Fig. 1. Binarization results of the wrapped phase calculated by four-step phase-shift calculation using different thresholds

Fig. 2. Process of generation of complementary Gray codes by MFBT method. (a) Schematic diagram of multi-frequency wrapped phase and its threshold division; (b) schematic diagram of the threshold division process along one line in Fig. 2(a); (c) Gray code pattern generated by multi-frequency wrapped phase binarization

Fig. 3. Decoding process based on the complementary Gray code method

Fig. 4. Generation of complementary Gray codes by BFMT

Fig. 5. Simulation of the binarization division process of wrapped phase obtained by multi-frequency four-step phase-shift algorithm and their corresponding results. (a) Deformed fringe with multi-frequency four-step phase shifting; (b) multi-frequency wrapped phase; (c) distribution of a certain row of the multi-frequency wrapped phase; (d) binarization results divided by setting the threshold according to the MFST method; (e) binarization results divided by setting the threshold according to the MFBT method

Fig. 6. Comparison of decoding to obtain the phase order and restore the continuous phase distribution of object using MFST, MFBT, and BFMT. (a) Decoding order of one row; (b) unwrapped phase

Fig. 7. Multi-frequency four-step phase-shift deformed fringes and wrapped phase. (a) Multi-frequency four-step phase-shift deformed fringe; (b) wrapped phase of corresponding deformed fringes

Fig. 8. Phase order decoding and phase unwrapping results corresponding to the three methods. (a) Unwrapped phase; (b) decoding phase order of one row; (c) profile of the unwrapped phase along one row

Fig. 9. Fringes used to obtain the continuous phase of isolated object and the corresponding phase unwrapping results by MFBT, BFMT, and CGC