Determination of electrostatic field distribution at the nanometer scale at the vicinity of a polarized specimen is of great interest for solving the reconstruction issue in atom probe tomography. In this work, we present a method based on the Rutherford scattering theory to quantify the electric field maps obtained by scanning an electron beam across on a needle like specimen submitted to a high voltage in a transmission electron microscope. After a validation of the geometrical model on simulated datasets, electron beam deflection maps were acquired in scanning mode using a holder developed to perform atom probe tomography experiments in transmission electron microscopes. The experimental results allow pointing out the link between the crystal orientation and the electrostatic field distribution at the vicinity of a pure tungsten specimen. The methodology presented, which does not depend on the thickness of the sample, is foreseen to serve as an additional input for present and future atom probe reconstruction methods.