Ocular wavefront transformation is perhaps the most widely used theory in wavefront optics for vision correction because the pupil size of a human eye changes due to accommodation or the change of illumination, and because the pupil constriction is most likely not concentric.[1, 2, 3] For example, in laser vision correction, the pupil size of an eye is relatively large when an ocular wavefront is captured under an aberrometer. To obtain the entire ocular wavefront, it is recommended that the ambient light is kept low to dilate the pupil size during the wavefront exam so the surgeon can use either a large or a small treatment zone. However, if a smaller wavefront map is captured, it is impossible to devise an accurate treatment over a larger zone because the wavefront information over the captured zone is unknown. When the patient is under the laser, the pupil size changes because the ambient light changes. Furthermore, the cyclorotation of the eye due to the change from a sitting position to a lying position moves the pupil center between the wavefront capture and the laser ablation.  Theoretically, it was shown that correction of the error due to rotation and translation of the pupil gives significant benefits in vision correction. [5, 6]
Iris registration  was designed to correct the error from the misalignment between the pupil in front of the aberrometer and the pupil under the laser. Because the iris features are not affected by the change of pupil size, they can be used as reliable references to establish the relative geometrical displacement between two image frames.  A common coordinate system is thus established to facilitate the full correction of ocular aberrations. For practical applications, however, a full correction is not possible partly because of the fluctuation of the high-order aberrations and partly because of the instrument error. Therefore, it is desirable to have a theoretical tool for the error analysis of an imperfect correction for the misalignment of the eye between the pupil in front of the aberrometer and the pupil under the laser. Moreover, for a majority of the data analysis for ocular aberrations, it is a common practice that the pupil sizes of different wavefront exams are standardized to a given size. Therefore, the pupil resizing of a known wavefront is also a subject of discussion. In addition, the constriction and decentration of the pupil makes wavefront refraction change when high-order aberrations are present. This becomes a useful tool for the design of the optical surfaces for the correction of presbyopia. 
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