The human eye consists of several optical components, notably the cornea, the crystalline lens, the pupil, and the retina. The ocular aberrations of the entire eye are combinations of the aberrations from the cornea and from the crystalline lens. The aim of vision correction is to remove or to minimize the ocular aberrations of the entire eye. Different vision correction modalities use different means at different locations. For example, the spectacles are located in front of the eye at the spectacle plane, the contact lenses are located at the cornea plane, the laser ablations are similarly located at the cornea plane, and the intraocular lenses are located inside the eye, posterior to the pupil plane. For the same eye, the ocular aberrations are different when they are measured or represented at different planes.
When an optometrist is prescribing a spectacle lens for a myope, the power must be stronger than that of the patient's contact lens. This is because when the negative correcting lens is moved from the corneal plane to the spectacle plane, the power of the lens must be stronger to achieve the same effect. As can be seen in Sec. 7.2, the relationship between the refractions at two different planes can be easily derived from geometrical optics. However, for the entire ocular wavefront that includes the low-order spherocylindrical error and the high-order aberrations, a new theory needs to be developed. In general, the ocular aberrations are measured by an aberrometer over a plane that is conjugate to the exit pupil plane. The practical question is, how do the ocular aberrations change when they are measured at a different location, such as the curved corneal surface? This is the main subject of discussion in this chapter.
Traditionally, for the spherocylindrical error, the propagation of a wavefront is treated by a vertex correction formula[1, 2] to achieve the power correction, for example, for the so-called conventional refractive surgery. The same formula can be applied to the power calculation for the vision correction using contact lenses, intraocular lenses, and spectacles. However, such formulas are only useful for low-order aberrations. If high-order ocular aberrations are to be corrected accurately, a new formula representing the ocular aberrations when they are propagated to the correction plane is needed.  For consistency, we use a sign convention by following a ray from the left to the right going into the eye.
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