As someone who has had a metric tonne load of problems in seeing clearly, I’ve become quite interested in lens design.
There’s a great course on Opticampus that explains the rationale behind and mathematics of spectacles lens design. Lens design is a trade-off between the minimisation of different forms of aberrations brought about by practical considerations such as the shape of the lens, the quality of the material and the prescription that must be glazed.
Lens designers measure differences in refraction across tangential and sagittal meridians (orthogonal meridians describing refraction of light at different degrees from the optical centre of the lens). They must minimise the oblique astigmatism which is the difference in refractive power between the 2. A good way to describe this is that light may be bent more vertically than horizontal leading to a squatter image or vice versa.
They must also compensate for power error which arises from the focal point of a perfect lens as light hits it from its range of lateral and vertical points of incidence (theoretical and ignoring oblique astigmatism) being different from the Focal Point Sphere which represents the back surface of the eye. The FPS is generally more curved and hence the lens may focus behind the eye away from the optical centre.