This paper demonstrates instantaneous phase-stepping and subsequent phase analysis methods for interferometry and two-dimensional photoelasticity. The camera that has a pixelated form-birefringent micro-retarder array acquires phase-stepped fringes in a single camera frame. Then, the distributions of Stokes parameters that represent the state of polarization are calculated from a single image. In the case of the polarization interferometer, the phase difference of the two orthogonally polarized light beam can be easily determined from the Stokes parameters. On the other hand, the phase distributions of the isochromatics and the isoclinics are obtained in the case of the photoelasticity. It is emphasized that this method is applicable to real-time inspection of optical elements as well as the study of the mechanics of time-dependent materials because multiple exposures are unnecessary for sufficient data acquisition in the completion of data analysis.