Figure 5 shows the distribution of the volumes of ablated tissue, calculated by finite integration, for various magnitudes of spherical correction in myopia and hyperopia and for initial radius of curvature (
R) of 7.8 mm and optical zone (
S) of 6.0 mm. For similar magnitude of treatments, the ablation volume necessary for spherical correct in myopia is slightly greater than that for spherical correction in hyperopia.
The numeric results of comparison of the theoretical values predicted by actual and approximated calculations of the volumes of ablated tissue for initial radius of curvature (
R) of 7.8 mm and optical zone diameter (
S) of 4 to 8 mm are shown in
Table 1 . Volume approximations were within ±2.0% in all calculations for hyperopia and myopia with
S less than 7 mm. Similarly,
Figure 6 illustrates the accuracy of our formulas for volume approximation for myopia and hyperopia given by
equation 11 for
R of 7.5, 7.8, and 8.1 mm. Comparison of the ablated corneal volumes, as determined by the finite integration method, with the volume approximations of
equation 11 , shows that our formula provides an acceptable estimate of the ablated volume for spherical myopia and hyperopia for optical zone diameters up to 9 mm. Beyond 9 mm (
S ≥ 9.5 mm), our formula tends to underestimate the ablated volume compared with the finite integration calculations, especially for treatment of myopia. As expected, the higher the initial radius of curvature (i.e., the flatter the initial corneal surface), the better is the approximation provided by our formula.