Setup of the analytical model. The background light source is exactly along the LoS. The top blue arrow shows the rays of light from the background light source to the infinitesimal element ds (marked in a gray rectangle) at projected radius b, and LoS coordinate s. The lower blue arrow shows the ray of light from the same element to the observer at the bottom. The small red rectangle shows an infinitesimal extinction element for the incoming light (we integrate over all of these for the total extinction), and the small purple rectangle shows a similar extinction element for the outgoing light.