Lagrange invariant
From Wikipedia, the free encyclopedia
In optics the Lagrange invariant is a measure of the light propagating through an optical system. It is defined by
,
where y and u are the marginal ray height and angle respectively, and ȳ and ū are the chief ray height and angle.[1] Ж2 is proportional to the throughput of the optical system (related to étendue).[1] For a given optical system, the Lagrange invariant is a constant throughout all space, that is, it is invariant upon refraction and transfer.
The optical invariant is a generalization of the Lagrange invariant which is formed using the ray heights and angles of any two rays. For these rays, the optical invariant is a constant throughout all space.
[edit] References
- ^ a b Greivenkamp, John E. (2004). Field Guide to Geometrical Optics, SPIE Field Guides vol. FG01, SPIE. ISBN 0-8194-5294-7. p. 28.
