Coordinate system of the starless core on the (x,z)-plane with the ẑ direction towards the observer. The position in the plane of the sky is defined by r₀. Each line of sight, ŝ, corresponds to a distinct visual extinction, A_V, calculated from the gas volume density profile along this direction. At a location r_i on the sight line, the physical parameters (such as gas density, temperature, and radiation field) are assumed to be uniform on the dashed circle.