Identification of photon sources, stochastically embedded in an interstellar cloud

Photon transport is considered in an interstellar cloud containing one or several photon sources (stars), defined by q_i*delta(x - x_i), i = 1, 2,..., where the locations x_i are given in a stochastic way. First, the case is examined of a single source of intensity q_1 and located at x_1 with a probability density p_1 = p (x_1), concentrated in a subset V of R^3, representing the region occupied by the cloud. Then, a Boltzmann-like equation for the average photon distribution function <n> ( x, u; x_1) is derived and it is shown that p(x_1) can be evaluated starting from a far-field measurement of <n>. Finally, the case of two or more photon sources is discussed: the corresponding results are reasonably simple if p(x_1, x_2) = p_1(x_1)*p_2(x_2), i. e. if the locations of the two photon source are independent.