Investigation of phase object trace duplication in moiré deflectometry

In a deflectometry experiment for finding the temperature distribution around a hot wire as a phase object, the trace of the wire in a moiré pattern is duplicated, and it is observed that the separation of the wire traces varies when the distance between two gratings of a moiré deflectometry setup is changed. By investigation of moiré deflectometry, it is found that the object trace duplication cannot be interpreted by ray deflection theory, which is based on geometric optics. By using diffraction theory, the effect of a phase object on a moiré pattern is studied, and some generalized formulations are presented. It is demonstrated that the deformation of moiré fringes does not originate from the wavefront derivative, but superposition of two separated wavefronts causes fringe deformation. By this approach, the accuracy of ray deflection analysis is improved. Finally, the results of this model are simulated, and the simulation has good agreement with the experimental model.