Proton beams, generated in the interaction process of short ultra-intense laser pulses with thin foils, carry imprints of rear side target structures. These intensity patterns, imaged with a particle detector, sometimes show slight deformations. We propose an analytical model to describe these deformations by the spatial shape of a monoenergetic layer of protons in the beginning of free proton propagation. We also present results of simulations, which reproduce the detected structures and allow finally making quantitative conclusions on the shape of the layer. In experiments with electrically conducting targets, the shape is always close to a parabolic one independently on target thickness or laser parameters. Since the protons are pulled by the free electrons, there must be a strong correlation to the electron space charge distribution on the rear side of the illuminated foil. Simulations demonstrate that the deformations in the detected patterns of the proton layers are very sensitive to the initial layer shape. Analyzing spatial structures of the generated proton beams we can indirectly conclude on electron transport phenomena in the overdense part of the target.