Quétendue

Quétendue, usually written étendue in optics literature, is a geometric property of a light field that combines where light is and how much of it is allowed to travel in a given direction. It is defined as the product of a beam’s cross-sectional area A and the solid angle Ω it subtends: E = A Ω, with E measured in square meters times steradians (m^2 sr). This quantity serves as a measure of optical throughput, reflecting both spatial extent and angular spread of light.

In radiometry and imaging, étendue is a fundamental invariant in lossless optical systems. For an optical path with no clipping or absorption, étendue remains constant; any passive optical element cannot increase it. If parts of the beam are blocked or absorbed (for example by apertures or vignetting), the total étendue through the system can only decrease. Alongside this, radiance is conserved along ray paths in a lossless medium, a consequence of Liouville’s theorem, which is closely related to étendue.

Applications and implications: Étendue sets limits on system performance by linking entrance aperture, field of view, and numerical aperture. It influences the design and efficiency of imaging systems, spectrometers, fiber-optic coupling, and illumination layouts. Achieving optimal throughput often requires careful matching of étendue between source, optics, and detector; mismatches lead to wasted light or reduced resolution.

See also: Radiance, Liouville’s theorem, numerical aperture, optical throughput.