  We study the coherent properties of transmission through Kondo impurities, by
considering an open Aharonov-Bohm ring with an embedded quantum dot. We develop
a novel many-body scattering theory which enables us to calculate the
conductance through the dot, the transmission phase shift, and the normalized
visibility, in terms of the single-particle T-matrix. For the single-channel
Kondo effect, we find at temperatures much below the Kondo temperature $T_K$
that the transmission phase shift is \pi/2 without any corrections up to order
(T/T_K)^2. The visibility has the form 1-(\pi T/T_K)^2. For the non-Fermi
liquid fixed point of the two channel Kondo, we find that transmission phase
shift is \pi/2 despite the fact that a scattering phase shift is not defined.
At zero temperature the visibility is 1/2, thus at zero temperature exactly
half of the conductance is carried by single-particle processes. We explain
that the spin summation masks the inherent scattering phases of the dot, which
can be accessed only via a spin-resolved experiment. In addition, we calculate
the effect of magnetic field and channel anisotropy, and generalize to the
k-channel Kondo case.
