Illustration of the effective volume projected in ϕ–R space for the case with dust. Panel a shows the map of the selection fraction computed using the sub-binning method, and it shows a continuum of probability between 0 (unobservable) and 1 (fully observable). In panel b, we show the same voxels as in panel a, but for these the selection fraction is shown for the method without sub-binning. This shows that several voxels from panel a that have a probability of being observed would be considered unobservable or would be completely observed using the incorrect method of estimating the selection function. In both panels, the location of the Sun is indicated by the black star.