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Concept
Etendue
Summary
Etendue or étendue (ˌeɪtɒnˈduː; etɑ̃dy) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include acceptance, throughput, light grasp, light-gathering power, optical extent, and the AΩ product. Throughput and AΩ product are especially used in radiometry and radiative transfer where it is related to the view factor (or shape factor). It is a central concept in nonimaging optics.
From the source point of view, etendue is the product of the area of the source and the solid angle that the system's entrance pupil subtends as seen from the source. Equivalently, from the system point of view, the etendue equals the area of the entrance pupil times the solid angle the source subtends as seen from the pupil. These definitions must be applied for infinitesimally small "elements" of area and solid angle, which must then be summed over both the source and the diaphragm as shown below. Etendue may be considered to be a volume in phase space.
Etendue never decreases in any optical system where optical power is conserved. A perfect optical system produces an image with the same etendue as the source. The etendue is related to the Lagrange invariant and the optical invariant, which share the property of being constant in an ideal optical system. The radiance of an optical system is equal to the derivative of the radiant flux with respect to the etendue.
An infinitesimal surface element, dS, with normal nS is immersed in a medium of refractive index n. The surface is crossed by (or emits) light confined to a solid angle, dΩ, at an angle θ with the normal nS. The area of dS projected in the direction of the light propagation is . The etendue of an infinitesimal bundle of light crossing dS is defined as
Etendue is the product of geometric extent and the squared refractive index of a medium through which the beam propagates.
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