As a preliminary stage in manufacturing a lens or lens part for an objective, in particular a projection objective for a microlithography projection system, an optical blank is made from a crystal material. As a first step in manufacturing the optical blank, one determines the orientation of a first crystallographic direction that is defined in the crystallographic structure of the material. The material is then machined into an optical blank so that the first crystallographic direction is substantially perpendicular to an optical blank surface of the optical blank. Subsequently, a marking is applied to the optical blank or to a mounting element of the optical blank. The marking has a defined relationship to a second crystallographic direction which is oriented at a non-zero angle relative to the first crystallographic direction.