A new version of a moire microscope is presented that embodies the theory o
f optical moire interferometry. To interrogate the deformed specimen gratin
g, the device uses a transmission diffraction grating that allows for a sim
ple and quick change of the virtual reference grating vector without distur
bing the optical alignment of the other components in the optical train. To
analyze deformation from the acquired moire interference fringe patterns,
the displacement light-intensity moire optical law introduced by Sciammarel
la is revisited. The analysis of deformation is consistent with the continu
um principles of finite deformation and can readily be used to obtain micro
-mechanical quantities of interest such as the local strains, stretches and
rotations.