Theory of moiré sensing by means of contour functions

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Abstract
We present a mathematical analysis of moiré sensing in which the basic theoretical concept—and tool—is the concept of the contour function. We show that the mathematical analysis is simplified greatly by systematic recourse to this tool. The analysis that is presented permits a simultaneous treatment of two different modes of implementing the moiré technique: the direct mode (widely used and well known) and the converse mode (scarcely used). The converse mode consists of computing and designing a grating especially for one model of an object in such a way that if (and only if) the object is in conformity with the prescribed model, will the resulting moiré fringes be parallel straight lines. We give explicit formulas and algorithms for such computations.

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