A fine control of the variation of the refractive index as a function of structural damage is essential in the fabrication of diamond-based optical and photonic devices. We report here about the variation of the real part of the refractive index at lambda=632.8 nm in high quality single crystal diamond damaged with 2 and 3 MeV protons at low-medium fluences (10^13 - 10^17 ions cm^-2). After implanting the samples in 125x125 um^2 areas with a raster scanning ion microbeam, the variation of optical thickness of the implanted regions was measured with laser interferometric microscopy. The results were analyzed with a model based on the specific damage profile. The technique allows the direct fabrication of optical structures in bulk diamond based on the localized variation of the refractive index, which will be explored in future works.