Etendue Invariant

Let us consider a source of light - or focal plane - whose area A uniformly emits radiations of intensity Iv within a frequency band 5v. Assuming that the emitting surface is centered and perpendicular to the axis of an optical system, the total amount of energy per second W reaching the entrance pupil of area A, located at distance d from the source, is represented by the inverse square law

This relationship is well known in spectroscopy and photometry (Pecker and Schatzman [120], Sterken and Manfroid [149]). The solid angle Q of the field of view is Q = A!/d2 (Fig. 1.18), so the energy is represented by

In the expression of the energy W, the product A Q of the geometrical terms is called the optical Étendue after Jacquinot [81] who formalized this quantity as an invariant through a perfectly transmissive optical system. The optical Étendue is generally denoted

Aperture solid angle

Focal plane area

Pupil area

Field solid angle

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