Representation of image distortion by Moiré fringes at phase singularity state

When a grating is imaged by an optical imaging system, due to the aberrations of the system, the parameters of the image grating suffer minute gradual changes across the image. Superimposing an ideal grating image over the real grating image at the phase singularity state of the two gratings leads to phase contours, special Moiré fringes, which directly represent the distortions over the image. In this report, after a brief review of the required theoretical bases, we show when the parameters of a grating change linearly the corresponding Moiré fringes at the singularity state are represented by quadratic functions, and for nonlinear changes higher order functions are involved. Thus, by imposing desired changes on the parameters of a grating one can produce Moiré fringes satisfying functions of required orders. In the experimental part of the report we apply the technique to evaluate the image distortions imposed by a conventional camera and cameras installed in a mobile and in a tablet.