Optimal Implementation of Dynamical Visual Cryptography Scheme for Imaging-Based Testing of Human Visual System

Dynamic visual cryptography (DVC) can be formulated as a discrete-time reconstruction problem for time-averaged moiré fringes generated by oscillatory transformations of periodic gratings. When implemented on digital display hardware, the continuous oscillatory motion must be realized through discrete frames, which may prevent correct reconstruction of higher-order time-averaged fringes due to refresh-rate limitations. In this work, mathematical criteria are derived to ensure the reliable reconstruction of higher-order time-averaged moiré fringes under finite refresh rate constraints. Harmonic, stochastic, and rectangular temporal waveforms are examined within a unified framework based on the number of frames per oscillation period and the discrete structure of the resulting time-averaged intensity distribution. Stochastic waveforms are shown to not guaranty reproducible fringe formation. For harmonic modulation with a 240 Hz display refresh rate and a 50 Hz oscillation frequency, only four full frames per period are obtained, which is insufficient to reconstruct the third time-averaged moiré fringe requiring at least sixteen frames per period. Rectangular waveforms satisfy the derived reconstruction conditions when the pitch of the grating, the oscillation amplitude, and the resolution of the rendered grating meet explicit constraints. These results establish quantitative parameter bounds for a mathematically consistent software-based DVC implementation on digital displays.