A measuring unit is set up to determine a relative position and relative orientation between the measuring unit and an arrangement of at least three optical elements. The measuring unit comprises a length measuring device, which emits measuring beams at at least three locations spaced apart from one another, and at least one beam directing device set up to direct the measuring beams to optical elements of the arrangement. The beam directing device is controllable in order to guide at least one of the measuring beams to a plurality of optical elements of the arrangement in a time-sequential manner in order to carry out a plurality of length measuring operations in a time-sequential manner in such a manner that, in the plurality of length measuring operations, each measuring beam of the at least one measuring beam strikes precisely one of the optical elements. A total of six lengths are measured in this manner.