Multiétendue

Multiétendue is a concept in optics and radiometry that treats a light source or optical system as a collection of multiple étendues. An étendue (also written étendue) is a measure of the extent in phase space, defined as the integral of area times solid angle, weighted by cos θ. In a multi-étendue model, the source is decomposed into several sub-étendues, each occupying a distinct region of phase space and characterized by its own radiance and angular distribution. The total étendue of the system is the sum of the sub-étendues, ε_total = ∑ ε_i, provided the sub-étendues do not overlap in phase space; when they do, care must be taken to account for overlap.

Lossless optical systems conserve étendue for each sub-étendue; thus, the sum remains constant through the system. This framework is particularly useful in non-imaging optics and illumination design, where sources such as LED arrays, multi-color channels, or composite emitters produce several angular or spatial sectors. By treating these sectors separately, designers can analyze how each portion propagates through lenses, waveguides, or diffusers, and how the total emitted flux within a given acceptance solid angle is governed by the sum of its étendues.

Limitations and relations: Étendue imposes a fundamental limit on concentration and brightness; multiétendue does not bypass this limit but provides a modular way to account for complex sources. Related concepts include radiance, luminance, and the classic étendue invariant used in optical design.

See also: Étendue, Radiometry, Luminance, Non-imaging optics.