Fig. 1. Principle of quaternary encoding

Fig. 2. Coded patterns. (a) Proposed quaternary coded patterns; (b) quaternary Gray-coded patterns; (c) phase-coded patterns

Fig. 3. Decoding process of proposed method. (a) Quantized patterns; (b) decoding result

Fig. 4. Fringe projection system. (a) Projecting diagram; (b) experimental devices

Fig. 5. Images captured by camera. (a) Object to be measured; (b)-(e) four phase-shifting patterns; (f)-(h) three coded patterns obtained by proposed method

Fig. 6. Quantization of coded patterns. (a) Sectional view between 3rd coded pattern and 4 phase-shifting patterns; (b) ideal quantized patterns corresponding to 3rd coded pattern; (c) practical quantized patterns with spiny error; (d) quantized patterns after filtering

Fig. 7. Measuring result obtained by proposed method. (a) Fringe orders before and after correction; (b) reconstructed result

Fig. 8. Colorful object measurement. (a)-(c) Colorful scenes to be measured; (d)-(f) 3rd coded patterns; (g)-(i) reconstructed results

Fig. 9. Traditional stair-shaped coded patterns. (a) Quaternary Gray-coded patterns; (b) phase-coded patterns; (c) fringe orders calculated by phase-coded method