Illustration of the MC code’s geometry, coordinates, and calculation of the line-of-sight optical depth. A photon packet located at r₀ is moving in direction $\widehat{n}$. We computed the accumulated optical depth by dividing the line of sight into a sequence of points r₀ using an adaptive step-size algorithm. We then sampled a target optical depth, τ_rnd, and determined the position of the next scattering event via linear interpolation between the discretized points. We assumed a uniform magnetic field because the height of the line-forming region is much smaller than the NS radius.