Phasewraps

Phasewraps refer to the representation of a phase angle constrained to a principal interval by modulo 2π, which leads to abrupt discontinuities when the true phase crosses multiples of 2π. In many measurements, the phase is inherently cyclic and is typically reported as a wrapped phase φ that satisfies φ = θ mod 2π, where θ is the true phase. Common ranges for wrapped phase include (-π, π] or [0, 2π). The wrapping occurs because phase is typically defined only modulo 2π, due to the sinusoidal nature of measurement signals or the use of trigonometric encoders.

Phase wrap artifacts appear in plots and analyses as sudden jumps of size 2π, even though the underlying phase evolves smoothly. This is a central issue in fields such as interferometry, radar, optics, and magnetic resonance imaging, where the goal is often to recover a continuous phase function from wrapped measurements.

Phase unwrapping is the process of reconstructing an unwrapped, continuous phase by adding or subtracting integer multiples of 2π to remove wrap discontinuities. Unwrapping is not unique in the presence of noise or phase singularities and can be computationally challenging. Techniques include path-following algorithms that accumulate phase differences while avoiding large jumps, and global or least-squares methods that minimize inconsistency across the field. Hybrid approaches combine quality maps with robust optimization.

Applications include synthetic aperture radar and other interferometric imaging, MRI phase imaging, optical coherence tomography, wavefront sensing, and phase retrieval problems. Understanding and managing phase wraps is essential for accurate quantitative interpretation of phase data.