Stair Phase Coding Method Based on Arc Cosine with Only Four Patterns

The stair phase coding method is an important phase unwrapping method, but needs to project and capture many fringe patterns. Therefore, to reduce the number of fringe patterns, we propose a stair phase coding method based on arc cosine with only four patterns. We project and capture a set of three-step phase-shift sinusoidal fringe patterns and a cosine pattern encoding stair phase, and then we compute the wrapped phase and background light from the three-step phase-shift sinusoidal fringe patterns, normalized cosine pattern can be estimated via background light, and the cosine pattern encoding stair phase. Arc cosine calculation is applied to the normalized cosine pattern to obtain the stair phase, then the fringe order is determined from the stair phase. A semi-periodic fringe order correction algorithm based on the dilation image processing technique is proposed to ensure the accuracy of fringe order. The continuous phase is obtained from the wrapped phase and the fringe order. Experiments are carried out to verify the performance of the proposed method using a face model and a foam board with two hollows. The results show that our algorithm can achieve accurate three-dimensional measurement with only four patterns.