  We compute the onium-onium scattering amplitude at fixed impact parameter in
the framework of the perturbative QCD dipole model. Relying on conformal
properties of the dipole cascade and of the elementary dipole-dipole scattering
amplitude, we obtain an exact result for this onium-onium scattering amplitude,
which is proven to be identical to the BFKL result, and which exhibits the
frame invariance of the calculation. The asymptotic expression for this
amplitude and for the dipole distribution in an onium at fixed impact parameter
agree with previous numerical simulations. We show how it is possible to
describe onium-$e^{\pm}$ deep inelastic scattering in the dipole model, relying
on k_T-factorization properties. The elementary scattering amplitudes involved
in the various processes are computed using eikonal techniques.
