Efficient underwater 3D shape measurement with robust dual-phase complementary unwrapping

Phase-shifting profilometry (PSP) combined with Gray-code temporal phase unwrapping is widely used for underwater 3D measurement; however, its performance is severely degraded by light scattering and absorption in turbid water. A key challenge arises from the mismatch between the fringe order decoded from Gray-code patterns and the phase continuity of the wrapped phase. This mismatch is mainly caused by stripe blurring induced by underwater scattering. In addition, phase instability near the ±π discontinuities may further lead to phase-jump errors and phase unwrapping failures. To address this problem, a dual-phase complementary unwrapping method (DPC-Unwrap) is proposed. The method reconstructs absolute phase using two π-shifted wrapped phases with an embedded robust correction mechanism, without introducing additional projection patterns. A hybrid ternary-binary Gray-code scheme with asymmetric gray-level mapping is further adopted to improve decoding reliability and encoding efficiency under scattering interference. Water-tank experiments, turbidity-varying tests, and inland and offshore field measurements demonstrate that the proposed method suppresses phase-jump errors and achieves millimeter-level measurement accuracy. The proposed approach improves the robustness and efficiency of underwater FPP and applies to high-precision optical 3D measurement in complex natural waters.