Low_resolution_Thesis_CDD_221009_public - Visual Optics and ...

METHODS
representing the deviation of the conic with respect to a circumference. Conic curves
are classified in circumferences (Q=0), hyperbolas (Q-1). Figure Fig. 2. 15 graphically describes the effect of asphericity on
conic sections, as all the curves shown have the same apical radius. Therefore, the
surfaces of the ocular components (cornea and crystalline lens) can also be described
in terms of their radius and asphericity.
Fig. 2. 15. The effect of asphericity on the shape of a conicoid. All the curves have
the same apical radius of curvature (Atchison and Smith, 2000).
The three-dimensional extension of this description based on conic sections can be
made in terms of quadrics (rigorous extension of conic sections to three dimensions),
conicoids (surfaces with revolution symmetry in which all the longitudinal sections are
conic sections, as in Section 1.2.1 and Equation 1.1) and biconics (asymmetric
surfaces with two preferential axes, which are conics). Consequently the surfaces of
the eye are usually be described in terms of conics. A single apical radius of curvature
and one single asphericity for conics, and two radii and two asphericities for biconics.
The representation of ocular surfaces in terms of conic-based surfaces, although
very useful in many cases, constitutes only a coarse approximation of the real cornea.
A point by point numerical description of the surface is often impractical. In these
cases, fittings to a base of Zernike polinomials (Section 1.4.4) can be a good
compromise (Schwiegerling et al., 1995).
In all cases, but specially with conic-based surfaces, it is important to choose the
correct number of free parameters in the fitting to achieve the maximum accuracy. If
the surface is (or could be) tilted or decentered, it is desirable to include two tilting and
two centering parameters. In the studies presented in this thesis, many of the surfaces
show a prioritary center (abation patters or multifocal designs). We found optimal
results when the fitting was accomplished in two phases: one to locate the center and
tilt of the surface (for example, after fitting an sphere) and another one (after removing
tilt and decentration) to retrieve the radius and asphericity. As the optimal approach
depends on the specific application and the characteristics of the surface, the
procedures will be described in detail in the corresponding Chapter.
Annex A will analyse the existing correlation between radius and asphericity
appearing when fitting different corneal surfaces to conics.
2.2.2. Comparing surfaces
In many of the studies of this thesis, the outcome results from the comparison of two
or more surfaces. For example, the ablation pattern appears after comparing the
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