  In this paper we provide a consistent framework to address the notorious
decomposition of the single-photon total angular momentum (TAM) into a spin
(SAM) and an orbital (OAM) component. In particular, we find that the canonical
SAM and OAM, generators of internal and spatial rotations respectively in the
space of physical states, are mutually compatible but unsharp quantum
observables, therefore POVM (Positive Operator-Valued Measures) describe their
joint measurements. On the other hand, a non-canonical SAM and OAM can be
constructed that is mutually incompatible but represent sharp quantum
observables, thus PVM (Projector-Valued Measurements), reflecting their
consistency with the transversality condition characterizing singlephoton
wavefunctions. We discuss the implementations on joint measurements for both
decompositions and provide an explicit calculation of all these quantities for
circularly polarized Gaussian single-photon states.
