Fig. 2. a In the `traditional' formulation of the Monte Carlo method for solving radiative transfer, the radiation field is represented by a certain number of photon packages. Each of these packages originates in a random position of the cloud, corresponding to spontaneous emission, and travels in a random direction through the cloud until it either escapes or is absorbed. To include the CMB field, a separate set of packages is included, shown as dashed arrows, that originate at the cloud's edge. The packages traversing a cell during an iteration give in that cell. b  In our implementation, an equivalent estimate of is found by choosing a certain number of rays which enter the cell from infinity (or the cloud's edge, using the CMB field as a boundary condition) from a random direction and contribute to the radiation field at a random point in the cell's volume. As Sect. 3.4 argues, this formulation allows separation between the incident radiation field and the locally produced radiation field, which accelerates convergence in the presence of significant optical depth.