coherenceshape

Coherenceshape is a term used in optics and quantum optics to describe the geometric form of a light field's coherence function in space and time. It characterizes how the complex degree of coherence varies with separation between points and with delay, effectively outlining the region over which the field is mutually coherent.

Mathematically, the complex degree of coherence g(r1,r2,τ) = Γ(r1,r2,τ) / sqrt[Γ(r1,r1,0) Γ(r2,r2,0)]. For stationary fields, the dependence on r1 and r2 reduces to the relative coordinate s = r2 − r1. The coherence shape can be probed by plotting |g| as a function of s and τ; level sets |g| = const define the coherent region, whose shape may be circular, elliptical, or more complex depending on source statistics and propagation. In Gaussian Schell-model sources, the mutual coherence function is Gaussian in s, yielding an elliptical, well-characterized shape.

Measurement of coherenceshape relies on interferometric techniques such as Young's double-slit experiments, wavefront sensing, or full-field interferometry to reconstruct the coherence function and thus the coherence shape. The interpretation informs the effective coherence length, coherence area, and temporal coherence, influencing imaging and wavefront control.

Applications and relevance include imaging through scattering media, adaptive optics, optical coherence tomography, and quantum communication, where the geometry of coherence affects resolution and information transfer. The coherenceshape concept is related to, but distinct from, coherence length, coherence time, and spatial coherence width. It depends on source statistics, propagation effects, and medium properties, and may evolve under optical elements or turbulence.