Two formulae are derived which make it possible to determine the normalized source spectrum and the degree of spectral coherence of any planar, secondary, quasi-homogeneous source of a certain class, from the knowledge of the far-zone spectrum of the radiated field. The results are illustrated by computed curves. The new inversion formulas are also used to derive a generalized version of a scaling law (1986,Phys. Rev. Lett.,56, 1370) for the invariance of the normalized spectrum of light on propagation in free space.