Fourier-based analysis and synthesis of moirés in the superposition of geometrically transformed periodic structures

I. Amidror, R.D. Hersch

Journal of the Optical Society of America A, Vol. 15, No. 5, May 1998, 1100-1113

The best method for investigating moiré phenomena in the superposition of periodic layers is based on the Fourier approach. However, superposition moiré effects are not limited to periodic layers, and they also occur between repetitive structures which are obtained by geometric transformations of periodic layers. Based on the Fourier approach we present in this paper the basic rules which govern the moiré effects between such repetitive structures. We show how these rules can be used in the analysis of the obtained moirés, as well as in the synthesis of moirés with any required intensity profile and geometric layout. In particular we obtain the interesting result that the geometric layout of the moiré and the periodic-profile of the moiré are completely independent of each other; the geometric layout of the moiré is determined by the geometric layouts of the superposed layers, while the periodic-profile of the moiré is determined by the periodic-profiles of the superposed layers. The moiré in the superposition of two geometrically transformed periodic layers is a geometric transformation of the moiré formed between the original layers, the geometric transformation being a weighted sum of the geometric transformations of the individual layers. We illustrate our results by several examples, and in particular we show how one may obtain a fully periodic moiré even when the original layers are not necessarily periodic.

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