Fig. 1. Schematic diagram of principle of Gray-code assisted phase-shifting technique. (a) Sinusoidal fringe patterns captured through projector lens defocusing; (b) Gray-code patterns captured through projector lens defocusing; (c) mismatch between decoding order edge and wrapped phase

Fig. 2. Schematic diagram of misaligned Gray-code coding strategy. (a) Traditional Gray-code patterns; (b) captured misaligned Gray-code patterns after shifting patterns in Fig. 2(a) by half period; (c) decoding order k obtained by using misaligned Gray-code patterns in Fig. 2 (b) and corresponding wrapped phase φ_w

Fig. 3. Schematic diagram of dividing decoding order k into four sub-regions to obtain correct phase order k_p

Fig. 4. Schematic diagrams of order decoding and phase unwrapping of fringe period number expansion. (a)--(c) Three step phase-shifting sinusoidal fringe patterns; (d)--(g) misaligned Gray-code patterns after expanding period number; (h) unwrapped phase φ₁; (i) decoding order k₁; (j) phase order k₂; (k) primary unwrapping phase ϕ₀; (l) reference plane unwrapping phase ϕ_r; (m) measured object unwrapping phase Ф

Fig. 5. Experimental setup

Fig. 6. Comparsion of reconstructed results of four methods for static isolated objects

Fig. 7. Accuracy evaluation of standard ball with fringe period of 16. (a) Captured fringe patterns; (b) captured misaligned Gray-code patterns; (c) reconstructed result of standard ball; (d) fitted standard ball; (e) error distribution of standard ball

Fig. 8. Accuracy evaluation of standard ball with fringe period of 32. (a) Captured fringe patterns; (b) captured expanded misaligned Gray-code patterns; (c) reconstructed result of standard ball; (d) fitted standard ball; (e) error distribution of standard ball

Fig. 9. Reconstructed results of collapsed stack of wooden signs. (a) Captured pattern sequences; (b)(d) representative collapsed scenes; (c) 3D frames corresponding to Fig. 9(b); (e) 3D frames corresponding to Fig. 9 (d)