Time Average Geometric Moiré—Back to the Basics

摘要

Applicability of time average geometric moiré for elastic oscillating structures is analysed in this paper. Mathematical and numerical models describing the formation of time averaged fringes are carefully constructed without the assumption that dynamic deflections are described by a slowly varying function. Though time average geometric moiré is considered as a classical optical experimental technique, we show that well known relationship between the fringe order, amplitude of oscillation and pitch of the grating in state of equilibrium can be used only when the amplitude is small. Otherwise the inverse problem of fringe interpretation becomes much more complicated and is the object of analysis in this paper. We describe the interpretation of fringes produced by time average geometric moiré in detail and illustrate the complexity of the problem by numerical examples. Keywords Time average moiré - Bessel functions - Inverse problem - Pattern of fringes - Convergence