Cardinal points provide a way to analytically simplify a system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations. The cardinal points of a thick lens geometrical optics notes pdf air.

Aperture effects are ignored: rays that do not pass through the aperture stop of the system are not considered in the discussion below. The front focal point of an optical system, by definition, has the property that any ray that passes through it will emerge from the system parallel to the optical axis. Rays that leave the object with the same angle cross at the back focal plane. For objects a finite distance away, the image is formed at a different location, but rays that leave the object parallel to one another cross at the rear focal plane. Angle filtering with an aperture at the rear focal plane.

An infinitely small aperture would only allow rays that are emitted along the optical axis to pass. No matter where on the object the ray comes from, the ray will pass through the aperture as long as the angle at which it is emitted from the object is small enough. Note that the aperture must be centered on the optical axis for this to work as indicated. The pixels in these sensors are more sensitive to rays that hit them straight on than to those that strike at an angle. Various lens shapes, and the location of the principal planes.

This means that the lens can be treated as if all of the refraction happened at the principal planes. In the more general case, the distance to the foci is the focal length multiplied by the index of refraction of the medium. Note, however, that for a real lens the principal planes do not necessarily pass through the centre of the lens, and in general may not lie inside the lens at all. The front and rear nodal points of a thick lens. The front and rear nodal points have the property that a ray aimed at one of them will be refracted by the lens such that it appears to have come from the other, and with the same angle with respect to the optical axis. The nodal points therefore do for angles what the principal planes do for transverse distance.