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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 10 — Oct. 1, 2003
  • pp: 1900–1919

Moiré patterns between aperiodic layers: quantitative analysis and synthesis

Isaac Amidror  »View Author Affiliations

JOSA A, Vol. 20, Issue 10, pp. 1900-1919 (2003)

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Moiré effects that occur in the superposition of aperiodic layers such as random dot screens are known as Glass patterns. Unlike classical moiré effects between periodic layers, which are periodically repeated throughout the superposition, a Glass pattern is concentrated around a certain point in the superposition, and farther away from this point it fades out and disappears. I show that Glass patterns between aperiodic layers can be analyzed by using an extension of the Fourier-based theory that governs the classical moiré patterns between periodic layers. Surprisingly, even spectral-domain considerations can be extended in a natural way to aperiodic cases, with some straightforward adaptations. These new results allow us to predict quantitatively the intensity profile of Glass patterns; furthermore, they open the way to the synthesis of Glass patterns that have any desired shapes and intensity profiles.

© 2003 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques

Original Manuscript: March 7, 2003
Manuscript Accepted: June 5, 2003
Published: October 1, 2003

Isaac Amidror, "Moiré patterns between aperiodic layers: quantitative analysis and synthesis," J. Opt. Soc. Am. A 20, 1900-1919 (2003)

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  11. Note that this impulse is generated in the convolution by the (k1, k2) impulse in the spectrum R1(u, v) of the first image and the (k3, k4) impulse in the spectrum R2(u, v) of the second image.
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  14. It is interesting to note that just like its periodic counterpart (see Sec. 10.9 of Ref. 3), this proposition remains true for nonlinear transformations gi(x, y), too, i.e., when the original aperiodic layers undergo any given geometric transformations. In such cases, part 2 of the proposition simply gives the geometric transformation that is undergone by the resulting Glass pattern.
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  17. I. Amidror, “A new print-based security strategy for the protection of valuable documents and products using moiré intensity profiles,” in Optical Security and Counterfeit Deterrence Techniques IV, R. L. Van Renesse, ed., Proc. SPIE4677, 89–100 (2002). [CrossRef]

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