Variations on a classical theme: On the formal relationship between magnitudes per square arcsecond and luminance

The formal link between magnitudes per square arcsecond and luminance is discussed in this paper. Directly related to the human visual system, luminance is defined in terms of the spectral radiance of the source, weighted by the CIE V($\lambda$) luminous efficiency function, and scaled by the 683 lm/W luminous efficacy constant. In consequence, any exact and spectrum-independent relationship between luminance and magnitudes per square arcsecond requires that the latter be measured precisely in the CIE V($\lambda$) band. The luminance value corresponding to m_VC=0 (zero-point of the CIE V($\lambda$) magnitude scale) depends on the reference source chosen for the definition of the magnitude system. Using absolute AB magnitudes, the zero-point luminance of the CIE V($\lambda$) photometric band is 10.96 x 10^4 cd/m^2.