We propose quantitative estimates of the electric permittivity from the electric field remotely measured at a single back-scattered direction and for a finite and explicit band of incident frequencies. These fields are measured before and after injecting plasmonic nano-particles. These nano-particles are known to enjoy resonant effects while excited at certain particular frequencies called plasmonic resonances. The particular, but very useful, property of these resonant frequencies is that they encode the values of the unknown permittivity at the location of the injected nano-particles. Based on this feature, we propose an imaging functional build up from contrasting the fields before and after injecting the nano-particles, measured at one single back-scattered direction, and in an explicit band of incident frequencies. This imaging functional reaches its maximum values, in terms of the incident frequency, precisely at the mentioned plasmonic resonances. Such a behavior allows us to recover these resonances from which we recover the point-wise values of the permittivity distribution.