Recent measurements of the ''quasi-thermal'' noise in a stable plasma have exhibited an additionnal local an diffuse noise below the electron plasma frequency; this has been suggested to be due to impacts or emission of charged particles on the antenna surface. To investigate this problem beyond the previous semi-heuristic evaluations, we extend the quasi-thermal noise theory to antennas that are not transparent to particles. We apply the results for small radius spherical and cylindrical antennas in an isotropic equilibrium plasma at frequencies of the order of magnitude of the plasma frequency. For antennas near the plasma dc potential, the theoretical noise consists of the usual thermal noise on a transpareent antenna plus a component that has the following properties: (1) For small double-spheres antennas, it has an f-2 spectrum around the plasma frequency fp; just below fp, it is of the same order of magnitude of the thermal noise if the antenna length L an plasma Debye length LD satisfy L/LD>1. It is much larger if L/LDq1. (2) For fine cylindrical antennas, it is only broadly f-2 below fp; just below fp, it is much smaller than the quasi-thermal noise, except if the antenna surface is larger than L4/L2D. Practical consequences are given for recent experiments in the solar wind and terrestrial magnetosphere.