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A particular class of Montgomery’s self-imaging objects that we call continuously self-imaging gratings (CSIG’s) is introduced. When they are illuminated by a plane wave, these objects produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. The mathematical construction of these objects and their intrinsic properties are described. On a practical level, CSIG’s are compact and achromatic nondiffracting array generators. We show that a good CSIG approximation can be realized by a two-level phase grating that is experimentally tested.