Moiré effects produced by superpositions of micro-lens arrays

Moiré effects result from the superimposition of repetitive structures. The beauty of these moirés comes from the fact that macroscopic shapes seem to appear from the superposition of layers containing microscopic patterns. In addition, the moirés are dynamic and change when the layers are moved, or when the fabricated moiré samples are tilted. Aside from their visual appeal, moirés can also be used in security application, where their requirement of high resolution and fabrication accuracy are interesting to fight counterfeiting.

In the context of this thesis, we focus on three moiré types. The first is called the level-line moiré. It displays a static shape whose intensities or colours vary depending on the superposition conditions of its two constituting layers. One layer is a grating of straight lines, while the other is a grating of the same period, to which distorsions have been purposefully applied. The distortions are dictated by an elevation profile, whose level lines are visible when the two layers are superposed. The second moiré type we cosider is the 1D moiré. The layers to be superposed are the base and the revealer. The base is a grating of rectangular tiles that contain the same symbol, shape or text. The revealer is a grating of lines, whose period is slightly different from that of the base. The base is only seen through the transparent parts of the revealer and is therefore sampled only at specific locations. The 1D moiré shape is thus a magnified version of the base tiles and is repeated in a given direction. When the revealer is translated relative to the base, the moiré shapes translate in a certain direction. Finally, 2D moirés are obtained in a similar fashion to the 1D moirés. The base tile is compressed and replicated in both directions to create the base array. Similarly, the revealer is an array of dots or sampling holes instead of lines. The moiré shape is a magnified version of the base tile and it can move in any direction, depending on the displacement of the revealer.

Moreover, each of these moirés can be modified by applying transformations to the moirés or to their constituting layers. This is for example how spiraling moirés are designed. We have expanded the range of moiré features by creating a combination of these moiré types. The new moiré effects we created combine level-line moiré and 1D moiré or level-line moiré and 2D moiré. The moiré shapes can now both move and display varying intensities when the revealer is translated relative to the base.

To obtain moiré samples, several methods can be employed. First, the two layers can be printed on transparencies. Although a fast method, the resulting moirés lack intensity and cannot be obtained at very high resolutions. An alternative is to combine a printed (or micro-fabricated) base with a lens-based revealer. The micro-lens arrays increase the dynamic range of the moirés, which is particularly important for 1D and 2D moirés. Finally, the new method we hav