each of these scales 12 may be attached to carrier 52 as illustrated in the figures described below the optically contacting methods explained above are used for this attachment in fig4 and 5 such a scale 12 having a two dimensional measuring graduation marking 22 also referred to as a cross grating is illustrated as an example projections 32 having optically contactable surfaces 62 are formed on the surface of scale 12 facing carrier 52 these projections 32 may be spatially distributed two dimensionally either in a geometrically uniform manner in a normal grid or in a statistical distribution projections 32 may each be circular having a diameter of e g less than 30 mm e g 200 u03bcm to 4 mm and having a mutual spacing e g less than the thickness of scale 12 the mutual spacing being the edge spacing i e 4 mm in fig1 and 16 the height of projections 32 may be greater than e g 10 nm for example 20 nm to 50 u03bcm the flatness waviness of surfaces 62 of projection 32 may be in the range of less than e g 500 nm on a diameter of approximately 10 mm e g 30 nm per 0 10 mm surfaces 62 of projections 32 formed as optically contacting surfaces are arranged in a common plane typical values of the thickness of scale 12 are e g 1 mm to 15 mm the lower the diameter of projections 32 and the lower the mutual spacing the lower the height of projections 32 may also be the two dimensional spatial distribution of projections 32 may be implemented such that between projections 32 opening channels 200 are formed which extend relative to the x y plane to the edge of scale 12 this measure permits.