By Amidror Isaac
This e-book provides for the 1st time the speculation of the moiré phenomenon among aperiodic or random layers. it's a complementary, but stand-alone significant other to the unique quantity by way of an identical writer, which was once devoted to the moiré results that happen among periodic or repetitive layers. like the first quantity, this publication offers an entire basic objective and application-independent exposition of the topic. It leads the reader throughout the a variety of 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 e-book favours a pictorial, intuitive method that's supported via arithmetic, and the dialogue is followed by means of numerous figures and illustrative examples, a few of that are visually appealing or even spectacular.
The prerequisite mathematical history is restricted to an straight forward familiarity with calculus and with the Fourier idea.
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Extra resources for Aperiodic layers
The resulting spectrum can be expressed in terms of its real part and its imaginary part, and hence also in terms of the amplitude spectrum (or its square, the power spectrum) and the phase spectrum. But the phase spectrum of an image contains precisely all of its phase information. How do you explain this contradiction? Hint: As explained in Sec. 2 of Appendix F, a random process (or a stochastic process) can be viewed as an infinite set of signals (or images) that represent different instances of the same random process (much like different series of results obtained by rolling the same dice).
Background and basic notions connection between the two representations of the respective spectra in Figs. 13. Note that the displacement between the two layers is inversely proportional to the fringe spacing in the spectrum, and the direction of displacement is perpendicular to the fringes. 2-13. Fig. 12(a) shows the spectrum of the superposition of two slightly shifted copies of a random dot screen. As shown in the previous problems, this spectrum provides useful information about the displacement between the two copies of the random screen and about its orientation.
244], if we denote the Fourier transform of each function in Eq. 1) by the respective capital letter and the 2D convolution by **, the spectrum of the superposition is given by: R(u,v) = R1(u,v) ** ... 1: It should be noted, however, just as in the periodic case, that the multiplicative model is not the only possible superposition rule, and in other situations different superposition rules can be appropriate. For example, when images are superposed by making multiple exposures on a positive photographic film (assuming that we do not exceed the linear part of the film’s response), intensities at each point are summed up, which implies an additive rule of superposition.