We have developed an interference lithography method that enables the production of circular periodic patterns. The range of accessible patterns includes concentric circular rings, spiral- and spoke-like patterns, and dots positioned periodically on concentric circular tracks. The method is based on the use of transmission diffraction gratings to create circular beams with wave fronts that are not accessible with reflective or refractive optics. Diffraction gratings with equally spaced concentric circles are used to obtain diverging or converging conical waves with radial phase variation and spiral-like gratings are used to obtain waves with the phase varying in both radial and azimuthal directions. We have experimentally demonstrated the method with electron-beam written diffraction gratings, which we illuminated with a coherent laser beam to form the interference patterns. Many different designs are possible that bring two, three, or more beams together to form a desired interference pattern. The technique should in general be useful in applications requiring circular periodic patterns, which may include production of patterned magnetic media, spoke patterns for angular encoders, and photonic crystals with circular symmetry. (C) 2003 American Vacuum Society.