FOURIER-BASED ANALYSIS AND SYNTHESIS OF MOIRES IN THE SUPERPOSITION OF GEOMETRICALLY TRANSFORMED PERIODIC STRUCTURES

The best method for investigating moire phenomena in the superposition of periodic layers is based on the Fourier approach. However. superpo sition moire effects are not limited to periodic layers, and they also occur between repetitive structures that are obtained by geometric tr ansformations of periodic layers. We present in this paper the basic r ules based on the Fourier approach that govern the moire effects betwe en such repetitive structures. We show how these rules can be used in the analysis of the obtained moires as well as in the synthesis of moi res with any required intensity profile and geometric layout. In parti cular, we obtain the interesting result that the geometric layout and the periodic profile of the moire are completely independent of each o ther; the geometric layout of the moire is determined by the geometric layouts of the superposed layers, and the periodic profile of the moi re is determined by the periodic profiles of the superposed layers. Th e moire in the superposition of two geometrically transformed periodic layers is a geometric transformation of the moire formed between the original lavers, the geometric transformation being a weighted sum of the geometric transformations of the individual lavers. We illustrate our results with several examples, and in particular we show holy one may obtain a fully periodic moire even when the original layers are no t necessarily periodic. (C) 1998 Optical Society of America.