  We investigate the quasiparticle excitations in the FFLO- type helical state
of a superconductor with inversion-symmetry breaking and strong Rashba
spin-orbit coupling. We restrict to a state with single finite momentum of
Cooper pairs in the helical phase that is determined by minimization of the
condensation energy. We derive the dependence of quasiparticle dispersions on
the Rashba coupling strength and external field. It leads to a peculiar
momentum-space segmentation of the corresponding Rashba Fermi surface sheets
which has not yet been observed experimentally. We show that it may be directly
visualized by the method of quasiparticle interference that identifies the
critical points of the segmented sheets and can map their evolution with field
strength, bias voltage and Rashba coupling. We also indicate a strategy how to
determine the finite Cooper-pair momentum from experimental quantities. This
investigation has the potential for a more detailed microscopic understanding
of the helical superconducting state under the influence of Rashba spin-orbit
coupling.
