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Fourier\u2010based processing of one\u2010dimensionally ordered arrays is described by way of introduction, before analysing two\u2010dimensional crystals in projection with the aim of enhancing signal:noise ratio and thus of feint features that were initially obscured. This form of analysis is then extended to decomposing the moir\u00e9 patterns formed when sheets overlap, thereby enabling the separation of interfering image patterns. Analogous forms of an analysis can also be applied to objects with rotational symmetry. 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