Optically thin medium

An optically thin medium has $\tau \ll 1$, so attenuation and emission may be expanded to first order in optical depth.

For isotropic emission without significant absorption, integrating the spontaneous photon-production rate along the sightline gives the displayed energy intensity per solid angle. Photon intensity omits the factor $h\nu$. Summing unresolved transitions is necessary before comparing with an observed blended spectral feature.