Radial gratings as moir$eacute$ gauges

A theory on the formation of moiré patterns by mutually interfering radial gratings is developed. It is shown that the moiré fringes formed inside the circle, which has as diameter the centre-to-centre distance of the gratings, belong to the additive moiré type and they represent families of confocal equilateral hyperbolae. Outside this circle the subtractive moiré pattern is valid, which consists of circles of different radii whose centres lie on the perpendicular bisector of the centre-to-centre distance. For the radial grating moiré gauge the additive moiré pattern is of importance since two sectors of radial gratings are used with a large centre-to-centre distance. The radial gauge is convenient for determining the normal components of strains. The advantage of this type of gauge over the line grating gauge is that the radial grating corresponds to an infinite number of line gratings of progressively varying pitch. This allows a correct evaluation of displacement and strain at a suitably selected gauge length.