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Multi-differential measurements of dilepton spectra serve as a unique tool to characterize the properties of matter in the interior of the hot and dense fireball created in heavy-ion collisions. An important property of virtual photons is their spin polarization defined in the rest frame of the virtual photon with respect to a chosen quantization axis. Microscopic calculations of in-medium electromagnetic spectral functions have mostly focused on integrated yields which are proportional to the sum of the longitudinal and transverse components of the virtual photon's self-energy, while photon polarization results from the difference of these components. As the processes that drive the medium effects in the spectral function change with invariant mass and momentum, this becomes a powerful tool for studying the medium composition. We present the polarization observables of thermal virtual photons as a function of mass and momentum and confront the results with existing measurements from HADES and NA60. [ABSTRACT FROM AUTHOR]