online optical calculator logo
tutorials



rigorous stigmatism

Rigorous stigmatism

paraxial conjugation

Two points A and Ai are conjugated by an optical system when all incident light rays ( whatever their inclination ) coming from A give emerging light rays exactly focusing on Ai.
Conjugation is rigorous for some special optical systems and particular object positions. For example, rigorous stigmatism occurs for Weiesrtrass points when the optical system is a dioptrum or an ellipsoidal mirror. Rigorous stigmatism occurs also for a parabolic mirror between its focal point and a point at infinity on the symmetry axis.
It is assumed that considered optical systems in calculation pages have a symetry around an axis : the optical axis ( Oa ). The conjugated point Ai of an object point A on the optical axis is also on the optical axis.

weierstrass points of an elliptic mirror

Weierstrass points of an elliptic mirror

An elliptic mirror perfectly conjugates its two focal points F1 and F2 which are also called Weierstrass points.







rigourous focus of a collimated beam reflected by a parabolic mirror

Rigourous focus of a collimated beam reflected by a parabolic mirror

A parabolic mirror conjugates rigorously a point at infinity on the optical axis (generating light rays parallel to the optical axis ) and its focal point F ( also located on the optical axis ) which position depends on the local radius of curvature R at the mirror apex.



weierstrass points of a spherical refracting surface

Weierstrass points of a spherical refracting surface

For a given spherical refracting surface with a radius R interfacing two media with respective refractive indexes n0 and n1, there are two points A and Ai on the optical axis rigorously conjugated.

They are called "Weiestrass" points or "Young" points. A and Ai positions depend on R, n0 and n1.


References

"Optique Fondements et applications" - 2004 - author : José-Philippe Perez.

"Optique géométrique Imagerie et instruments" - 2007 - author : Bernard Balland.

"Optique géométrique paraxiale" - Institut d'optique théorique et appliquée - 1985 - author : Michel Cagnet.

"Formation des images Aberrations" - Institut d'optique théorique et appliquée - 1985 - author : Michel Cagnet.



contact : contact@optical-calculation.com - website : www.optical-calculation.com Copyright © 2009 CLAVIS S.A.R.L. All rights reserved