  A comparative study is performed on two heterodyne systems of photon
detectors expressed in terms of a signal annihilation operator and an image
band creation operator called Shapiro-Wagner and Caves' frame, respectively.
This approach is based on the introduction of a convenient operator $\hat \psi$
which allows a unified formulation of both cases. For the Shapiro-Wagner
scheme, where $[\hat \psi, \hat \psi^{\dag}] =0$, quantum phase and amplitude
are exactly defined in the context of relative number state (RNS)
representation, while a procedure is devised to handle suitably and in a
consistent way Caves' framework, characterized by $[\hat \psi, \hat
\psi^{\dag}] \neq 0$, within the approximate simultaneous measurements of
noncommuting variables. In such a case RNS phase and amplitude make sense only
approximately.
