The Talbot effect in the presence of a convergent beam of coherent light yields a demagnified image of a self-imaging object. In fact, the object does not even have to fulfill the self-imaging condition; the object with truncated self-imaging feature is sufficient to yield an image that is sufficiently accurate for many practical purposes. We have taken this approach to fabricating circular gratings with a reduced period compared to the period of the mask. Using a simple experimental setup and a concentric circular grating mask, we have created images whose periods are either one-half or one-third of the mask's period. Demagnified Talbot imaging of fully or truncated self-imaging objects provides an attractive approach to photolithographic fabrication of structures whose periods are somewhat greater than the wavelength of the light source.