phasecorrelated

Phasecorrelated is an adjective used to describe a relationship in which the phases of periodic components or waves are not independent but exhibit a systematic correlation. When phases are phasecorrelated, they carry information about structure, coherence, or common origin that is not captured by amplitude alone. Phasecorrelation can be assessed by examining phase distributions, phase locking, or cross-spectral phase relations between signals.

In physics and optics, phasecorrelated wave fields arise when sources are coherent or when a system enforces a fixed phase relationship between components. Phasecorrelation underpins interference and holography, where the relative phase determines fringe visibility and pattern formation. It informs measurements of coherence length, mode locking in lasers, and phase stabilization in interferometric experiments. In imaging and spectroscopy, phasecorrelated information captures spatial or temporal organization that amplitude data alone may miss.

In signal processing and computer vision, phase correlation is a practical technique used to estimate relative displacement between two signals or images. By computing the cross-power spectrum of two signals and performing an inverse Fourier transform, the resulting phase correlation function highlights a peak at the translation that aligns the data. This approach is particularly robust to scalar illumination changes and is widely used for image registration, motion estimation, and alignment tasks.

In statistics and cosmology, phase correlations among Fourier modes reveal departures from Gaussianity. A purely Gaussian random field has independent, uniformly distributed phases; phasecorrelations indicate nonlinear evolution, structure formation, or other nonrandom processes in datasets such as cosmic microwave background maps or large-scale structure surveys.