Etendue

Etendue or étendue (/ˌeɪtɒnˈduː/; French pronunciation: [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,^[1] 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.^[2]^{[page needed]}^[3]^{[page needed]}^[4]^{[page needed]}

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.^[5] 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.

^ "Optical extent / Etendue". CIE e-ILV: International Lighting Vocabulary (2nd ed.). International Commission on Illumination. 17-21-048. Retrieved 19 February 2022.
^ Chaves, Julio (2015). Introduction to Nonimaging Optics (2nd ed.). CRC Press. ISBN 978-1482206739.
^ Winston, Roland; Minano, Juan C.; Benitez, Pablo G. (2004). Nonimaging Optics. Academic Press. ISBN 978-0127597515.
^ Brennesholtz, Matthew S.; Stupp, Edward H. (2008). Projection Displays. John Wiley & Sons. ISBN 978-0470518038.
^ "Basic Optics: Radiance" (PDF) (Lecture notes). Astronomy 525. College of Saint Benedict and Saint John's University.

[e-ILV-etendue-1] "Optical extent / Etendue". CIE e-ILV: International Lighting Vocabulary (2nd ed.). International Commission on Illumination. 17-21-048. Retrieved 19 February 2022.

[IntroNio2e-2] Chaves, Julio (2015). Introduction to Nonimaging Optics (2nd ed.). CRC Press. ISBN 978-1482206739.

[NIO-3] Winston, Roland; Minano, Juan C.; Benitez, Pablo G. (2004). Nonimaging Optics. Academic Press. ISBN 978-0127597515.

[Projection_Displays-4] Brennesholtz, Matthew S.; Stupp, Edward H. (2008). Projection Displays. John Wiley & Sons. ISBN 978-0470518038.

[5] "Basic Optics: Radiance" (PDF) (Lecture notes). Astronomy 525. College of Saint Benedict and Saint John's University.

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Etendue

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