faseunwrapping

Phase unwrapping is the process of reconstructing a continuous phase field from a wrapped phase map, where measured phase values are confined to a principal range (for example −π to π). Wrapped phase arises in many measurement systems because phase is inherently periodic, and unwrapping seeks to remove 2π discontinuities to recover the true phase.

In one dimension, unwrapping can be done by adjusting successive samples with multiples of 2π so that adjacent phase differences are small. In two dimensions, unwrapping is more complex because errors can propagate and local inconsistencies may appear around noise, shadows, or sharp edges. Robust methods are therefore required to handle noise and phase discontinuities.

Common approaches include:

- Path-following algorithms, which integrate phase differences along a path from a reference point. Variants include Flynn’s algorithm and Goldstein’s branch-cut method, which place cuts where unwrapping is unreliable to prevent error spread.

- Quality-guided unwrapping, which builds a quality map (e.g., magnitude, signal-to-noise ratio) and unwraps from high-quality regions outward to minimize error propagation.

- Minimum-norm or least-squares methods, which formulate unwrap as solving a Poisson equation for the unwrapped phase using the gradient of the wrapped phase and curl-free constraints.

- Multi-wavelength and temporal strategies that combine information from different wavelengths or time steps to resolve ambiguities and increase robustness.

Applications span interferometric synthetic aperture radar (InSAR), optical interferometry, holographic metrology, phase-contrast MRI, and surface profilometry. Challenges include noise, phase discontinuities, low fringe visibility, and data gaps. Preprocessing, weighting, and sometimes multi-stage approaches are used to improve reliability and accuracy.