Periodic structures, such as gratings and grids, are required in a variety of applications including spectroscopy, photonic and phononic devices, and as substrates for basic studies in materials science. Interference lithography readily forms periodic patterns in photoresist, but conventional approaches, using a Lloyd's mirror or Mach-Zehnder configuration, suffer from a number of shortcomings including difficulty in aligning patterns with respect to pre-existing structures on a substrate and difficulty in precisely repeating a given spatial period. Coherent diffraction lithography (CDL), a mask-based approach, utilizes the well-known Talbot effect to accurately replicate the one- or two-dimentional pattern on a mask by reimaging the mask pattern in photoresist. Moreover, with appropriate alignment marks on the mask, one can align the replicated pattern relative to pre-existing patterns on the substrate. The authors describe the design, construction, and utilization of a dedicated CDL apparatus that permits replication, at a well-defined mask-substrate gap, of the periodic structure of a phase mask. The system also incorporates interferometric-spatial-phase imaging for aligning the replicated pattern relative to fixed fiducials on a substrate. They obtained high quality replications of a mask pattern, consisting of a 600 nm period grating, from the 1st to the 52nd plane of reimaging, i.e., from 1.55 to 40.16 mu m.