Magnetic recording has now played an important role in the development of non-volatile information storage technologies, so it becomes essential to quantitatively understand the magnetization distribution in magnetic microstructures. In ferromagnetic disks, squares and triangles with submicron sizes, it is energetically favorable for the magnetization to form a closed in-plane vortex and a perpendicular vortex core at the center. This vortex magnetic structure is a new candidate for future magnetic memory device because both the vortex chirality and the core polarity can be manipulated by applying an external magnetic field or a spin-polarized current. Further development of vortex-based memory devices requires quantitative measurement of vortex domain structures, which is still lacking.In this paper, magnetization configuration in a vortex structure has been quantitatively studied by scanning transmission X-ray microscope (STXM) utilizing X-ray magnetic circular dichroism (XMCD) effect in Shanghai Synchrotron Radiation Facility. Samples have been fabricated on the 100 nm silicon-nitride membranes. The patterns are first transferred to PMMA photoresist using e-beam lithography, then a 50 nm thick Ni80Fe20 film is deposited by e-beam evaporation. Magnetic vortex configurations are characterized with the X-ray energy at Fe L3 absorption edge and Ni L3 absorption edge, respectively. The image taken at Fe edge shows greater contrast than that at Ni edge. Experimental results indicate that the magnetic vortex state remains stable in permalloy circle, square and triangle structures with diameters from 2 to 5 m. The STXM images indicate that the magnetization in circular geometry changes continuously along the concentric circles without clear domain boundaries. In contrast, magnetization in square geometry consists of four distinct domains with clear diagonal domain boundaries. Similarly, three domains can be observed in triangle geometry. In order to quantify the in-plane magnetization configuration in magnetic vortices, we also use micromagnetic simulation to calculate the magnetization distributions of these three geometries. By extracting Mx along the circular profiles in both experimental and simulated vortex images, we find that the experimental magnetic profiles in the STXM images are consistent with the simulation data quantitatively. These magnetic structures are also studied by magnetic force microscopy (MFM). Since MFM is only sensitive to the dipolar magnetic field around the domain boundary, the MFM images show different configurations from the STXM images.