title: Investigation of the moiré patterns of defected radial and circular gratings using the reciprocal vectors approach.
abstract: In this work, for the first time to the best of our knowledge, an investigation on the moiré patterns of superimpositions of two radial or two circular gratings consisting of topological defects and their mutual superimpositions with each other, or with linear forked gratings or defected zone plates, is presented. For characterization of the resulting moiré patterns, we use the reciprocal vectors approach. In this approach, by considering local spatial frequencies for the superimposed structures, their reciprocal vectors are determined from the transmission function of the structures. The local reciprocal vector of the resulting moiré pattern at a given point is determined in terms of the local reciprocal vectors of the superimposed structures defined at the same point. In this approach, the topological singularities of the superimposed structures are described by the azimuthal component of the reciprocal vectors. This formulation is very simple, uniform, and comprehensive. In this work, we offer a detailed discussion on the different resulting moiré patterns for the above-mentioned superimpositions and some potential applications of the proposed superimpositions are introduced. In addition, different resulting moiré patterns are simulated.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Yeganeh
authors.forename: Saifollah
authors.initials: S
authors.lastname: Rasouli