By Amidror Isaac
This ebook provides for the 1st time the speculation of the moiré phenomenon among aperiodic or random layers. it's a complementary, but stand-alone better half to the unique quantity via an identical writer, which was once devoted to the moiré results that happen among periodic or repetitive layers. like the first quantity, this e-book presents a whole basic goal and application-independent exposition of the topic. It leads the reader in the course of the numerous phenomena which take place within the superposition of correlated aperiodic layers, either within the snapshot and within the spectral domain names. in the course of the complete textual content the booklet favours a pictorial, intuitive method that's supported by means of arithmetic, and the dialogue is followed through a number of figures and illustrative examples, a few of that are visually beautiful or even spectacular.
The prerequisite mathematical heritage is proscribed to an ordinary familiarity with calculus and with the Fourier idea.
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Extra resources for Aperiodic layers
3(e)–(h), but with a small rotation in one of the two layers. As we can see in (e) and (g), the singular moiré-free superpositions of Fig. 3(e),(g) turn into clearly visible spiral or elliptic Glass patterns, which are similar to those obtained in (a) and (c), but slightly shifted away from the origin. In fact, as we will see in Sec. 3, the bright and dark areas which form the Glass pattern occur due to variations in the local correlation between the superposed layers. The particular case in which the correlation is constant throughout the superposition will be explained in Sec.
3) the spectrum of the superposition is no longer the spectrum-convolution given by Eq. 2), but rather the sum of the individual spectra: R(u,v) = R1(u,v) + ... 4) In cases where no explicit rule is known that relates the individual spectra Ri(u,v) to the spectrum R(u,v) of the superposition, R(u,v) can still be found directly by applying the Fourier transform to r(x,y). Q Let us now explain what we mean by periodic and by aperiodic or random layers. A 1D function f(x) is said to be periodic if there exists a non-zero number p such that for any R, f(x + p) = f(x).
Other layer transformations may give rise to Glass patterns having hyperbolic, elliptic or other geometrically shaped dot trajectories, as shown for example in Figs. 2(a),(c) [Glass73]. However, unlike periodic moirés, Glass patterns do not reappear when we invert or rotate one of the superposed layers by 180° (see Figs. 6(a),(b)). 5 Thus, when two identical layers having the same arbitrary structure are slightly rotated on top of each other (see Fig. 1(c)), a visible Glass pattern is generated about the center of rotation, indicating the high correlation between the two layers in this area.
Aperiodic layers by Amidror Isaac