Shape moiré

Shape moiré is one type of moiré patterns demonstrating the phenomenon of moiré magnification [cite paper
title = Optical inspection of arrays and periodic structures using moire magnification
author = M.C. Hutley
coauthors = R.F. Stevens
publisher = IEE Colloquium, Microengineering in Optics and Optoelectronics
date = 1999-11-16
url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=IEESEM001999000187000008000001&idtype=cvips&gifs=yes] [cite journal
title = Properties of moiré magnifiers
author = Hala Kamal
coauthors= Reinhard Völkel and Javier Alda
journal = Optical Engineering
volume= 37 (11)
pages= 3007–3014
month = November | year = 1998
url = http://4z.com/people/emin-gabrielyan/public/070227-moire-ref/Kamal98a.pdf
accessdate = 2007-03-26
format=PDF] . 1D shape moiré is the particular simplified case of 2D shape moiré. 1D patterns may 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. 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 of optical shapes "p"_m, magnified along the vertical axis is expressed by the following formula::$p\_m=-frac\{p\_b\; cdot\; p\_r\}\{p\_b-p\_r\}$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::$frac\{v\_m\}\{v\_r\}=-frac\{p\_b\}\{p\_b-p\_r\}$Negative values of "v"_m / "v"_r signify the movement of optical shapes in reverse direction.

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 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.

External links

*Shape moiré intro page: [http://4z.com/people/emin-gabrielyan/public/070320-shape-moire/ USA] , [http://switzernet.com/people/emin-gabrielyan/070320-shape-moire/ Switzerland]

References