etendue

Etendue, also called geometric extent or light gathering power, measures how much a light beam spreads across both space and angle. It is calculated as the product of the beam's cross-sectional area and the solid angle it occupies, typically in units of mm2.sr (square millimeters times steradians). In practical terms, etendue tells you how "fat" and "wide" a bundle of light rays is as it travels through an optical system.

The crucial property of etendue is that it cannot decrease in a passive optical system. This is a consequence of the second law of thermodynamics: you cannot concentrate light from a large, spread-out source into a small, narrow beam using only mirrors, lenses, and prisms. A projector cannot make an image brighter than its source by shrinking it. A camera cannot gather more total light by using a telephoto lens. This conservation rule applies to every ray in the system, from entrance pupil to exit pupil.

In imaging systems, etendue determines the fundamental trade-off between field of view and light collection. A telescope with a large objective gathers more etendue, but adding eyepieces or reducing the exit pupil does not increase the total etendue available to your eye. In projectors, etendue sets the limit on achievable brightness and image size simultaneously: you cannot project a large, bright image onto a screen from a small light source no matter how good your optics are. In illumination and laser applications, matching etendue between the source and the optical system is critical; a mismatch wastes light or leads to vignetting and hot spots.

Etendue violations are common errors in optical design. Trying to couple light from a large, divergent source into a small fiber core, or to image a large field onto a small sensor with a compact lens, both run up against etendue limits. The product AΩ (area times solid angle) at the input must equal or exceed AΩ at the output, accounting for any refractive index changes. Optical designers use etendue as a quick sanity check before detailed ray tracing.

The term comes from the French word for "extent" or "reach." It is standard in radiometry, photometry, and optical engineering, though some texts use the older term "throughput" or the German "Lichtstrom" (light flux product). In practice, engineers often work with entrance pupil diameter, numerical aperture, and field angle separately, but etendue unifies these into a single invariant that governs what any passive system can achieve.