We present the major element compositions (SiO₂, TiO₂, Al₂O₃, FeO, MgO, CaO, Na₂O, and K₂O) of unpolished micron-sized volcanic glass shards within cryptotephra layers associated with the prominent 1458/59 CE sulfate peak in a shallow firn core (VK22) drilled near the Russian Antarctic Vostok Station in East Antarctica. The measurement was performed by a quantitative scanning electron microscopy–energy dispersive X-ray spectrometry (SEM–EDX) technique using a reverse Monte Carlo simulation combined with a robust successive approximation algorithm, effectively accounting for both matrix and geometric effects and consequently contributing to an accurate determination of characteristic X-ray intensities of specific elements in unpolished glass shards. The results show a bimodal composition of glass shards, corresponding to dacitic and rhyolitic types.