Shape moiré is one type of
moiré pattern
In mathematics, physics, and art, moiré patterns ( , , ) or moiré fringes are large-scale interference patterns that can be produced when an opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré ...
s demonstrating the phenomenon of moiré magnification.
1D shape moiré is the particular simplified case of 2D shape moiré.
One-dimensional
In physics and mathematics, a sequence of ''n'' numbers can specify a location in ''n''-dimensional space. When , the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the ...
patterns may appear when superimposing an
opaque
Opacity or opaque may refer to:
* Impediments to (especially, visible) light:
** Opacities, absorption coefficients
** Opacity (optics), property or degree of blocking the transmission of light
* Metaphors derived from literal optics:
** In lingu ...
layer containing tiny horizontal
transparent
Transparency, transparence or transparent most often refer to:
* Transparency (optics), the physical property of allowing the transmission of light through a material
They may also refer to:
Literal uses
* Transparency (photography), a still, ...
lines on top of a layer containing a complex shape which is periodically repeating along the
vertical axis
A Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of number, numerical coordinates, which are the positive and negative numbers, signed distance ...
.
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:
:
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:
:
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