A numerical optimizing method serves to reduce harmful effects caused by intrinsic birefringence in lenses of a fluoride crystal material of cubic crystal structure in an objective, particularly a projection objective for a microlithography system. Under the optimizing method, an optimizing function which takes at least one birefringence-related image aberration into account is minimized. The birefringence-related image aberration is determined from a calculation for a light ray passing through the fluoride crystal lenses. To the extent that the birefringence-related image aberration is a function of parameters of the light ray, it depends only on geometric parameters of the light ray. The numerical optimizing method is used to produce objectives in which an optical retardation as well as an asymmetry of the optical retardation are corrected. The lenses are arranged in homogeneous groups, where each homogeneous group is corrected for the optical retardation asymmetry.