  Fabry-P\'{e}rot interferometry has emerged as a tool to probe anyon
statistics in the quantum Hall effect. The interference phase is interpreted as
a combination of a quantized statistical phase and an Aharonov-Bohm phase,
proportional to the device area and the charge of the anyons propagating along
the device edge. This interpretation faces two challenges. First, the edge
states have a finite width and hence the device area is ill-defined. Second,
multiple localized anyons may be present in states that overlap with the edge,
and it may not be clear whether a second anyon traveling along the edge will go
inside or outside the region with a localized anyon and therefore whether or
not it should pick up a statistical phase. We show how one may overcome both
challenges. In a case where only one chiral edge mode passes through the
constrictions defining the interferometer, as when electrons in a constriction
are in a Laughlin state with $\nu=1/(2n+1)$ or the integer state at $\nu=1$, we
show that the interference phase can be directly related to the total electron
charge contained in the interferometer. This holds for arbitrary
electron-electron interactions and holds even if the bulk of the interferometer
has a higher electron density than the region of the constrictions. In contrast
to the device area or to the number of anyons inside a propagating edge
channel, the total charge is well-defined. We examine, at the microscopic
level, how the relation between charge and phase is maintained when there is a
soft confining potential and disorder near the edge of the interferometer, and
we discuss briefly the complications that can occur when multiple chiral modes
can pass through the constriction.
