Abstract: A multi-coordinate measuring system having a diffraction element that receives light emitted by a light source and diffracts the light into at least a first, second, third and fourth partial beam bundles where the first, second, third and fourth partial beam bundles are directed in different coordinate directions onto a substrate. The substrate has first, second, third and fourth waveguides located thereon. The substrate has a coupling element that directs the first, second, third and fourth partial beam bundles into the first, second, third and fourth waveguides, respectively. The substrate also has a first coupling element for bringing the first and second partial beam bundles into interference and a second coupling element for bringing the third and fourth partial beam bundles into interference. A detector system then detects the interference of the first and second partial beam bundles and the third and fourth partial beam bundles.