  We perform scanning gate experiments on ballistic constrictions in the
presence of small perpendicular magnetic fields. The constrictions form the
entrance and exit of a circular gate-defined ballistic stadium. Close to
constrictions we observe sets of regular fringes creating a checker board
pattern. Inside the stadium conductance fluctuations governed by chaotic
dynamics of electrons are visible. The checker board pattern allows us to
determine the number of transmitted modes in the constrictions forming between
the tip-induced potential and gate-defined geometry. Spatial investigation of
the fringe pattern in a perpendicular magnetic field shows a transition from
electrostatic to magnetic depopulation of magnetoelectric subbands. Classical
and quantum simulations agree well with different aspects of our observations.
