Prismatic effects of lenses

All lenses act as prisms when one looks through the lens at any point other than the optical center. The amount of the induced prismatic effect depends on the power of the lens and the distance from the optical center. Specifically, the amount of prismatic effect (measured in prism diopters) is equal to the distance (in centimeters) from the optical center multiplied by the lens power (in diopters). This equation is known as the Prentice rule:

• ∆ = hD

where

• ∆ = prismatic effect (in prism diopters)

• h = distance from the optical center (in centimeters)

• D = lens power (in diopters)

Image displacement

When reading at near through a point below the optical center, a patient wearing spectacle lenses of unequal power may notice vertical double vision. With a bifocal segment, the gaze is usually directed 8–10 mm below and 1.5–3.0 mm nasal to the distance optical center of the distance lens (in the following examples, we assume the usual 8 mm down and 2 mm nasal). As long as the bifocal segments are of the same power and type, the induced, vertical prismatic displacement is determined by the powers of the distance lens alone.

If the lens powers are the same for the 2 eyes, the displacement of each is the same (Figs 4-27, 4-28). However, if the patient’s vision is anisometropic, a phoria is induced by the unequal prismatic displacement of the 2 lenses (Figs 4-29, 4-30). The amount of vertical phoria is determined by subtracting the smaller prismatic displacement from the larger if both lenses are myopic or hyperopic (see Fig 4-29) or by adding the 2 lenses if the patient is hyperopic in 1 eye and myopic in the other (see Fig 4-30).

For determination of the induced horizontal phoria, the induced prisms are added if both eyes are hyperopic or if both eyes are myopic. If 1 eye is hyperopic and the other is myopic, the smaller amount of prismatic displacement is subtracted from the larger (see Fig 4-30). Image displacement is minimized when round-top segment bifocal lenses are used with plus lenses and flat-top segment bifocal lenses are used with minus lenses (Fig 4-31).

Image jump

The usual position of the top of a bifocal segment is 5 mm below the optical center of the distance lens. As the eyes are directed downward through a lens, the prismatic displacement of the image increases (downward in plus lenses, upward in minus lenses). When the eyes encounter the top of a bifocal segment, they meet a new plus lens with a different optical center, and the object appears to jump upward unless the optical center of the add is at the very top of the segment (Fig 4-32). Executive-style segments have their optical centers at the top of the segment. The optical center of a typical flat-top segment is located 3 mm below the top of the segment. The closer the optical center of the segment approaches the top edge of the segment, the less the image jump. Thus, flat-top segments produce less image jump than do round-top segments because the latter have much lower optical centers. Patients with myopia who wear round-top bifocal lenses would be more bothered by image jump than would patients with hyperopia because the jump occurs in the direction of image displacement.

Figure 4-27 Prismatic effect of bifocal lenses in isometropic hyperopia.

Figure 4-28 Prismatic effect of bifocal lenses in isometropic myopia.

Figure 4-29 Prismatic effect of bifocal lenses in anisometropic hyperopia.

Figure 4-30 Prismatic effect of bifocal lenses in antimetropia.

Figure 4-31 Image displacement through bifocal segments.

(From Wisnicki HJ. Bifocals, trifocals, and progressive-addition lenses. Focal Points: Clinical Modules for Ophthalmologists. San Francisco: American Academy of Ophthalmology; 1999, module 6. Reprinted with permission from Guyton DL. Ophthalmic Optics and Clinical Refraction. Baltimore: Prism Press; 1998. Redrawn by C. H. Wooley.)

Compensating for induced anisophoria

When anisometropia is corrected with spectacle lenses, unequal prism is introduced in all secondary positions of gaze. This prism may be the source of symptoms, even diplopia. Symptomatic anisophoria occurs especially when a patient with early presbyopia uses his or her first pair of bifocal lenses or when the anisometropia is of recent and/or sudden origin, as occurs after retinal detachment surgery, with gradual asymmetric progression of cataracts, or after unilateral intraocular lens implantation. The patient usually adapts to horizontal imbalance by increasing head rotation but may have symptoms when looking down, in the reading position. Recall that horizontal vergence amplitudes are large compared with vertical fusional amplitudes, which are typically less than 2∆. We can calculate the amount of induced phoria by using the Prentice rule (Fig 4-33; Clinical Example 4-5).

Figure 4-32 Image jump through bifocal segments. If the optical center of a segment is at its top, no image jump occurs.

