  We study a Gaussian model of the membrane of red blood cells: a "phantom"
triangular network of springs attached at its vertices to a fluid bilayer with
curvature elasticity and tension. We calculate its fluctuation spectrum and we
discuss the different regimes and non-monotonic features, including the precise
crossover at the mesh size between the already known limits with two different
tensions and the renormalisation of the bending rigidity at low wavevectors. We
also show that the non-diagonal correlations reveal, in "dark field", the
cytoskeletal defects. As a first step toward a non-invasive defect
spectroscopy, the specific case of lacking bonds is studied numerically and
analytically.
