Moiré Extensometers

Theocaris, P. S.

doi:10.1016/b978-0-08-012974-7.50013-7

Cited by 16 publications

(26 citation statements)

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“…(1) If f 1 and f 2 are also linearly dependent over Z (so that z = r = 1), or in other words if f 1 and f 2 are commensurable (i.e., the ratio of their lengths is rational), 5 then Md(f 1 , f 2 ) is a lattice of rank 1 which is located on the line spanned by f 1 and f 2 .…”

Section: The Application To the Frequency Spectrummentioning

confidence: 99%

“…offers a wide range of interesting properties for exploration: starting from the overall structure of the superposition (which may be periodic or not) and culminating in the interesting and sometimes even spectacular moiré effects which may appear in the superposition. The superposition moiré phenomenon has a vast number of important applications in many different fields [1][2][3][4][5], while in other circumstances (like in the case of color reproduction) it may have an unwanted, adverse effect [6]. It is therefore important to fully understand this phenomenon and its various properties, along with the other global properties of the layer superposition as a whole.…”

Section: Introductionmentioning

confidence: 99%

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Amidror

Hersch

1998

Journal of Mathematical Imaging and Vision

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Abstract.A new approach is presented for investigating the superposition of any number of periodic structures, and the moiré effects which may result. This approach, which is based on an algebraic analysis of the Fourierspectrum using concepts from the theory of geometry of numbers, fully explains the properties of the superposition of periodic layers and of their moiré effects. It provides the fundamental notations and tools for investigating, both in the spectral domain and in the image domain, properties of the superposition as a whole (such as periodicity or almost-periodicity), and properties of each of the individual moirés generated in the superposition (such as their profile forms and intensity levels, their singular states, etc.). This new, rather unexpected combination of Fourier theory and geometry of numbers proves very useful, and it offers a profound insight into the structure of the spectrum of the layer superposition and the corresponding properties back in the image domain.

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Section: The Application To the Frequency Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Untitled

Amidror

Hersch

1998

Journal of Mathematical Imaging and Vision

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“…The mixing can be performed optically or digitally. Optical mixing is usually referred to as "holographic interferometry" 19,20 if the beating is with an interferogram recorded on photographic film and as moiré interferometry 22,23 if the beating is between two sets of intensity fringes recorded on a digital camera. Digital mixing is called "speckle interferometry," 21 where the speckle is interpreted as a random phase mask; then the beating is the crosscorrelation function of the mask before and after deformation.…”

Section: Introductionmentioning

confidence: 99%

“…Deformation measurement has been intensively investigated during the past 30 years, [19][20][21][22][23] but it has been exclusively limited to two-dimensional (2D) measurements of surface deformation. The universal principle applied to this problem consists of first producing an interferogram, i.e., modulating a signature of the surface before deformation as a phase modulation on an optical carrier.…”

Section: Introductionmentioning

confidence: 99%

Diffraction from deformed volume holograms: perturbation theory approach

Tian

Cuingnet²,

et al. 2005

J. Opt. Soc. Am. A

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We derive the response of a volume grating to arbitrary small deformations, using a perturbative approach. This result is of interest for two applications: (a) when a deformation is undesirable and one seeks to minimize the diffracted field's sensitivity to it and (b) when the deformation itself is the quantity of interest and the diffracted field is used as a probe into the deformed volume where the hologram was originally recorded. We show that our result is consistent with previous derivations motivated by the phenomenon of shrinkage in photopolymer holographic materials. We also present the analysis of the grating's response to deformation due to a point indenter and present experimental results consistent with theory.

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“…The classical moiré method, referred to as geometric or coarse moiré, has been widely used in experimental stress analysis [2][3][4][5][6][7]. However, because the gratings utilized in the geometric moiré method have a frequency lower than 100 lines mm −1 , this method can only be applied to measure large deformation.…”

Section: Introductionmentioning

confidence: 99%

A study on the digital nano-moiré method and its phase shifting technique

Xie

Liu

Fang

et al. 2004

Meas. Sci. Technol.

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A novel digital nano-moiré method is proposed to measure the in-plane nanoscopic deformation of an object. In the measurement, the periodic lattice of a single-crystal material acts as a specimen grating while a digital reference grating (DRG) is prepared by computer software. These two gratings overlap to generate a moiré fringe pattern. The preparation of the grating, the formation principle of digital nano-moiré fringes and its relative phase shifting technique are described in detail. A typical experiment was conducted with a highly oriented pyrolytic graphite (HOPG) sample. The residual deformation of the irradiated HOPG sample was measured using this method. The experiment result verifies the feasibility of this method, and demonstrates the potential for further applications.

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Moiré Extensometers

Cited by 16 publications

References 0 publications

Untitled

Untitled

Diffraction from deformed volume holograms: perturbation theory approach

A study on the digital nano-moiré method and its phase shifting technique

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