Purpose: To demonstrate techniques for analyzing astigmatism in the context of anterior segment surgery. The techniques are applied to refractive and corneal astigmatism and to astigmatism associated with the surgery.
Method: The analysis is based on the 3-dimensional first-order ray optics known as linear optics, in which astigmatism is axial. Anterior segment surgery, whose only direct effect is to change corneal curvature, is optically equivalent to placing a thin lens immediately in front of the (preoperative) eye; the surgery can be described as anterior thin-lens equivalent. In principle, however, surgery may also change the relative axial positions of refracting elements. In such cases, anterior segment surgery is anterior thick-system equivalent and the analysis of astigmatism is considerably more complicated, with astigmatism manifesting in power and in other ways. Fundamentally, the method is based on the ray transference, a 4 x 4 matrix that contains the 4 fundamental optical properties of a system. Each property may contain an antistigmatic component, and it is this component that is analyzed.
Results: The data are not consistent with the anterior thin-lens model of anterior segment surgery but rather with the anterior thick-lens model. Many components of refraction and corneal power, their means, and their surgically induced changes were calculated and are presented in tabular and graphical form. Graphical representations include polar profiles and stereo-pair scatterplots in dioptric power space. Results are also presented for all the fundamental properties of the surgery.
Conclusion: Ocular astigmatism can manifest in more ways than just refraction and corneal power. Traditional approaches, which treat astigmatism as cylinder in some sense and only as manifested in power, are unsatisfactory. In particular, current approaches weight astigmatism too heavily relative to stigmatism and to other optical phenomena and are inadequate for thick systems such as the eye. The ray transference and the 4 fundamental properties it contains provide the basis for the only methods that can adequately cope with analysis of astigmatism in general and in surgically induced astigmatism in particular.