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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.20.001900


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Abstract

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

Citation
Isaac Amidror, "Moiré patterns between aperiodic layers: quantitative analysis and synthesis," J. Opt. Soc. Am. A 20, 1900-1919 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-10-1900


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References

  1. L. Glass, “Moiré effect from random dots,” Nature 223, 578–580 (1969).
  2. L. Glass and R. Pérez, “Perception of random dot interference patterns,” Nature 246, 360–362 (1973).
  3. I. Amidror, The Theory of the Moiré Phenomenon (Kluwer Academic, Dordrecht, The Netherlands, 2000).
  4. I. Amidror, “Glass patterns and moiré intensity profiles: new surprising results,” Opt. Lett. 28, 7–9 (2003).
  5. http://lspwww.epfl.ch/books/moire/kit.html.
  6. I. Amidror, “A unified approach for the explanation of stochastic and periodic moirés,” J. Electron. Imaging (to be published).
  7. I. Amidror, “Glass patterns in the superposition of random line gratings,” J. Opt. A, Pure Appl. Opt. 5, 205–215 (2003).
  8. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, Reading, N.Y., 1986).
  9. R. N. Bracewell, Two Dimensional Imaging (Prentice-Hall, Englewood Cliffs, N.J., 1995).
  10. Y. Nishijima and G. Oster, “Moiré patterns: their application to refractive index and refractive index gradient measurements,” J. Opt. Soc. Am. 54, 1–5 (1964).
  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.
  12. A. Rosenfeld and A. C. Kak, Digital Picture Processing, Vol. 1, 2nd ed. (Academic, Boca Raton, Fla., 1982).
  13. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  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.
  15. S. C. Dakin, “The detection of structure in Glass patterns: psychophysics and computational models,” Vision Res. 37, 2227–2246 (1997).
  16. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, Amsterdam, 1993), pp. 99–139.
  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. SPIE 4677, 89–100 (2002).

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