Graph Theory

Read e-book online Aperiodic layers PDF

By Amidror Isaac

ISBN-10: 1402054572

ISBN-13: 9781402054570

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 ebook presents an entire common objective and application-independent exposition of the topic. It leads the reader throughout the numerous phenomena which take place within the superposition of correlated aperiodic layers, either within the snapshot and within the spectral domain names. through the entire textual content the booklet favours a pictorial, intuitive technique that is supported by way of arithmetic, and the dialogue is observed by way of plenty of figures and illustrative examples, a few of that are visually beautiful or even spectacular.

The prerequisite mathematical heritage is proscribed to an uncomplicated familiarity with calculus and with the Fourier thought.

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Sample text

As we will see below, local correlation between two superposed aperiodic layers is the reason for the appearance of a Glass pattern in that area of the superposition. For example, the Glass patterns shown in Fig. 1(c) consist of a brighter area in the center because within this area the two superposed layers are well correlated (the dots of both layers almost coincide), while in the remaining areas of the figure the correlation between the two layers is low. Another related term is that of cross correlation between two images (or functions).

For the sake of comparison, (f) shows a periodic counterpart of the screen shown in (e), along with its purely impulsive spectrum (see also Fig. 12 in Vol. I). The background gray level in all of the spectra represents the value zero, while white represents positive values and black represents negative values. In the image domain, however, black represents zero and white represents one, as in our usual convention (see Sec. 2). ฀(a)฀A฀single, centered฀square฀white฀dot฀on฀a฀black฀background฀and฀its฀spectrum.

4), the introduction of some residual periodicity into the aperiodic layers may cause in the superposition the appearance of darker bands that surround the bright center of the Glass pattern. See also Problem 7-19. 8: A superposition of three aperiodic layers A, B and C, where layer B is a slightly scaled-up copy of layer A, and layer C is a slightly rotated copy of layer A. Layer A has been slightly shifted to the right, in order to move the two Glass patterns it generates away from the origin.

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Aperiodic layers by Amidror Isaac


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