If the perfect image point also moves linearly on the vertical axis plane when the object point moves on the vertical axis plane, the imaging of this optical system is ideal. It can be proved that when a small object very close to the optical axis is imaged by the optical system with a very thin monochromatic beam very close to the optical axis, it looks perfect. This shows that the paraxial region of any actual optical system (including a single sphere and a single lens) has ideal imaging properties.
In order to understand the imaging properties and laws of optical system in general, an optical model called ideal optical system is established based on the study of paraxial imaging laws. This model completely ignores the specific optical system structure and is only characterized by the positions of several pairs of basic points and the size of a pair of basic quantities.