Ultrafast spatial phase unwrapping algorithm with accurately correcting transient phase error

In fringe projection profilometry, the wrapped phase is easily polluted by many factors such as noise, shadow, and so on. In this Letter, we propose an ultrafast bi-staggered spatial phase unwrapping (BSPU) method. By constructing another staggered phase, the fringe order jump (FOJ) and local transient phase error (LTPE) can be accurately and quickly located at the same time owing to a simple difference operation. For the first time, to the best of our knowledge, a pioneering threshold separation model is established to precisely distinguish FOJ and LTPE. Based on the continuity assumption, LTPE is effectively corrected by introducing the concept of "non-integer fringe order." The range of measurable discontinuity height is improved owing to the distinction between real phase jump and random error in the spatial phase unwrapping. In addition, it is thousands of times faster than the traditional path-dependent algorithm and even has higher measurement accuracy. Experimental results show the effectiveness and robustness of the proposed method in various complex measurement environments.