Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern

High accurate phase analysis of waveforms as fringe patterns is essential for a wide range of scientific and engineering disciplines. However, precise phase analysis under extremely low signal-to-noise conditions is a challenging task for conventional phase-shifting methods. Here, a novel accurate phase recovering technique, called the spatiotemporal phase-shifting method (ST-PSM), is developed to measure the phase information robustly by utilizing two-dimensional intensity data in spatial- A nd temporal-domains simultaneously. Our simulation results indicated that ST-PSM had strong tolerance to random noise, and a self-neutralizing function to eliminate the periodical phase error due to the nonlinearity of detector, intensity saturation, vibration or phase-shifting error. The effectiveness was demonstrated experimentally from a non-contact shape measurement in fringe projection profilometry under extreme underexposure and overexposure recording conditions. Furthermore, by incorporating modern GPU parallel computing technology, a 4-step phase-shifted fringe pattern with 8 K image size can be calculated within one second. Due to its robustness and high accuracy with a fast calculation, therefore, we believe this technique has a significant impact on a variety of research and scientific fields.