  We address the question of interpolation of the virtual Compton scattering
process off a polarized nucleon target between the deeply virtual regime for
the initial-state photon and its near on-shell kinematics making use of the
photon helicity-dependent Compton Form Factors (CFFs) as a main ingredient of
the formalism. The five-fold differential cross section for the reaction with
all possible polarization options for the lepton and nucleon spins is evaluated
in terms of CFFs in the rest reference frame of the initial-state nucleon. We
suggest a rather simple parametrization of the Compton hadronic tensor in terms
of CFFs which are free from kinematical singularities and are directly related,
at large photon virtualities, to Generalized Parton Distributions. We also
provide a relation of our basis spanned by a minimal number of Dirac bilinears
to the one introduced by Tarrach for the parametrization of the virtual Compton
tensor and utilize the former to establish a set of equalities among our CFFs
and Generalized Polarizabilities. As a complementary result, we express Compton
scattering in the Born approximation in terms of CFFs as well.
