Self-correction of fringe order jump error induced by system nonlinearity based on phase-coding method

Temporal phase unwrapping based on phase-encoding is a technique widely used in 3D measurement for its high-speed advantage. However, eliminating fringe order jump error induced by the system’s luminance nonlinearity is still a key challenge. We propose a fringe order jump error self-correction method to address this issue. First, we encode the shifting phase and stair phase separately and combine them into the same pattern based on four-step phase shifting. This allows us to calculate the fringe order and wrapped phase simultaneously and avoid the overlapping of two set phases. Then, we add auxiliary patterns to obtain information on the order-located period’s odd-evenness characteristic. Theoretically, we demonstrate that under the influence of the nonlinear effect, the order calculation value for a particular period fluctuates between the ideal values of two adjacent orders. Thus, the correct order value can be directly determined by acquiring the period characteristic information, without the need for complex error compensation. Simulations demonstrate that the method performs good robustness where random noise and luminance saturation exist simultaneously in addition to system nonlinearity. Our experiments confirm the effectiveness of this method for high-accurate and fast fringe order determination.