By Amidror Isaac
This e-book provides for the 1st time the idea of the moiré phenomenon among aperiodic or random layers. it's a complementary, but stand-alone better half to the unique quantity by way of an analogous writer, which was once devoted to the moiré results that take place among periodic or repetitive layers. like the first quantity, this booklet offers a whole basic function and application-independent exposition of the topic. It leads the reader in the course of the a variety of phenomena which take place within the superposition of correlated aperiodic layers, either within the photograph and within the spectral domain names. through the complete textual content the ebook favours a pictorial, intuitive procedure that's supported by way of arithmetic, and the dialogue is followed by means of numerous figures and illustrative examples, a few of that are visually beautiful or even spectacular.
The prerequisite mathematical historical past is proscribed to an user-friendly familiarity with calculus and with the Fourier thought.
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Additional info for Aperiodic layers
We will return to this question in more detail in Chapter 7. 5 Multilayer superpositions So far we have only mentioned phenomena that occur in the superposition of two aperiodic layers. What happens, now, when three or more aperiodic layers are superposed? As we may guess, each layer pair whose two layers are sufficiently correlated will generate in the superposition a Glass pattern of its own, but uncorrelated pairs will not generate Glass patterns. For example, if in a given superposition of three aperiodic layers all of the three layers are mutually correlated, three different Glass patterns will be generated in the superposition (see Fig.
In any case, dot screens having such ring-like spectra are certainly not purely random nor purely periodic, since in both of these cases the screen’s spectrum is only modulated by the individual dot’s spectrum (see Eqs. 10) in Appendix F). 2-9. The Fourier spectrum of a fully periodic structure such as a periodic dot screen or a periodic line grating is purely impulsive (see, for example, Fig. 10(f), or Fig. 12 in Vol. I). Suppose now that we slightly perturb the periodicity by adding some random noise to the locations of the periodic elements (this operation is often called “jittering”).
9: (a) The same three-layer superposition as in Fig. 8, showing only the lower right-hand part of the figure where the three Glass patterns are located. (b) Same as in (a), but without layer A. (c) Same as in (a), but without layer B. (b) Same as in (a), but without layer C. superposed dots contributes its own modulation to the overall spectrum; this results in the typical diffuse nature of this spectrum. 34 2. 10: Explanation of the Fourier spectrum of a random dot screen. For each image r(x,y), Re[R(u,v)] and Im[R(u,v)] show the real and the imaginary parts of the spectrum R(u,v) as obtained on computer by 2D DFT.
Aperiodic layers by Amidror Isaac