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 through an identical writer, which was once devoted to the moiré results that ensue among periodic or repetitive layers. like the first quantity, this booklet offers an entire basic objective and application-independent exposition of the topic. It leads the reader throughout the a number of phenomena which happen within the superposition of correlated aperiodic layers, either within the picture and within the spectral domain names. through the complete textual content the e-book favours a pictorial, intuitive process that is supported through arithmetic, and the dialogue is followed via plenty of figures and illustrative examples, a few of that are visually beautiful or even spectacular.
The prerequisite mathematical heritage is proscribed to an hassle-free familiarity with calculus and with the Fourier idea.
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Extra info for Aperiodic layers
Can you think of possible applications of laser speckle to the detection and measurement of displacements or deformations? Some of these applications are briefly described in the following problems. More details can be found, for example, in [Erf78], [Cloud95] and [Gåsvik95]. 2-15. Detection and measurement of slight in-plane displacements or deformations. Speckle metrology is a valuable alternative to the classical moiré-based methods in metrology. Instead of using periodic gratings, speckle techniques make use of the random pattern of dark and bright spots (known as speckle) that is formed when a diffusely reflecting object is illuminated by coherent laser light.
Can be artificially generated by computer, even if they do not correspond to any physical reality. Note that different superposition rules in the image domain will have different spectrum composition rules in the spectral domain, which are determined by properties of the Fourier transform. For example, in the case of the additive superposition rule, where Eq. 1) is replaced by: r(x,y) = r1(x,y) + ... 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) + ...
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.