Efficient and robust phase unwrapping via virtual gratings and hybrid coding

High-frequency phase unwrapping remains a key challenge in fringe projection profilometry (FPP), where robustness and efficiency often conflict. To address this, we present virtual gratings and hybrid phase unwrapping (VGHPU), a novel, to the best of our knowledge, framework that integrates expanded Gray-code (EGC) with a specialized phase-shift coding pattern through virtual grating-based demodulation. In VGHPU, EGC offers robust segmentation of fringe periods, while virtual gratings exploit spatial phase-shift characteristics for accurate and efficient phase recovery. By combining the strengths of both pattern types, VGHPU achieves reliable high-frequency phase unwrapping using only three auxiliary projections. Experimental results validate that VGHPU accurately reconstructs both geometry and surface color of complex objects using fringe patterns with 76 period numbers, validating its robustness and efficiency.