Shape moiré patterns

 

Emin Gabrielyan

2007-03-20

Switzernet Sŕrl

Scientific Park of Swiss Federal Institute of Technology

Lausanne, Switzerland

emin.gabrielyan@switzernet.com

 

Shape moiré patterns appear when superimposing an opaque layer containing tiny horizontal transparent lines on top of a layer containing a complex shape which is periodically repeating along the vertical axis. The opaque layer with transparent lines is called the revealing layer. The layer containing the periodically repeating shapes is called the base layer. The period of shapes in the base layer is denoted as . The period of transparent lines in the revealing layer is denoted as . The periods of both layers must be sufficiently close. The superimposition image reveals the shapes of the base layer stretched along the vertical axis. The magnified shapes appear periodically along the vertical axis. The dimensions along the horizontal axis are not changed. If the complex shape of the base layer is a sequence of symbols (e.g. a horizontal text) compressed along the vertical axis, then the superimposition of the revealing layer can restore the original proportions of these symbols. The magnification factor  along the vertical axis is expressed by the following formula:

Negative values of  signify mirrored appearance (the magnified shapes will be inverted along the vertical axis) of the stretched shapes.

 

When the revealing layer is moved along the vertical axis, the magnified shapes move along the vertical axis at a faster speed. The speedup factor is expressed by the following formula:

Negative values of  signify the movement of optical shapes in reverse direction.

 

When , the magnified shapes appear normally, but they move in reverse direction compared to the movement of the revealing layer. See the figure below.

[gif]

 

When , the magnified shapes appear inverted along the vertical axis, but they move in the same direction as the revealing layer. See the figure below.

[eps], [gif], [tif]

 

 

 

© 2007 Emin Gabrielyan and Switzernet Sŕrl

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