An optical position measuring system including a periodic grating structure and a scanning unit. The scanning unit includes a light source that directs light towards the periodic grating structure and an optical lens device that receives light from the periodic grating structure and creates an image of the periodic grating structure in an image plane, the optical lens device having a periodic lens array with a grating period, AG (r) or the mutual distance between adjoining lenses of said lens array defined by the equation: wherein AG(r) is the A G ⁡ ( r ) =  β ⁡ ( r )  * [ t ⁡ ( r ) ⁢   * [ k + i + n ] + ψ ] (  β ⁡ ( r )  + 1 ) array, t(r) the period of the periodic grating structure, |β(r)| the absolute amount of the image scale β of the lens array ψ a presettable defined phase shift r the radius of the grating arrangement, wherein in the case of a linear grating r=∞, and AG, t and |β| are constants, i, k, n ε N, i.e. are natural numbers, including zero.