A novel quantitative scanning electron microscopy–energy dispersive X-ray spectrometry (SEM–EDX) technique was developed to measure the size and geochemical composition of unpolished volcanic glass shards smaller than 10 µm in diameter within cryptotephra layers in polar ice cores. This was achieved by 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 method was applied to analyze the major element composition (SiO₂, TiO₂, Al₂O₃, FeO, MgO, CaO, Na₂O, and K₂O) of cryptotephra deposits 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 results show a bimodal composition of glass shards, corresponding to dacitic and rhyolitic types.