One-layer spectral contrast (source code)

= One-layer spectral contrast

A non-scattering isothermal atmospheric layer in <local thermodynamic equilibrium>, of <temperature> $T_a$ and slant <optical depth> $t_\lambda$, lies above a <blackbody> background at $T_b$. The <specific intensity> is
$$
I_\lambda=B_\lambda(T_b)e^{-t_\lambda}+B_\lambda(T_a)(1-e^{-t_\lambda}).
$$
Thus an increase in <opacity> shifts the <specific intensity> toward the layer's <Planck function>. If a line is more opaque than its continuum, it appears in absorption for $T_a<T_b$, in emission for $T_a>T_b$, and has no contrast for $T_a=T_b$. This is a local explanation, not a claim that all features diagnose one uniform layer.