Beating Shapes Relying on Moiré Level Lines

We consider the problem of obtaining a recognizable shape as superposition moiré of two line gratings. The method we propose generates moiré lines located between the shape foreground and background centers and the shape boundaries. Upon relative displacement of the superposed base- and revealing-layer gratings, the moiré lines move and give the impression of beating shapes. Original bilevel shapes are converted into elevation profiles that are embedded by small local shifts within the base-layer grating layout. The elevation profile's level lines are revealed as moiré by superposing the base and revealing layers. Similar level line moirés can be obtained by applying an identical geometric transformation to both the base and the revealing layers. In order to create grayscale or color images embedding several distinct moiré shapes, we create as base layer a dither array made of several ditherband gratings, each one embedding its specific elevation profile. Further variants include the possibility of incorporating elevation profiles within both the base and the revealing layers, or having two elevation profiles sharing a same base layer by tiling the available space. The moiré-level line techniques can be advantageously used for decorative or for anti-counterfeiting applications. Their base- and revealing-layer gratings may be produced by printing techniques, by imaging on film, or by arrays of cylindrical microlenses.