Constant source transfer through a thin layer
= Constant source transfer through a thin layer
{title2=$I_{\rm out}=I_{\rm in}e^{-\tau}+S(1-e^{-\tau})$}
Along a radial ray through a layer with constant <source function>, the incident <specific intensity> is attenuated by $e^{-\tau}$ and the layer adds $S(1-e^{-\tau})$. At small <optical depth>, $I_{\rm out}=I_{\rm in}+(S-I_{\rm in})\tau+O(\tau^2)$. Whether the source exceeds the incident <specific intensity> determines the first-order emission or absorption contrast.