We apply off-axis electron holography and Lorentz microscopy in the transmission electron microscope to map the electric field generated by a sharp biased metallic tip. A combination of experimental data and modelling provides quantitative information about the potential and the field around the tip. Close to the tip apex, we measure a maximum field intensity of 82 MV/m, corresponding to a field k factor of 2.5, in excellent agreement with theory. In order to verify the validity of the measurements, we use the inferred charge density distribution in the tip region to generate simulated phase maps and Fresnel (out-of-focus) images for comparison with experimental measurements. While the overall agreement is excellent, the simulations also highlight the presence of an unexpected astigmatic contribution to the intensity in a highly defocused Fresnel image, which is thought to result from the geometry of the applied field.

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