Weak measurements typically require two non-orthogonal states, which are not eigenstates of an observable. This is why weak values of the orbital angular momentum operator seem counterintuitive or involve additional auxiliary observables, such as polarization. We show how the use of states emerging from spiral phase plates or holograms with fractional step height can be used to construct weak values of the orbital angular momentum operator.
Jörg B. Götte, Jörg B. Götte,
"Weak measurements with non-integer orbital angular momentum states", Proc. SPIE 8999, Complex Light and Optical Forces VIII, 899917 (25 February 2014); doi: 10.1117/12.2041671; https://doi.org/10.1117/12.2041671