Schematic showing how the global two-layer model computes the flux of the reprocessed starlight from the irradiation surface to the optically thick interior. The irradiation surface is decomposed into thin ring elements of radius r′ lying at height z = z_s(r′) above the midplane. Each ring element is further divided into segments of azimuthal width r′dφ′. The disk interior that is optically thick to infrared thermal radiation receives the reprocessed starlight on its surface (thermal photosphere) lying at height z = z_IR(r). The flux of the reprocessed starlight from each ring element to position [r, z_IR(r)] is calculated by integrating the contributions |$d{\boldsymbol F}_{\rm rep,\downarrow }$| from the constituting segments.