The correction of near vision astigmatism –

Compared To The Cylindrical Correction For Distance Vision

Some manufacturers offer progressive lenses with the possibility of optimizing the near portion of the lens. Why is this necessary? What is the background to the optimization? This paper discusses the difference between the cylindrical correction prescribed for distance vision and the modification necessary to fully correct the eye’s astigmatism when the wearer uses the lenses for near vision.

By Mo Jalie

Most optometry textbooks explain why the cylinder which corrects an eye for distance vision cannot correct the eye for near vision except in two specific cases, the first being that the eye has no accommodative power and the second (and most unlikely situation) that the eye is able to accommodate by two different amounts along its principal meridians. In all other cases, the cylinder required for distance vision must be increased by a small percentage in order to fully correct the eye’s astigmatism.

The reason for this can be deduced from figure 1. Figure 1(a) shows an eye corrected for distance vision by an astigmatic lens whose power in the vertical meridian is F90 and in the horizontal meridian,

F 180. The vergence in the refracted pencil arriving at the eye in the vertical meridian is K 90 and in the horizontal meridian, K180 where K 90 = F 90 / (1 – dF 90) and K180 = F 180 / (1 – dF180).

The ocular astigmatism, i.e., the actual astigmatism inherent in the eye is K180 – K 90.

A numerical example might be easier to follow. Suppose that a subject wears the prescription +5.00/+3.00 x 90 for distance vision, then F 90 = +5.00 and F180 = +8.00. The vergence arriving at the eye, assuming its first principal point lies 14 mm behind the lens, is

The actual ocular astigmatism possessed by the eye is +9.01 - +5.38 = +3.63 DC x 90. Suppose now that the wearer views a near object at one-third meter from the lens. The vergence (L) arriving at the lens is -3.00 D and (ignoring the lens thickness) the vergence leaving the lens is (-3.00 + F90) = +2.00 D and the vergence leaving the lens in the horizontal meridian is (-3.00 + F180) = +5.00 D. The vergences arriving at the eye, B90 and B180 are

B 90 = 2 / (1 – 0.014 x 2) = +2.06 and B180 = 5 / (1 – 0.014 x 5) = +5.38.

The difference between these two vergences is +3.32 D which is +0.31 D less than the physical astigmatism possessed by the eye. In order to fully correct the ocular astigmatism for near vision the vergence arriving at the eye in the horizontal meridian must be increased by the actual astigmatism of the eye to +5.69 D, (+2.06 D + 3.63 D), so the vergence leaving the lens in the horizontal meridian must be +5.27 D. The power of the lens in the horizontal meridian must become +8.27 D, i.e., the cylindrical power for near vision should be increased to +3.27 D.

Now, consider the prescription, +1.00 / +4.00 x 90 with a prescribed addition of +1.00 for near. The expected prescription for near vision is +2.00 / +4.00 x 90, however, as we have seen, this cylindrical correction does not fully correct the astigmatism for near vision. To find the correct near vision prescription, the spherical component of the near vision prescription is obtained by adding the prescribed near addition to the sphere of the prescription which in this example gives +2.00 D, but the cylindrical component must be increased by a small amount since the cylinder which corrects the eye for near vision is slightly greater than the cylinder which corrects the eye’s astigmatism in distance vision. The axis direction is more difficult to determine by theoretical analysis and is best determined by measurement during the refraction procedure.

Optometrists are taught in University [1] that the cylinder which corrects an eye for distance vision does not fully correct the astigmatism of the eye in near vision unless the eye has no accommodation such as in cases of aphakia, or the very unlikely situation where the eye is able to accommodate by different amounts along its principal meridians. This second situation must be extremely rare since it implies, for example, that the crystalline lens is toroidal and the toricity changes by just the right amount to correct the near vision astigmatism, or, perhaps the crystalline lens is tilted and that upon accommodation, the tilt changes by just the right amount to correct the astigmatism. It is improbable that this latter case would ever happen!

Increasing the cylinder for near

It can be shown[2] that in all other cases, the cylinder for near should be increased by the small percentage, δC, where δC is given by δC = -2 d (L + A) / 10% , (1) where d is the distance from the eye’s first principal point to the lens, in millimetres, L is the reading distance expressed in dioptres and A is any prescribed addition for near. Note that L will carry a minus sign in this expression, (Fig. 2).

