Modelization of the Moiré Phenomenon

Based on the Fourier theory, a mathematical modelization of the moiré phenomenon has been developed that can be used for both analysis and synthesis of moiré effects. This approach provides a full qualitative and quantitative understanding of the various phenomena which occur in the superposition of periodic layers (line gratings, dot screens, etc.), both in the image and in the spectral domains [Amidror94a, Amidror96, Amidror97, Amidror98]. This approach has been also extended to the even more interesting cases of polychromatic moirés [Amidror97a] and moirés between curved layers (curvilinear gratings, non-linear transformations of periodic dot screens, etc.) [Amidror98b]. Applications include finding moiré-free screen combinations and moiré minimization [Amidror94]; synthesis of moiré effects having any desired geometric layout and intensity profile [Amidror94a, Amidror98b]; and various tools for document authentication and anti-counterfeiting (patent pending). A forthcoming book, The Theory of the Moiré Phenomenon by I. Amidror (published by Kluwer Academic Publishers, 1999) provides a comprehensive introduction to the moiré theory and includes our main research results.