Analysis of moiré fringe multiplication phenomena

Sensitivity and accuracy of measurements made by the moiré effect can be increased by a fringe multiplication factor. For a given displacement or deformation, the number of fringes that cross the field is increased by this factor. Multiplications as high as thirty are demonstrated. High sensitivity measurements are possible with coarse active gratings. With two amplitude gratings of equal nominal frequencies multiplication patterns exhibiting pure two-beam interference are produced when transmittance is 0.5. With gratings in which frequencies are dissimilar by integral factor beta, multiplication by bbeta is achieved, where b is an integer. Guild's theory of moiré fringes is extended to this case of grossly dissimilar grating frequencies. The combination of a symmetrical double-order blazed reference grating with a coarse bar-and-space active grating appears most attractive for many metrological applications.