Method for producing a substrate (202) for an optical element (200) of a
lithography system (100), comprising the steps: a) Providing (S1) a
crystal substrate (204) which has a
crystal lattice (206) with at least a first, second, third and fourth
crystal direction (302, 306, 308, 310) and a surface (214) which is arranged substantially perpendicular to the first crystal direction (302), wherein a geometric projection (306', 308', 310') of the second, third and fourth crystal direction (306, 308, 310) onto the surface (214) each characterizes an azimuthal installation orientation (138) of the crystal substrate (204) in an optical
system (102, 104, 136) of the
lithography system (100) with respect to a minimum stress-induced
birefringence upon
irradiation of a polarized
radiation (210), and the installation orientation (138) is an orientation with respect to a rotation of the crystal substrate (204) about a central axis (220) passing through the surface (214) and arranged parallel to the first crystal direction (302), and b) determining (S2) an angular position (δ1, δ2, δ3) of at least one of the geometric projections (306', 308', 310') of the second, third and fourth crystal directions (306, 308, 310) onto the surface (214).