Shape moiré is one type of

moiré pattern In mathematics, physics, and art, moiré patterns ( , , ) or moiré fringes are large-scale wave interference, interference patterns that can be produced when a partially opaque grating, ruled pattern with transparent gaps is overlaid on ano ...

s demonstrating the phenomenon of moiré magnification. 1D shape moiré is the particular simplified case of 2D shape moiré. One-dimensional patterns may appear when superimposing an

opaque Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shie ...

layer containing tiny horizontal transparent lines on top of a layer containing a complex shape which is periodically repeating along the

vertical axis In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular o ...

Description

Shape moiré is sometimes referred as band moiré. 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 ''p''_b. The period of transparent lines in the revealing layer is denoted as ''p''_r. 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 size along the vertical axis, ''p''_m, of the magnified optical shape is expressed by the following formula: :

p_m=-\frac

Negative values of ''p''_m 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: :

\frac=-\frac

Negative values of ''v''_m / ''v''_r signify the movement of optical shapes in reverse direction.

Examples

When ''p''_r > ''p''_b, the magnified shapes appear normally, but they move in reverse direction compared to the movement of the revealing layer. See the figure below: When ''p''_r < ''p''_b, the magnified shapes appear inverted along the vertical axis, but they move in the same direction as the revealing layer. See the figure below:

Line moiré

Line moiré Line moiré is one type of moiré pattern; a pattern that appears when superposing two transparent layers containing correlated opaque patterns. Line moiré is the case when the superposed patterns comprise straight or curved lines. When moving the ...

can be considered as a particular case of shape moiré when the shape embedded in the base layer is simply a straight or curved line.

References

External links

*Shape moiré intro page
USASwitzerland
{{DEFAULTSORT:Shape moire Geometry Interference Patterns Printing