  Observations of the fluorescent Fe K-alpha emission line from the inner
accretion flows of stellar mass black holes in X-ray binaries and supermassive
black holes in Active Galactic Nuclei have become an important tool to study
the magnitude and inclination of the black hole spin, and the structure of the
accretion flow close to the event horizon of the black hole. Modeling spectral,
timing, and soon also X-ray polarimetric observations of the Fe K-alpha
emission requires to calculate the specific intensity in the rest frame of the
emitting plasma. We revisit the derivation of the equation used for calculating
the illumination of the accretion disk by the corona. We present an alternative
derivation leading to a simpler equation, and discuss the relation to the
previously published results.
