  Here, we report on our results where self-consistent calculations are
performed to investigate the interference conditions, numerically. We employ
the successful 4$^{th}$ order grid technique to obtain the actual electrostatic
quantities of the samples used at the quantum Hall based Aharonov-Bohm
interferometers. By knowing the electron density distribution we calculate the
spatial distribution of the edge-states, which are considered as mono-energetic
current channels. Our results are in accord with the experimental findings
concerning the electron density distribution. Finally, we also comment on the
"optimized" sample design in which highest visibility oscillations can be
measured.
