Unification of formulation of moiré fringe spacing in parametric equation and Fourier analysis methods

Abolhassani, Mohammad; Mirzaei, Mahmood

doi:10.1364/ao.46.007924

Cited by 17 publications

(9 citation statements)

References 5 publications

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“…The moiré fringe spacing is about 2.5 nm and the angle between the moiré fringes and ( 11 1) Matrix planes is about 30.2 according to eqn (2) and (3). 52 The theoretical moiré fringes according to the OR between the Y 2 Ti 2 O 7 lattice and matrix without distortion are illustrated in Fig. 7a.…”

Section: Resultsmentioning

confidence: 99%

A new method for fast statistical measurement of interfacial misfit strain around nano-scale semi-coherent particles

2017

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Section: Resultsmentioning

confidence: 99%

A new method for fast statistical measurement of interfacial misfit strain around nano-scale semi-coherent particles

2017

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“…The special characteristic in the binary grating superposition is that the appearance of different moiré forms depends on not only the periods but also the opening ratios, so the n=−∞ a (1) n cos( 2π nx 40 ), r 2 (x, y) = ∞ n=−∞ a (2) n cos( 2π n 20 (x cos( π 18 ) + y sin( π 18 ))),…”

Section: Discussion Of the Coexistence Of The Real Moiré And Pseudo-mmentioning

confidence: 99%

“…Because the conditions 0 < τ 1 /T 1 < 1 and 0 < τ 2 /T 2 < 1 are always satisfied, a 1 1 and a 2 1 are not equal to 0. The (1, ±1) moiré cases are always the real moiré cases, no matter what the opening ratio is.…”

Section: Description Of the Generated Moiré Case By Using The Fouriermentioning

confidence: 99%

An image domain approach to the interpretation of the visible moiré phenomenon

Yu¹,

Wang²,

Lin³

2013

J. Opt.

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An approach to the interpretation of the visible moiré phenomenon in the image domain has been proposed. The analysis of the Fourier series expansion presents an initial criterion for distinguishing the real moiré and pseudo-moiré cases. A geometric calculation of the superposed grating lines is utilized to obtain the parameters for describing the real and pseudo-moiré cases. On the basis of the study, the average intensities of the waveforms of the real moiré and pseudo-moiré cases are calculated in order to provide the interpretation. It indicates that different moiré cases result from the garbled discernment of human eyes, which is introduced by the microstructure versus macrostructure effects. The variations of intensity and average intensity in the microstructure result in the confusion of the average intensities of the real moiré and pseudo-moiré waveforms. The interpretation is significant for the visible real and pseudo-moiré effects, both in the multiplicative superposition and in the additive superposition composed from periodic cosinusoidal gratings and binary gratings in the image domain. The approach also considers the coexistence of the real moiré and pseudo-moiré cases. The rule for their coexistence has been summarized in the image domain.

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“…The indicial equations method [12] hardly obtains the period and orientation of moiré in the repetitive, periodic-like grating superposition for the variation of them. Therefore, the local frequency method will be utilized.…”

Section: A Calculation Of Parameters Of the Moiré In The Image Domainmentioning

confidence: 99%

Interpretation of visible moiré between repetitive periodic-like gratings in the image domain

Wang

Lin

2014

Appl. Opt.

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An image domain approach to the interpretation of visible moiré phenomena in repetitive grating multiplicative superposition has been proposed. The local frequency method provides the instantaneous period and orientation of generated moiré. These parameters of the moiré have been sorted into real and pseudo patterns by the Fourier expansions analysis. With the combination of these two steps, the concept "equivalent period contribution threshold" has been introduced. It is found that different thresholds bring different integral domains and results for the calculation of average intensities of generated moiré waveforms. This proves that different thresholds would introduce different average intensity distribution (macrostructure effects) in different moiré patterns. With the local intensity variation (microstructure effects), the human eye would confuse different macrostructure effects but only consider them the same. The interpretation is that the macrostructure versus microstructure effects garble discernment of the human eye and result in different visible moiré phenomena. This is significant for visible moiré effects in various repetitive grating (both of cosinusoidal and binary patterns) superpositions in the image domain. It also presents and summarizes the coexistence of real and pseudo moirés in repetitive, periodic-like layer superposition.

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Unification of formulation of moiré fringe spacing in parametric equation and Fourier analysis methods

Cited by 17 publications

References 5 publications

A new method for fast statistical measurement of interfacial misfit strain around nano-scale semi-coherent particles

A new method for fast statistical measurement of interfacial misfit strain around nano-scale semi-coherent particles

An image domain approach to the interpretation of the visible moiré phenomenon

Interpretation of visible moiré between repetitive periodic-like gratings in the image domain

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