Periodic wrappings in coded aperture imaging

Abstract

We classify all coded masks onto which cyclic difference sets can be wrapped periodically using a generalization of the Finger and Prince construction. In particular, we establish simple numerical criteria which determine whether any given mask can be wrapped periodically in this way and, for each mask which can, we provide explicit constructions which will produce at least one such wrapping. We show that all periodic wrappings currently reported in the literature are special cases of our explicit constructions, and we often provide simpler alternatives. Using these constructions we show that all Singer cyclic difference sets of practical size and open fraction can be wrapped exactly onto masks which are very nearly as compact and symmetrical as hexagons, without the need for pixel padding.