OPTICAL CORRECTION

Aspheric lenses for the normal power range

By Professor Mo Jalie

So far, we have considered the use of aspherical surfaces for high-power plus lenses that lie beyond the range of powers, which can be corrected for aberrational astigmatism with spherical surfaces. In recent years, aspherical surfaces have been employed on lenses of low power as are required for the usual range of prescriptions. In 1980, the author obtained patents' for lenses in the power range +7.00 to -20.00 for a series of spectacle lenses, which incorporate a hyperboloidal curve for the major surface of the lens. the major surface being the convex surface for plus powers and the concave surface for minus lenses.

The use of aspheric forms for the low- to medium-power range allows the production of thinner and lighter lenses for the normal range of prescriptions. The reduction in thickness is the result of a two-stage process. First. The lens is made much flatter in form by employing a shallower base curve. For example, the centre thickness of a series of +4.00D lenses made in CR39 material at 70mm diameter and with edge thickness of 1.0ram in the forms indicated would have the centre thickness shown in Figure 1. It can be seen that, simply by flattening the lens form, we obtain a saving in centre thickness.

The flatter the lens, the thinner it becomes. If the lens is made with a -1.50 base curve instead of the usual -5.25 inside curve which would be necessary to make the lens point-focal, then a saving in centre thickness of 0.6mm would be obtained. Needless to say, this flatter form does not have good optical properties. It is afflicted with positive aberrational astigmatism when the eye rotates to view through off-axis portions of the lens. Just how poor the off-axis performance becomes due to flattening the lens form is illustrated in Figure 2. Figure 2a illustrates a field diagram for a +4.00 D lens made with a -5.25 back curve and it can be seen that the tangential and sagittal oblique vertex sphere powers are the same for all direction of gaze. This form is free from oblique astigmatism and represents a point-focal form for this power. Figure 2b illustrates the off-axis performance of a +4.OOD lens made with a -1.50 back surface power using spherical surfaces and it is seen that the real effect of the lens when the eye has rotated 35 ° from the optical axis is +4.05/+0.87. It will be appreciated that there is almost 1.00 D of aberrational astigmatism 35 ° from the optical axis for this very shallow bending. However, to eliminate the aberrational astigmatism an aspherical surface can be employed whose form is such that it introduces negative surface astigmatism to neutralise the astigmatism of oblique incidence. A correctly chosen aspherical surface will completely neutralise the aberrational astigmatism arising from oblique incidence.

Figure 2c illustrates the off-axis performance of the +4.00 D lens made with a-1.50 back surface power and a convex aspherical surface whose p-value has been chosen to neutralise the astigmatism of oblique incidence. This form has the same oblique vertex sphere powers as the point-focal form with spherical surfaces whose performance is depicted in Figure 2a. The surface is a convex hyperboloid whose p-value is -1.8 and it can be seen that the field diagram is almost identical to that shown in Figure 2a for the design with spherical surfaces. The second stage of the thinning process occurs since, for a given diameter, the required aspherical surface has a smaller sag than a spherical surface of the same vertex radius. The smaller front surface sag causes a further reduction in the centre thickness of the lens.

The original patent proposed that a hyperboloid should be employed for the major surface of the lens since the rate of flattening of a hyperboloid is just what is required to neutralise aberrational astigmatism. Figure 3 shows just what additional saving in centre thickness is achieved when the convex spherical surface is replaced by a suitable convex hyperboloidal surface whose asphericity is chosen to restore the off-axis performance of the lens. A further saving of 0.6ram is achieved for a 70mm diameter when the spherical surface is aspherised to eliminate the aberrational astigmatism arising from oblique incidence. The aspheric lens form has a total saving in centre thickness of 1.2mm when compared with the traditional spherical form.

Needless to say, any higher order aspherical surface could be used but, in practice, it would not depart significantly from a hyperboloid since this curve regulates the astigmatism at the correct rate. The optical performance of an aspheric design can be made to match any design philosophy. The lens may be made point-focal, just like the designs illustrated in Figure 2, or it may be made in Percival form or, more typically, a compromise bending between these two forms to provide a reasonable performance over a wide range of fitting distances as discussed in Chapter 2. An even greater saving in thickness is obtained when a higher refractive index material is used. If the same power base curve is used the saving is two-fold. Firstly, there is the obvious reduction in the sags of the curves since longer radii of curvature are employed. Secondly, since the use of the same power base curve on a higher refractive index material requires a longer radius of curvature at the vertex, to, effectively, the lens is flatter still and requires greater asphericity on the convex surface to restore the off-axis performance.

This is illustrated in Figure 3 which shows how the centre thickness of a 70mm diameter +4.00 D lens would reduce when made in 1.60 and 1.70 index materials. The asphericity of the convex surfaces indicated in the figure has been chosen to provide the same off-axis performance for each lens. Another important advantage of these low-power aspheric designs for hypermetropia can be gleaned from Figure 4. The original best-form +4.00 design with spherical surfaces required a centre thickness of 6.6ram in order to obtain an edge thickness of 1.0ram at 70ram diameter. If this uncut lens is edged down to a finished diameter of 50mm, it will have an edge thickness of 4.1ram which is not acceptable for a lens of this power.

The aspheric design made in 1.60 index material, on the other hand, has a centre thickness of 4.5 mm and would have an edge thickness of 2.6ram when edged down to a finished diameter of 5Omm. The aspheric design lends itself far better to a system of supply of large-diameter plus uncut lenses, which need to be edged to smaller diameters depending upon the choice of shape and size of the lens.

Aspheric lenses for myopia:

The principle of flattening a curved lens form to make it thinner and then aspherising one surface to restore the off-axis performance of the flatter form lens can be applied equally to minus lenses. For example, the reduction in thickness, which is obtained for -4.00 D lenses made in CR39 material with uncut diameters of 70 mm and centre thickness of 2.0 mm is shown in Figure 4. It can be seen that the traditional best form design made using spherical surfaces might employ a +4.75D base curve, when the resulting edge thickness would be 8.0 mm. Then, flattening the base curve to +0.75D produces an edge thickness of 7.1 mm, which is a saving of 0.9mm at the edge. Finally, aspherising the flatter form lens to provide the same off-axis performance as the best-form spherical design results in an edge thickness of 6.4mm which is a further saving of 0.7mm, the final aspheric design being 1.6 mm thinner than the traditional spherical form.

The author's original proposal for the correction of myopia was to employ a concave hyperboloidal surface but lens manufacturers prefer to aspherise the convex surface of the lens since it is easier to incorporate the cylinder on the concave surface as a minus base toric. Several aspheric minus lens series, therefore, incorporate a convex aspherical surface. the purpose of which is to increase the convexity of the front surface towards the edge of the lens (Figure 5). Typically a convex oblate ellipsoid might be used whose tangential curvature increases at a faster rate than that of a spherical surface of the same vertex radius, as illustrated in Figure 5. Usually. However, a two- or three-term polynomial convex curve is chosen since this does not place a restriction on the maximum diameter of the lens. For higher power minus lenses, the principle of blending has been applied to the humble workshop flattened lenticular to produce a blended concave lenticular with a truly invisible dividing line. These blended lenticulars for myopia, such as the Wrobel Super- lenti and the Rodenstock Lentilux designs. enjoy excellent cosmetic properties and allow very high minus prescriptions, in excess of -20.00D. to be dispensed in relatively thin and lightweight form.