Fig. 1. Data processing flow of the proposed method

Fig. 2. Schematic of decoding process. (a) Wrapped phase; (b) the first order of codeword; (c) high-frequency discolation Gray code; (d) the first order of discolation codeword; (e) corrected first order of codeword; (f) the second order of codeword; (g) low-frequency discolation Gray code; (h) the second order of discolation codeword; (i) corrected second order of codeword; (j) final fringe order

Fig. 3. Simulation results of different methods. (a) Proposed method; (b) traditional phase coding method

Fig. 4. Experimental setup

Fig. 5. Parts of captured images in the experiment. (a) First frame of sinusoidal phase shifting fringe pattern; (b) first frame of piecewise step phase coding fringe pattern; (c) first frame of step phase coding fringe pattern; (d) high-frequency Gray code pattern; (e) low-frequency Gray code pattern

Fig. 6. Process of measured data. (a) Wrapped phase ϕ(x,y); (b) first order of codewords k₁(x,y); (c) second order of codewords k₂(x,y); (d) fringe order k(x,y); (e) absolute phase φ(x,y)

Fig. 7. Reconstructed results of three methods. (a) Traditional phase coding method; (b) traditional Gray code method; (c) the proposed method

Fig. 8. Three dimensional measurement experiment of phase shift fringe with projection period of 100. (a) A frame of sinusoidal fringe pattern; (b) reconstructed result

Fig. 9. Measurement experiment on a complex mask. (a) First frame of sinusoidal phase shifting fringe pattern; (b) first frame of piecewise step phase coding fringe pattern; (c) first frame of step phase coding fringe pattern; (d) high-frequency Gray code pattern; (e) low-frequency Gray code pattern; (f) reconstructed result

Fig. 10. Measurement experiment on a standard ladder. (a) Reconstructed result; (b) height distribution along 600th line