A method including determining with a three-dimensional (3D) measuring instrument 3D coordinates of an object for each of a plurality of poses of the 3D measuring instrument; capturing with a camera first- and higher-order diffraction components of markers near or on the object, the camera having a diffractive optical element (DOE), a lens, and a photosensitive array; and registering with a processor the determined 3D coordinates based at least in part on the determined 3D coordinates and on the imaged zero- and higher-order diffraction components.