Optical absorption in irradiated and non-irradiated single crystals of CaSO₄ and CaSO₄:Dy is studied. The intrinsic defect centres SO₄^-, SO₃^-, SO₂^-, O₃^-, and O^- are identified in irradiated samples. However, these centres are generally observed only if stabilised by Dy impurity ions within the structure. Dy²⁺ absorption is also observed in irradiated doped samples. Luminescence via energy transfer to Dy ions is corroborated by this study. Areas where these results may be used to develop further understanding of the thermoluminescence process in CaSO₄:Dy are discussed.