Deep-learning-enabled single-shot fringe projection profilometry based on inner shifting-phase encoding

Single-shot fringe projection profilometry (FPP) offers significant advantages for dynamic three-dimensional (3D) measurement. However, existing deep learning-based single-shot methods still struggle to simultaneously and accurately extract the wrapped phase and fringe order. Because the former is a continuous physical quantity while the latter is a discrete integer label, their joint estimation from a single periodic pattern is inherently ambiguous, especially for isolated objects lacking spatial continuity. To address this problem, a deep learning-enabled single-shot FPP method is proposed by integrating inner shifting-phase encoding with a physically constrained dual-network architecture. The fringe order is embedded into the phase-shifting component of a single high-frequency fringe pattern, and two lightweight convolutional neural networks are then employed: one regresses the numerator and denominator of the wrapped phase, while the other classifies the inner shifting-phase value to recover the fringe order. This physically consistent decoupled design avoids the optimization conflicts of end-to-end regression and enables unambiguous absolute phase recovery. Experiments show that the proposed method could achieve high-accuracy absolute phase recovery comparable to traditional multi-frame techniques for measurements of complex and isolated objects, while maintaining low computational complexity. The dynamic experimental results demonstrate its application potential for dynamic 3D measurement.