Phase unwrapping for noisy phase maps using rotational compensator with virtual singular points

Abstract

In the process of phase unwrapping for an image obtained by an interferometer or in-line holography, noisy image data may pose difficulties. Traditional phase unwrapping algorithms used to estimate a two-dimensional phase distribution include much estimation error, due to the effect of singular points. This paper introduces an accurate phase-unwrapping algorithm based on three techniques: a rotational compensator, unconstrained singular point positioning, and virtual singular points. The new algorithm can confine the effect of singularities to the local region around each singular point. The phaseunwrapped result demonstrates that accuracy is improved, compared with past methods based on the least-squares approach.

Performance Evaluation of Phase Unwrapping Algorithms for Noisy Phase Measurements

“…[20] It can compute the compensators through superposing the effect of each SP by adding an integral of isotropic singular function along any loops. After that, the unwrapped phase at a point is retrieved by summing the wrapped phase difference and compensators at this point with the unwrapped phase of the previous point.…”

“…The studied algorithms are selected because they may give acceptable unwrapped phase results in such applications. The following algorithms are examined in this paper: Goldstein et al's path-following method, [6] Flynn's minimum weighted discontinuity method, [10] algorithm based on sorting by reliability following a non-contiguous path (Quality-Sort), [12] the least-squares method with discrete cosine transform (LS-DCT), [17] singularity-spreading phase unwrapping method (SSPU), [19] rotational compensator method (RC), [20] rotational and direct compensator method (RC þ DC), [22] and localized compensator method (LC). [21] A short description of each studied method will be illustrated, with the emphasis on the basic ideas.…”

“…To evaluate the accuracy of the compared phase unwrapping algorithms, [6,10,12,17,[19][20][21][22] we provide known phase maps that are not wrapped. The simulated phase data are two cases of phase maps with the same gradient (0.1, À0.1) cycle= pixel, and the image area 100 Â 100 pixels.…”

“…The path dependency, which is considered as error or consequence of the inconsistencies, is spread throughout the whole domain in order to avoid any large localized errors. Algorithms based on spreading singularity [18][19][20][21] are also classified into the same category of least-square The true phase value r…”

Phase unwrapping for noisy phase map using localized compensator

“…The method based on least-square approaches [14][15][16][17][18][19][20], the singularity-spreading phase unwrapping method [21], and the methods using a rotational compensator [22,23] are categorized into this type. These methods do not introduce the unnatural gaps; however, they distort regular regions that contain no singular points.…”