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.
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