Abstract
Purpose:
To investigate how the sphere and cylinder are affected by pupil size when high order ocular aberrations are present.
Methods:
The effect of spherical aberration on refraction has long been known. However, a quantitative analysis of such an effect was not available until recently. In this study, a theoretical approach is used to analyze the overall effect of pupil constriction when high order ocular aberrations are present. The ocular aberrations are first represented by Zernike polynomials. An analytical expression is given for a new set of Zernike coefficients when the pupil constricts. Based on the new set of Zernike coefficients, the sphere and cylinder over the constricted pupil can be calculated. A relationship between the refraction and high order aberrations can be established.
Results:
With the presence of positive spherical aberration, pupil constriction makes the eye more hyperopic. With the presence of negative spherical aberration, pupil constriction makes the eye more myopic. The ratio of the spherical equivalent before and after constriction is a quadratic function of the constriction ratio. For secondary spherical aberration, it is the opposite: positive secondary spherical aberration makes the eye more myopic and negative secondary spherical aberration makes the eye more hyperopic. The ratio of the spherical equivalent before and after constriction is a quartic function of the constriction ratio. Similarly, the cylinder power is affected by the existence of secondary and tertiary astigmatism. For secondary astigmatism, the ratio of the cylinder before and after constriction is a quadratic function of the constriction ratio. For tertiary astigmatism, the ratio of the cylinder before and after constriction is a quartic function of the constriction ratio.
Conclusions:
When high order ocular aberrations exist, the sphere and cylinder depend upon the pupil size and the particular high order aberration terms. Understanding the relationship between refraction and pupil size may help design optimal vision correction means such as spectacles, contact lens, and refractive surgery.
Keywords: 626 aberrations •
676 refraction •
678 refractive surgery