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 spouse to the unique quantity by way of an analogous writer, which used to be devoted to the moiré results that take place among periodic or repetitive layers. like the first quantity, this e-book offers an entire normal objective and application-independent exposition of the topic. It leads the reader during the numerous phenomena which take place within the superposition of correlated aperiodic layers, either within the snapshot and within the spectral domain names. during the entire textual content the ebook favours a pictorial, intuitive procedure that is supported by way of arithmetic, and the dialogue is observed by means of quite a few figures and illustrative examples, a few of that are visually beautiful or even spectacular.

The prerequisite mathematical heritage is restricted to an common familiarity with calculus and with the Fourier idea.

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**Example text**

13(a) shows the same screen superposition as Fig. 12(a), but this time the respective spectra are represented by their magnitude Abs[F(u,v)] and their phase Arg[F(u,v)] rather then by their real part Re[F (u,v)] and their imaginary part Im[F (u,v)]. Explain the 42 2. 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.

10 shows, step by step, how one can understand the Fourier spectrum of a random dot screen. Explain this figure, and using it explain the diffuse nature of the spectra of random screens. Hint: Part (a) of the figure shows a single white square dot on a black background; this image is expressed mathematically by the function d(x,y) = rect(x/τ , y/τ ) where τ is the width of the square dot. The Fourier transform (spectrum) of this function is given by D(u,v) = τ 2 sinc( τ u) sinc( τ v) [Bracewell95 p.

Fig. 11 shows the same images as Fig. 10, but this time the respective spectra are represented by their magnitude Abs[F(u,v)] and their phase Arg[F(u,v)] rather then by their real part Re[F(u,v)] and their imaginary part Im[F(u,v)]. Explain the connection between the two representations of each of the spectra in Figs. 11. 2-5. The Fourier spectrum of a random dot screen: influence of the dot shape. What would have changed in the spectra of Fig. 10 if the individual screen dots were circular rather than square?