An analysis of the formation of Moiré fringes by the intensity addition of two high-frequency fringe systems shows that the resulting Moiré fringes will retain sinusoidal intensity distribution regardless of whether the contributing fringe systems follow the Airy formula or the cos2law. This, it is shown, is due to the creation in each diffracted order of a ‘double source juxtaposition’. True Airy-type Moiré fringes were realized in holography. The contributing fringe systems were of a multiple-beam Fizeau-Tolansky type. The holographic reconstruction, for each diffracted order of the multiple sources of the interferometer, results in the formation of narrow, sensitive, high-resolution Moiré fringes. These may be applied to real time tests of a micro-object's deformation.