  A probability distribution function is presented which provides a realistic
description of the detection of scattered photons. The resulting probabilities
can be described analytically by means of a superposition of several special
functions. These exact expressions can be evaluated numerically only for small
distances and limited time residuals, due to computer accuracy limitations. In
this report we provide approximations for the exact expressions in different
regions of the distance-time residual space, defined by the detector geometry
and the space-time scale of an event. These approximations can be evaluated
numerically with a relative error with respect to the exact expression at the
boundaries of less than 0.001.
