An objective for a microlithography projection system has at least one fluoride crystal lens. The effects of birefringence, which are detrimental to the image quality, are reduced if the lens axis of the crystal lens is oriented substantially perpendicular to the {100}-planes or {100}-equivalent crystallographic planes of the fluoride crystal. If two or more fluoride crystal lenses are used, they should have lens axes oriented in the (100)-, (111)-, or (110)-direction of the crystallographic structure, and they should be oriented at rotated positions relative to each other. The birefringence-related effects are further reduced by using groups of mutually rotated (100)-lenses in combination with groups of mutually rotated (111)- or (110)-lenses. A further improvement is also achieved by applying a compensation coating to at least one optical element of the objective.