The magnetic vortex structure is an equilibrium configuration frequently found in patterned magnetic nanostructures. It is characterized by an in-plane curling of the magnetization with clockwise or anticlockwise chirality and by an out-of-plane vortex core that can have a positive or negative polarity. The small size of the vortex core, on the order of 10nm, makes it technologically interesting due to potential data storage, but also difficult to measure or image directly. In this work, we used Scanning Electron Microscopy with Polarization Analysis (SEMPA) to directly image magnetic vortex cores in patterned NiFe/Ta bilayer structures. With SEMPA we can simultaneously measure the in-plane and the out-of-plane component of the surface magnetization and thereby determine both the vortex chirality and the vortex core polarity in a single measurement. Our magnetic simulation of the vortex core, considering only the exchange and magnetostatic energy, is in good agreement with the SEMPA measurement of the magnetization when other experimental factors are taken into account.