A multilayer mirror (M) reflecting extreme ultraviolet (EUV) radiation from a first wavelength range in a EUV spectral region, the mirror comprising: a substrate (SUB); a stack of layers (SL) on the substrate, the stack of layers comprising layers comprising a low index material and a high index material, the low index material having a lower real part of the refractive index than the high index material at a given operating wavelength λ in the first wavelength range, a spectral purity filter on top of the stack of layers, the spectral purity filter effective as an anti-reflection layer for ultraviolet (UV) radiation from a second wavelength range in a UV spectral region to increase a EUV-UV-reflectivity ratio of the multilayer mirror, characterized in that the spectral purity filter (SPF) comprises a non-diffracting graded-index anti-reflection layer (Gl-AR) effective to reduce reflectivity in the second wavelength range, the non-diffractive graded-index anti-reflection layer (GI-AR) comprising a sub-wavelength structure (SWS) comprising structural elements (SE) with lateral dimensions smaller than the UV wavelength in the second wavelength range in such a way that the sub-wavelength structure (SWS) is effective for the ultraviolet radiation in the second wavelength range as an effective medium with graded refractive index, capable of reducing an optical contrast at a radiation entry surface of the stack of layers and suppress at least partly the ultraviolet radiation reflection, wherein the sub-wavelength structure (SWS) is a periodic structure comprising an array of tapered structural elements (SE) forming a periodic surface relief structure, a period length (PSWS) of the periodic sub-wavelength structure (SWS) being in a range from 25 nm to 100 nm. a substrate (SUB); a stack of layers (SL) on the substrate, the stack of layers comprising layers comprising a low index material and a high index material, the low index material having a lower real part of the refractive index than the high index material at a given operating wavelength λ in the first wavelength range, a spectral purity filter on top of the stack of layers, the spectral purity filter effective as an anti-reflection layer for ultraviolet (UV) radiation from a second wavelength range in a UV spectral region to increase a EUV-UV-reflectivity ratio of the multilayer mirror, characterized in that the spectral purity filter (SPF) comprises a non-diffracting graded-index anti-reflection layer (Gl-AR) effective to reduce reflectivity in the second wavelength range, the non-diffractive graded-index anti-reflection layer (GI-AR) comprising a sub-wavelength structure (SWS) comprising structural elements (SE) with lateral dimensions smaller than the UV wavelength in the second wavelength range in such a way that the sub-wavelength structure (SWS) is effective for the ultraviolet radiation in the second wavelength range as an effective medium with graded refractive index, capable of reducing an optical contrast at a radiation entry surface of the stack of layers and suppress at least partly the ultraviolet radiation reflection, wherein the sub-wavelength structure (SWS) is a periodic structure comprising an array of tapered structural elements (SE) forming a periodic surface relief structure, a period length (PSWS) of the periodic sub-wavelength structure (SWS) being in a range from 25 nm to 100 nm. <EOS>