Cores of magnetic vortices in micron-sized NiFe disk structures, with thicknesses between 150 and 50 nm, were imaged and analysed by high resolution magnetic soft X-ray microscopy. A decrease of the vortex core radius was observed, from ∼ 38 to 18 nm with decreasing disk thickness. By comparing with full 3D micromagnetic simulations showing the well-known barrel structure, we obtained excellent agreement taking into account instrumental broadening and a small perpendicular anisotropy. The proven magnetic spatial resolution of better than 25 nm was sufficient to identify a negative dip close to the vortex core, originating from stray fields of the core. Magnetic vortex structures can serve as test objects for evaluating sensitivity and spatial resolution of advanced magnetic microscopy techniques.