EtendueGesetz

EtendueGesetz, also known as the etendue conservation law, is a fundamental principle in optics that describes the conservation of light beam "spread" or "extent" through an optical system. It is particularly relevant in the design and analysis of optical instruments such as telescopes, microscopes, and light collection systems.

The etendue of a light beam is a measure of the solid angle the beam subtends multiplied by the area it covers. This quantity remains invariant as light propagates through ideal optical systems that do not introduce losses or aberrations. Mathematically, the etendue (G) is expressed as G = A * Ω, where A is the area of the optical beam's cross-section and Ω is the solid angle it subtends.

The principle of etendue conservation states that, in lossless and aberration-free optical systems, the etendue of an optical beam cannot be decreased. This imposes fundamental limits on the focusing and imaging capabilities of optical devices, affecting their resolution and brightness. For example, attempting to focus light from a large area onto a smaller detector cannot reduce the total etendue, which explains why brighter and more extensive light sources are more advantageous for certain applications.

The etendue law is critical in areas such as optical fiber design, illumination engineering, and radiometry. It guides engineers in optimizing system components to maximize light collection efficiency without violating fundamental physical constraints. Understanding the etendue principle also aids in determining the ultimate performance limits of optical systems, ensuring realistic expectations in design and application.