Noncoherence

Noncoherence refers to the absence or loss of a fixed phase relationship between waves or states in a system. In optics, coherence is a measure of the predictability of the phase of a light field across space and time. Noncoherent or incoherent light lacks stable phase correlations, causing interference patterns to wash out and resulting in diffuse illumination. Common noncoherent light sources include incandescent filaments, the sun, and many LEDs.

In quantum mechanics, coherence describes the ability of a system to exhibit superposition with well-defined relative phases. Noncoherence (or decoherence) occurs when interactions with the environment destroy relative phase information, turning a pure superposition into a statistical mixture. This is formalized using density matrices: a fully incoherent state is diagonal in the chosen basis, with off-diagonal elements suppressed by decoherence.

In signal processing and communications, noncoherent detection or reception refers to methods that do not rely on the phase of a carrier signal. Instead, measurements are based on signal energy or envelope, providing robustness to phase noise at the cost of reduced sensitivity or bandwidth efficiency. Noncoherent methods are common in AM radio receivers and some optical detectors.

Measurement of coherence uses correlation functions. First-order coherence g1 and second-order coherence g2, among others, characterize spatial, temporal, and statistical properties. In practice, noncoherence sets practical limits on imaging resolution, interferometry, and spectroscopy, but can also simplify system design where phase information is unavailable or unnecessary.