For a reading distance of one-third metre, L = -3.00 D and choosing a distance of 15 mm for d (note that the eye’s first principal point lies about one and two-thirds mm behind the cornea), the only variable is the near addition, A. The near cylinder should be increased by the percentage amounts shown in the table in figure 3. Note that the smaller the near addition, the more the near vision cylinder should be increased. In particular, even wearers of single vision lenses who need them only for distance vision but who are highly astigmatic might benefit from a different cylinder power and axis for continuous near vision and this compensation might be provided in some of the freeform single vision lenses.

It can be seen that these percentage increases are quite small and, in practice, only astigmats with high cylinder powers are normally affected. For a young person who does not need an addition for close work, the distance cylinder power is under-corrected by 9%, which for a 2.00 D cylinder is 0.18 D and for a 4.00 D cylinder, 0.36 D.

In the opening example, where no addition was prescribed, using equation (1), the near vision cylinder should be increased by 8.4% which is an extra cylinder power of 0.25 D and the near vision prescription should be +2.00 / +4.25, axis as yet, unknown. Although equation (1) is a binomial approximation it provides a result very close to the one obtained by paraxial ray-tracing.

Changes in axis direction of the cylinders

I now come to the question “What is the axis direction?”.

Consider the subject shown in figure 4(a), whose head is in the primary position of gaze, the subject looking straight ahead in distance vision. In figure 4(b) the subject has been fitted with a pair of contact lenses on which the vertical meridian has been indicated.

When the eyes converge and depress for near vision, the actions of the external ocular muscles, notably the medial, the inferior and the superior oblique muscles typically cause extorsion of the globe, it has been assumed in this figure by some 5°. Obviously, the extorsion will vary from person to person, but as can be seen from the meridians shown by the contact lenses, not only will there be a change in cylinder power, but the axis direction of the cylinders will change due to the cyclorotation. The right eye axis will change to 95° and the left eye axis to 85° (Fig. 5). In practice, the axis direction should be determined by the eyecare practitioner during the sight test routine, especially for those subjects who have very precise near vision requirements. Several lens design systems allow these changes in cylinder power and/or axis direction, for example, Rodenstock, whose marketing literature includes the statement “[…] different cylinder strengths and axis positions for distance and close up can be implemented in one progressive lens.” Carl Zeiss Vision also state that they can personalize the near vision zone of their progressive lenses. You might ask, “Why are so few prescriptions ordered with different cylinder powers for near vision”? I can think of several answers but perhaps the chief one is that, in practice, most cylinder powers are quite small, rarely exceeding 1.00 D and even more rare, greater that 2.00 D. However, research, such as that from Rosenfield et al[3], has shown that the correction of small astigmatic refractive errors may be important in optimizing patient comfort when working with a computer, so that reducing aberrational astigmatism in the near portion of a single vision lens designed for distance will benefit the wearer.

I hope that this brief paper has been informative and of interest and has described some of the clever technology which is now incorporated in the latest generation of personalized progressive power lenses.

References: [1] R abbetts R.B. (2007) Clinical Visual Optics (4th ed.), Elsevier, Oxford. [2] Jalie M. (2021), Principles of Ophthalmic Lenses (6th ed.), ABDO, Godmersham.

[3] Rosenfield M, Hue JE, Huang RR & Bababekova Y. (2011) “The effects of induced oblique astigmatism on symptoms and reading performance while viewing a computer screen”. Ophthalmic Physiol Opt.;32(2):142-8.

Mo Jalie

Professor Mo Jalie DSc, SMSA, FBDO (Hons), Hon FCGI, Hon FCOptom, MCMI, is Visiting Professor in Optometry to the optometry course at Ulster University in the UK and to the educational facility Essilor Academy Europe. He also works as a consultant to the ophthalmic industry. He was the Head of Department of Applied Optics at City & Islington College from 1986 to 1995 where he had taught optics, ophthalmic lenses and dispensing from 1964. He is recognised as an international authority on the design of spectacle lenses and has written several books. Furthermore he is the author of some 200 papers on ophthalmic lenses, contact lenses, intra-ocular lenses and dispensing and a consultant editor to the Optician magazine. He holds patents for aspheric spectacle lenses and intra-ocular lenses. He has also produced several educational CDs and runs a web-based course in Spectacle Lens Design leading to the qualification FBDO (Hons) SLD.