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Aspheric Lenses 95

Figure 9.3 demonstrates the surface created by rotating an ellipse about
an axis of symmetry. We can notice the changing radii of curvature in both
the tangential and sagittal planes of the lens. This surface astigmatism is
designed to neutralize the oblique astigmatism produced as the wearer
looks away from the centre of the lens. Original aspheric designs utilized
conicoid surfaces, which are produced by rotating a conic section about an
axis of symmetry to produce a three dimensional surface. Modern aspheric
lenses, however, often employ higher order surfaces that allow for more
complex shapes than the simple conic sections.

Fig. 9.3: Anatomy of an aspheric surface. This elliptical curve has a radius of
curvature that gradually changes away from the centre. When the ellipse is being
rotated about the axis of symmetry, it produces a three-dimensional conicoid surface

Fig. 9.4: Tangential and sagittal planes of refraction
Since, flattening a lens introduces astigmatic and power error, the
peripheral curvature of the aspheric surface should change in a manner
that neutralizes this effect. For example, plus lenses with asphericity on
the front surface requires a flattening of curvature away from the centre of
the lens to reduce the effective gain in oblique power and astigmatic error.
Asphericity on the back surface will require steepening of curvature away
from the centre of the lens. The opposite holds true for minus lenses, which
can also benefit from asphericity.