Temporal Phase Unwrapping Based on Unequal Phase-Shifting Code

In fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU), reducing the number of projecting patterns has become one of the most important works in recent years. To remove the
$2\pi $
ambiguity independently, this paper proposes a TPU method based on unequal phase-shifting code. Wrapped phase is still calculated from
$N$
-step conventional phase-shifting patterns with equal phase-shifting amount to guarantee the measuring accuracy. Particularly, a series of different phase-shifting amounts relative to the first phase-shifting pattern are set as codewords, and encoded to different periods to generate one coded pattern. When decoding, Fringe order with a large number can be determined from the conventional and coded wrapped phases. In addition, we develop a self-correction method to eliminate the deviation between the edge of fringe order and the
$2\pi $
discontinuity. Thus, the proposed method can achieve TPU but need to only project one additional coded pattern (e. g. 3+1), which can significantly benefit dynamic 3D shape reconstruction. The theoretical and experimental analysis verify that the proposed method performs high robustness on the reflectivity of the isolated object while ensuring the measuring speed.