Cardinal point (optics)

In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the focal points, the principal points, and the nodal points; there are two of each. For ideal systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points. For simple cases where the medium on both sides of an optical system is air or vacuum, four cardinal points are sufficient: the two focal points and either the principal points or the nodal points. The only ideal system that has been achieved in practice is a plane mirror, however the cardinal points are widely used to approximate the behavior of real optical systems. Cardinal points provide a way to analytically simplify an optical system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations.

Explanation

The cardinal points lie on the optical axis of an optical system. Each point is defined by the effect the optical system has on rays that pass through that point, in the paraxial approximation. The paraxial approximation assumes that rays travel at shallow angles with respect to the optical axis, so that

sin

⁡

θ

≈

θ

{\textstyle \sin \theta \approx \theta }

,

tan

⁡

θ

≈

θ

{\textstyle \tan \theta \approx \theta }

, and

cos

⁡

θ

≈

1

{\textstyle \cos \theta \approx 1}

. Aperture effects are ignored: rays that do not pass through the aperture stop of the system are not considered in the discussion below.