(From Wisnicki HJ. Bifocals, trifocals, and progressive-addition lenses. Focal Points: Clinical Modules for Ophthalmologists. San Francisco: American Academy of Ophthalmology; 1999, module 6. Reprinted with permission from Guyton DL. Ophthalmic Optics and Clinical Refraction. Baltimore: Prism Press; 1998. Redrawn by C. H. Wooley.)

Figure 4-33 Calculation of induced anisophoria.

CLINICAL EXAMPLE 4-5

This example demonstrates the Prentice rule. Consider a patient with the following reading point, 8 mm below distance optical center:

In this example, there is an induced right hyperdeviation of 2.40∆. Conforming to the usual practice in the management of heterophorias, approximately two-thirds to three-fourths of the vertical phoria should be corrected—in this case, 1.75 D.

The correction of induced vertical prism may be accomplished in several ways:

Press-on (Fresnel) prisms With press-on prisms, 2.00∆ of base down (BD) prism may be added to the right segment in the preceding example or 2.00∆ of base up (BU) prism to the left segment.

Slab-off The most satisfactory method of compensating for the induced vertical phoria in anisometropia is the technique of bicentric grinding, known as slab-off (Fig 4-34). In this method, 2 optical centers are created in the lens that has the greater minus (or less plus) power, thereby counteracting the base-down effect of the greater minus lens in the reading position. It is convenient to think of the slab-off process as creating base-up prism (or removing base-down prism—slab-off) over the reading area of the lens.

Bicentric grinding is used for single-vision lenses as well as for multifocal lenses. By increasing the distance between the 2 optical centers, this method achieves as much as 4.00∆ of prism compensation at the reading position.

Reverse slab-off Prism correction in the reading position is achieved not only by removing base-down prism from the lower part of the more minus lens (slabbing off) but also by adding base-down prism to the lower half of the more plus lens. This technique is known as reverse slab-off.

Historically, it was easy to remove material from a standard lens. Currently, because plastic lenses are fabricated by molding, it is more convenient to add material to create a base-down prism in the lower half of what will be the more plus lens. Because plastic lenses account for most lenses dispensed, reverse slab-off is the most common method of correcting anisometropically induced anisophoria. In theory, a minus powered spectacle lens will have less edge thickness with slab-off than with reverse slab-off.

Figure 4-34 Bicentric grinding (slab-off). A, Lens form with a dummy lens cemented to the front surface. B, Both surfaces of the lens are reground with the same curvatures but removing base-up prism from the top segment of the front surface and removing base-down prism from the entire rear surface. C, The effect is a lens from which base-down prism has been removed from the lower segment only.

When the clinician is ordering a lens that requires prism correction for an anisophoria in downgaze, it is often appropriate to leave the choice of slab-off versus reverse slab-off to the optician by including a statement in the prescription, such as, “Slab-off right lens 3.00∆ (or reverse slab-off left lens).” In either case, the prescribed prism should be measured in the reading position, not calculated, because the patient may have partially adapted to the anisophoria.

Dissimilar segments In anisometropic bifocal lens prescriptions, vertical prism compensation can also be achieved by using dissimilar bifocal segments with their optical centers at 2 different heights. The segment with the lower optical center should be placed in front of the more hyperopic (or less myopic) eye to provide base-down prism. (This method contrasts with the bicentric grinding method, which produces base-up prism and is therefore employed on the lesser plus or greater minus lens.)

In the example in Figure 4-35, a 22-mm round segment is used for the right eye, and the top of its segment is at the usual 5 mm below the distance optical center. For the left eye, a 22-mm flat-top segment is used, again with the top of the segment 5 mm below the optical center.

Because the optical center of the flat-top segment is 3 mm below the top of the segment, it is at the patient’s reading position and that segment will introduce no prismatic effect. However, for the right eye, the optical center of the round segment is 8 mm below the patient’s reading position; according to the Prentice rule, this 2.50 D segment will produce 2.50 × 0.8 = 2.00∆ base-down prism.

Single-vision reading glasses with lowered optical centers Partial compensation for the induced vertical phoria at the reading position can be obtained with single-vision reading glasses when the optical centers are placed 3–4 mm below the pupillary centers in primary gaze. The patient’s gaze will be directed much closer to the optical centers of the lenses when reading.

Figure 4-35 Dissimilar segments used to compensate for anisophoria in anisometropic bifocal prescriptions.

Contact lenses Contact lenses can be prescribed for patients with significant anisometropia that causes a symptomatic anisophoria in downgaze. Reading glasses can be worn over the contacts if the patient’s vision is presbyopic.

Refractive surgery Corneal refractive surgery may be an option for some patients with symptomatic anisometropia or anisophoria.

Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.