Realistic arrival time distribution from an isotropic light source

The event reconstruction in high energy neutrino telescopes is based on the expression of the time delay distribution of the detected photons propagating to some distance from their emission point through a uniform and scattering medium. Considering a realistic detector with a finite time resolution, we derive an expression for the probability density function of the time delay of detected photons. The asymptotic properties of this function as well as its corresponding cumulative probability distribution are calculated and discussed.