Reliable phase unwrapping algorithm based on rotational and direct compensators.

TLDR: A new phase unwrapping approach for noisy wrapped phase maps of continuous objects to improve the accuracy and computational time requirements of phase unwrap using a rotational compensator (RC) method based on compensating the singularity of discontinuity sources.

Abstract: Phase unwrapping still plays an important role in many data-processing chains based on phase information. Here, we introduce a new phase unwrapping approach for noisy wrapped phase maps of continuous objects to improve the accuracy and computational time requirements of phase unwrapping using a rotational compensator (RC) method. The proposed algorithm is based on compensating the singularity of discontinuity sources. It uses direct compensation for adjoining singular point (SP) pairs and uses RC for other SP pairs. The performance of the proposed method is tested through both simulated and real wrapped phase data. The proposed algorithm is faster than the original algorithm with the RC and has proved efficiency compared to other phase unwrapping methods.

Figures

Fig. 2. Complex cases for the position patterns of SP pairs and the DCs for the adjoining SPs pairs. Open and filled squares represent positive and negative SPs, respectively. (a) SPs are distributed in discrete values. (b) SPs are distributed by using the USP technique. In (b), the thick dashed line denotes the branch cut that connects two SPs of opposite signs, and the DC positions are denoted by thick arrows.

Table 1. Comparison of the Accuracy for the Simulation Data Shown in Fig. 3

Fig. 3. Comparison of the unwrapped phase results for simulated phase data: (a) original phase data, (b) wrapped data, (c) positions of all SP pairs, (d) positions of the pairs of nonadjoining SPs, (e) positions of the pairs of adjoining SPs, (f) unwrapped result by LS-DCT, (g) unwrapped result by RC, and (h) unwrapped result by RCþDC (proposed). In (a), (b), and (f)–(h), the phase increases with the increases of brightness. In (f)–(h), contour lines of the phase with the interval of one cycle are also shown.

Fig. 4. Required computational time of each algorithm for various image sizes. The horizontal axis N denotes one-dimensional area size in pixels. RC shows the required time cost for RCmethod, RCþDC shows the required execution time for the proposed method, and LS-DCT shows the required time cost for LS-DCT method. The computational time is measured with a PC including an Intel Core 2 DUO central processing unit (CPU) with a 2:13GHz clock in the single CPU operation mode.

Fig. 5. Unwrapped phase result of experimental data for candle flame: (a) wrapped data, (b) SPs distribution map (positive and negative SPs are represented by white and black dots, respectively), (c) unwrapped result of the RC algorithm, and (d) unwrapped result of RCþDC (proposed algorithm).

Table 2. Comparison of the Execution Time Cost between RC Algorithm and the Proposed Algorithma