is available