Polarization system for wavelength ranges between 170 and 230 nm, comprising the following features: - a first substrate made of a first substrate material having a first layer system applied thereto, and at least one second substrate, which is subsequent in a beam path formed by a beam source, made of a second substrate material having a second layer system applied thereto; - wherein the first and second layer system comprise a first stack (3b, 4b) applied to the substrate and a second stack (3c, 4c) applied directly to the first stack; - wherein the first stack comprises an alternating sequence of high- and low-refractive-index oxidic layers; - wherein the second stack comprises an alternating sequence of high- and low-refractive-index fluoridic layers; - wherein the first layer system an unpolarized beam forming the beam path, which beam, in a first partial beam transmitting the substrate, impinges on the layer system at an angle Φ which is greater than the Brewster angle for the substrate material used, wherein the first partial beam largely comprises a P-polarized first component and divides at least into a second partial beam reflected by the layer system, wherein the second partial beam largely comprises an S-polarized second component; - wherein the first layer system is designed with regard to its number of oxidic and fluoridic layers such that the proportion of the reflected and S-polarized second component is at least 90% of the second partial beam; wherein the second layer system the second partial beam, which has a proportion of the largely S-polarized second component of at least 90% and, in a third partial beam transmitting the substrate, impinges on the layer system, wherein the third partial beam largely comprises the P-polarized first component and divides at least into a fourth partial beam reflected by the second layer system, wherein the fourth partial beam largely comprises the S-polarized second component, wherein the proportion of the largely S-polarized second component in the fourth partial beam after the second layer system is greater than the proportion of the largely S-polarized second component in the second partial beam after the first layer system, wherein the substrate materials used are quartz glass and calcium fluoride, wherein the first substrate material is calcium fluoride and each further substrate material is quartz glass. - a first substrate made of a first substrate material having a first layer system applied thereto, and at least one second substrate, which is subsequent in a beam path formed by a beam source, made of a second substrate material having a second layer system applied thereto; - wherein the first and second layer system comprise a first stack (3b, 4b) applied to the substrate and a second stack (3c, 4c) applied directly to the first stack; - wherein the first stack comprises an alternating sequence of high- and low-refractive-index oxidic layers; - wherein the second stack comprises an alternating sequence of high- and low-refractive-index fluoridic layers; - wherein the first layer system an unpolarized beam forming the beam path, which beam, in a first partial beam transmitting the substrate, impinges on the layer system at an angle Φ which is greater than the Brewster angle for the substrate material used, wherein the first partial beam largely comprises a P-polarized first component and divides at least into a second partial beam reflected by the layer system, wherein the second partial beam largely comprises an S-polarized second component; - wherein the first layer system is designed with regard to its number of oxidic and fluoridic layers such that the proportion of the reflected and S-polarized second component is at least 90% of the second partial beam; wherein the second layer system the second partial beam, which has a proportion of the largely S-polarized second component of at least 90% and, in a third partial beam transmitting the substrate, impinges on the layer system, wherein the third partial beam largely comprises the P-polarized first component and divides at least into a fourth partial beam reflected by the second layer system, wherein the fourth partial beam largely comprises the S-polarized second component, wherein the proportion of the largely S-polarized second component in the fourth partial beam after the second layer system is greater than the proportion of the largely S-polarized second component in the second partial beam after the first layer system, wherein the substrate materials used are quartz glass and calcium fluoride, wherein the first substrate material is calcium fluoride and each further substrate material is quartz glass.