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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. 13, Iss. 5 — May. 1, 1996
  • pp: 974–987

Fourier-based analysis of phase shifts in the superposition of periodic layers and their moiré effects

Isaac Amidror and Roger D. Hersch  »View Author Affiliations


JOSA A, Vol. 13, Issue 5, pp. 974-987 (1996)
http://dx.doi.org/10.1364/JOSAA.13.000974


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Abstract

A Fourier-based approach is presented for the investigation of multilayer superpositions of periodic structures and their moiré effects. This approach fully explains the properties of the superposition of periodic layers and of their moiré effects, both in the spectral domain and in the image domain. We concentrate on showing how this approach provides also a full explanation of the various phenomena that occur because of phase shifts in one or more of the superposed layers. We show how such phase shifts influence the superposition as a whole and, in particular, how they affect each moiré in the superposition individually: We show that each moiré in the superposition undergoes a different shift, in its own main direction, whose size depends both on the moiré parameters and on the shifts of the individual layers. However, phase shifts in the individual layers do not necessarily lead to a solid shift of the whole superposition, and they may rather cause modifications in its microstructure. We demonstrate our results by several illustrative figures.

© 1996 Optical Society of America

History
Original Manuscript: July 14, 1995
Revised Manuscript: September 18, 1995
Manuscript Accepted: October 20, 1995
Published: May 1, 1996

Citation
Isaac Amidror and Roger D. Hersch, "Fourier-based analysis of phase shifts in the superposition of periodic layers and their moiré effects," J. Opt. Soc. Am. A 13, 974-987 (1996)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-5-974


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References

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  14. See, for example, A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 117.
  15. See, for example, A. Rosenfeld, A. C. Kak, Digital Picture Processing, 2nd ed. (Academic, Orlando, Fla., 1982), Vol. 1, p. 75.
  16. G. Birkhoff, S. MacLane, A Survey of Modern Algebra, 4th ed. (Macmillan, New York, 1977), pp. 237–238.
  17. Although there exist different possible choices of fundamental frequency vectors f1, f2for p(x, y), each of these choices automatically determines a corresponding pair of fundamental period vectors P1, P2[by Eq. (A1)], and hence it determines also the fundamental period parallelogram that they define and the corresponding virtual-grating periods T1, T2. Note that all the different possible choices represent the same 2-D lattices Lfand LPof p(x, y).

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