Cardinal point (optics)#Principal planes and points

Principal planes are two defined in an imaging system in sufficient for many purposes a simple working model Paraxial optics planes in which simplifies the openings of the light rays will be accepted. In the space between the main planes of the light rays are intended to extend parallel to the optical axis.

The principal planes are the planes of reference for distance measurements, the one in the object space, the other in image space. Corresponding distances are the focal length and the object and the image distance associated to the lens equation. The latter is a simple tool (linear equation) for describing the picture through an engineered optical system.

A thin lens and a weakly curved spherical mirror fulfill as far as possible the conditions of paraxial optics. As necessary for the imaging property reference planes can be adopted to the apexes of the surfaces already tangent. Since the two surfaces almost coincide with a thin lens, we speak here of only one adopted in the mid- major level.

When working with the lens equation are ignored except for the chromatic all other aberrations. These occur on the more, the larger the angle between the radiation and the optical axis. Therefore, the concept of paraxial optics, in which the principal planes belong to compact optical systems only expandable when the lens aberrations are corrected with the aid corresponding to more elaborate working models. This interpretation of paraxial optics is called Gaussian optics.

The points of intersection of the principal planes with the optical axis are the main points that are denoted by H ( object side ) and H '( image-side principal point ) ( in the illustration H1 and H2).

For complex imaging systems, the image-side principal plane can also "before" the object-side lie. An afocal lens system has no principal planes, or are they at infinity.

Top-level design for a lens

The principal plane H ' contains the intersection of the axis-parallel incident and from the lens to the focal point F' deflected beam ( red) with the undeflected extended axially parallel incident beam (dotted line in the illustration ).

The same applies to the object side:

If the lens is relatively thin ( in the thin lens is by definition ), these distances are zero. The main planes remain on the apexes of the surfaces which coincide in one plane.

Top-level design for a system of two thin lenses

The construction is analogous to that for a lens (see above). It should be noted only that the principal planes H1 and H2 represent two refracting surfaces and that belong to each of two equal focal lengths (object and image side ). It is also possible that the two thin lenses are made of different materials ( n'1 ≠ N'2 ).

The two above equations change slightly (but with fundamentally different expressions for the focal lengths ) to:

When together of thin lenses () the distances go to zero. The main level H1 or H2 or one instead of two adopted plane H represents the system, for example, two thin lenses cemented together.

By combining the individual constructions described with the aid of Figures 2 and 3 we find the top-level design for a system of two lenses with a significant thickness ( " thick lens ").

Notes and References

• Paraxial optics