Extention of the Distribution of Photon Counts with Censoring in Two-photon Laser Scanning Microscopy

Simsek and Iyengar dealt with a problem arises in two-photon laser scanning microscopy (TPLSM) when the detector has a dead period, and derived the distribution of the number of photons detected by using two different approaches [6, 7]. When deriving this distribution, they made standard distributional assumptions for the pulse process and exponential distribution for fluorescence lifetimes. Although exponential waiting times are well supported by theoretical considerations, it is useful to know the effect upon the results of plausible other waiting time distributions. The extension of the model to Gamma family is briefly summarized. Then, the performance of Gamma waiting times is compared with both exponential times and actual Poisson process. Based on this, it is concluded that as the shape parameter of Gamma gets larger, we have actual Poisson process as the limiting distribution.