The nuclear overlap zone in non-central relativistic heavy ion collisions is
azimuthally very asymmetric. By varying the angle between the axes of
deformation and the transverse direction of the pair momenta, the transverse
HBT radii oscillate in a characteristic way. It is shown that these
oscillations allow determination of source sizes, deformations as well as the
opacity and duration of emission of the source created in any non-central high
energy nuclear collisions. The behavior of the physical quantities with
centrality of the collisions is discussed --- in particular changes caused by a
possible phase transition to a quark-gluon plasma.Comment: Revised version, to appear in Phys. Rev. Letter