A device for a 3D measurement of object coordinates of a measurement object or parts of the measurement object in a coordinate measuring machine is provided. The device includes at least one illumination device configured to generate at least one illumination light beam and to illuminate the measurement object, at least one lens, wherein the lens has a longitudinal chromatic aberration, at least one color sensor arranged in an image plane of the lens, wherein the color sensor is configured to capture a measurement light beam generated by the measurement object in response to the illumination light beam and to determine at least one spectrally dependent image space content; at least one evaluation unit configured to determine at least one item of depth information from the spectrally dependent image space content.