Analysis of the Superposition of Periodic Layers and TheirMoiré Effects through the Algebraic Structure of Their FourierSpectrum

  • Authors:

  • Isaac Amidror;Roger D. Hersch

  • Affiliations:

  • Lab. de Systèmes Périphériques (LSP), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland;Lab. de Systèmes Périphériques (LSP), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 1998

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Abstract

A new approach is presented for investigating thesuperposition of any number of periodic structures, and the moiré effects which may result. This approach, which is based on analgebraic analysis of the Fourier-spectrum using concepts from thetheory of geometry of numbers, fully explains the properties of thesuperposition of periodic layers and of their moiré effects. Itprovides the fundamental notations and tools for investigating, bothin the spectral domain and in the image domain, properties of thesuperposition as a whole (such as periodicity or almost-periodicity),and properties of each of the individual moirés generated in thesuperposition (such as their profile forms and intensity levels, theirsingular states, etc.). This new, rather unexpected combination ofFourier theory and geometry of numbers proves very useful, and itoffers a profound insight into the structure of the spectrum of thelayer superposition and the corresponding properties back in the imagedomain.