Figure 1.

Loop path integral in the clockwise direction"

Figure 2.

The schematic of PMP"

Figure 3.

The second-order differential calculation window of wrapped phase"

Figure 4.

The Venn diagram of the residual point"

Figure 5.

The principle of local optimization operation of residues (a)The positive and negative residues identified by residual theory (b)Equivalent residues (c)Local optimization (d)The equivalent residues after optimization"

Figure 6.

Branch-cut generation map (a)Branch-cut generated by Goldstein method (b)Branch-cut generated by this study"

Figure 7.

The principle of PMP measuring optical path"

Figure 8.

The patterns of simulated sinusoidal fringe (a)Initial phase 0 (b)Initial phase π/2 (c)Initial phase π (d)Initial phase 3π/2"

Figure 9.

The results of the residual identification and branch-cuts' connection of simulated data (a)Noise distribution map (b)Residues map identified by the Goldstein method (c)Residues map identified by the proposed method (d)Equivalent residues map (e)The branch-cuts generated by the Goldstein method (f)The branch-cuts generated by the proposed algorithm"

Table 1.

Numbers of the residues and length of the branch-cut of simulated data"

Figure 10.

The results of phase unwrapping of simulated data (a)The phase unwrapping result of the Goldstein method (b)The 3D map of the unwrapped phase of Goldstein method (c)The phase unwrapping result of QGM (d)The 3D map of the unwrapped phase of QGM (e)The phase unwrapping result of the proposed algorithm (f)The 3D map of the unwrapped phase of the proposed algorithm"

Figure 11.

The experimental platform of PMP"

Figure 12.

The fringe patterns of the object to be measured (a)Initial phase 0 (b)Initial phase π/2 (c)Initial phase π (d)Initial phase 3π/2"

Figure 13.

The results of the residual identification and branch-cuts' connection of simulated data (a)Modulation map (b)Residues map identified by the Goldstein method (c)Residues map identified by the proposed method (d)Equivalent residues map (e)The branch-cuts generated by the Goldstein method (f)The branch-cuts generated by the proposed algorithm"

Table 2.

Numbers of the residues and length of the branch-cut of real dat"

Figure 14.

The results of phase unwrapping of real data (a)The phase unwrapping result of the Goldstein method (b)The 3D map of the unwrapped phase of Goldstein method (c)The phase unwrapping result of QGM (d)The 3D map of the unwrapped phase of QGM (e)The phase unwrapping result of the proposed algorithm (f)The 3D map of the unwrapped phase of the proposed algorithm"