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Formulation of the moiré fringes formed by superimposing linear gratings with slowly varying parameters.

In this report we present formulation of moiré fringes that are formed by superimposing two basically similar linear amplitude gratings but with slowly varying parameters. We show that the resulting fringes, in general, in the first approximation satisfy quadratic functions, and they represent phase contours in the neighborhood of the phase singularity associated with the superposition of two exactly similar linear gratings with parallel rulings. By fabricating linear gratings with slowly varying parameters and superimposing them on similar gratings with fixed parameters, it is verified that quadratic functions fit satisfactorily on the traces of the resulting moiré fringes, and the deflections in the parameters are deduced from the fitting. Having in mind that changes in many physical quantities are convertible into the changes of grating parameters, the technique provides a useful means for accurate and reliable studies of many physical effects.