Phase unwrapping with the branch-cut method: role of phase-field direction

Abstract

Phase unwrapping with the branch-cut method has been successfully used in many different applications in recent years. Most methods to set the branch cuts minimize the overall cut length. However, this technique fails in different cases, since this criterion is based mainly on statistical examinations. We show how the orientation and direction of the phase map help to create additional physical criteria that can be used to optimize the setting of the branch cuts. We show how these new criteria can be implemented into an energy function that will be minimized by a simulated annealing algorithm in order of a correct setting of the branch cuts. Finally, we present experimental results from electronic speckle pattern interferometry and digital holography phase maps.

Quantitative phase imaging based on Fresnel diffraction from a phase plate

“…4(a)) and applying an inverse Fourier transform of the filtered and shifted spectrum, the wrapped phase image is obtained. After subtracting a reference phase map from the object phase map, a Goldstein's branch-cut unwrapping method is applied to reconstruct a continuous phase of ob- ject [39]. The thickness distribution which is achieved from the net unwrapped phase information of silica beads, d = φ λ/ [2π(n O − n m )], is illustrated in Fig.…”

A robust phase unwrapping method for 3D borehole radar interferometric imaging

“…They can be separated into two groups: path-following methods and minimum-norm methods [6]. The most commonly used methods are the path-following methods, especially the Goldstein's branch cut algorithm [7]. The Goldstein's branch cut algorithm is controlled by phase discontinuities; otherwise known as residues.…”

Self-marking phase-stepping electronic speckle pattern interferometry (ESPI) for determining a phase map with least residues

“…(10) clearly shows that only the slowly varying signal term sinð1=2DjÞ is of interest, which is modulated by a highly varying speckle noise term sin½1=2ð2y s þ DjÞ. Various filtering rules [17][18][19][20] are therefore applied to the correlation fringes to extract the signals of interest. However, depending on the filtering rules, more or less distortions are introduced into the calculated phase data, causing an error in the results.…”