Etendue

The étendue (French: expansion ) measures the expansion of a beam in geometrical optics . The étendue is made up of the cross section and the solid angle . For an infinitesimal bundle of rays, the infinitesimal étendue is defined as: ${\displaystyle E}$

${\displaystyle \mathrm {d} E=(\mathrm {d} {\vec {a}}\cdot {\vec {k}})\;\mathrm {d} \Omega }$

in which

• ${\displaystyle \Omega }$the solid angle ,
• ${\displaystyle {\vec {a}}}$is the area vector of the cross-section and
• ${\displaystyle {\vec {k}}}$is the directional vector of the radiation normalized to the refractive index .

The étendue is a conservation quantity of geometrical optics, so it does not change when a beam passes through an ideal optical system . It is a Lagrange invariant .

For an imaging system, the étendue is also known as the light guide value and measures the étendue of the maximum transmitted radiation.

Examples

For non- imaging systems , such as those found in lighting technology , the étendue of a light source describes how strongly the light is already fanned out:

• Has a light source such as If, for example, a fluorescent lamp has a correspondingly large étendue, tightly bundled light can only be generated with an extremely large reflector if no light output is to be lost .
• A point light source such as a metal halide lamp has a much smaller étendue and thus allows the directional emission of large parts of the light with a relatively small reflector.

Web links

• Georg Mischler. Lighting design glossary.