2.3 Usable Accommodation & Range of Vision

The Physiology of Near Focus

The human eye is dynamic, capable of shifting its focal point from distant horizons to near print in a fraction of a second. This ability to alter the refractive power of the crystalline lens is called accommodation. Accommodation occurs when the ciliary muscle contracts, releasing tension on the suspensory ligaments (zonules of Zinn). This allows the elastic crystalline lens to assume a more rounded, highly curved shape, increasing its positive dioptric power.

As we age, the crystalline lens gradually loses its elasticity, and the ciliary muscle becomes less effective. This age-related reduction in near-focusing ability is known as presbyopia. To assist presbyopes, opticians dispense multifocal lenses, which add positive dioptric power (an Add power) to the lower portion of the lens. Understanding the relationship between a patient's remaining accommodation and their prescribed Add power is essential for determining their functional range of vision.

Amplitude of Accommodation (Acc)

The amplitude of accommodation is the maximum change in dioptric power that the eye's optical system can achieve. It is measured in diopters (D) and represents the difference in refractive power between the eye when it is completely relaxed (focused at its far point) and when it is fully accommodated (focused at its near point).

The amplitude of accommodation is highest in childhood and steadily declines throughout life. To estimate a patient's amplitude of accommodation based on their age, clinicians often use Hofstetter's formulas. The formula for estimating the minimum expected amplitude of accommodation is:

Minimum Amplitude = 15 - 0.25 * Age

For example:

• Age 20: Minimum Amplitude = 15 - 0.25(20) = 15 - 5 = 10.00 D.
• Age 40: Minimum Amplitude = 15 - 0.25(40) = 15 - 10 = 5.00 D.
• Age 60: Minimum Amplitude = 15 - 0.25(60) = 15 - 15 = 0.00 D.

In clinical practice, a patient is only comfortable using up to half of their total amplitude of accommodation for sustained reading or near tasks. The remaining half is kept in reserve. If a patient is forced to use more than half of their amplitude, they will quickly experience asthenopia (eyestrain), headaches, and transient blur. This comfort threshold explains why near vision support (bifocals or reading glasses) is typically required when the amplitude of accommodation drops below 3.00 to 4.00 diopters, which usually occurs around age 40 to 45.

Far Point and Near Point of Accommodation

To analyze a patient's range of vision, we must identify two boundary points:

1. Far Point (Punctum Remotum): The furthest point in space that is focused clearly on the retina when accommodation is fully relaxed. For an emmetrope (an eye with no distance refractive error), the far point is at infinity. For an uncorrected myope, the far point is at a finite distance in front of the eye.
2. Near Point of Accommodation (NPA / Punctum Proximum): The closest point in space that is focused clearly on the retina when the eye is exerting its maximum accommodative effort.

For an emmetrope (or a patient whose distance prescription has fully corrected their refractive error), the Near Point of Accommodation (in meters) is calculated as the reciprocal of their amplitude of accommodation:

NPA (meters) = 1 / Acc

For example, a 40-year-old patient with an amplitude of accommodation of 5.00 D has a near point of:

NPA = 1 / 5.00 D = 0.20 meters = 20 cm

As presbyopia progresses, the NPA recedes. By age 50, the amplitude may drop to 1.50 D, pushing the NPA out to:

NPA = 1 / 1.50 D = 0.67 meters = 67 cm

Since standard reading distance is about 40 cm, this patient can no longer read comfortably without corrective lenses.

Range of Vision with Bifocals/Add Powers

When a near addition (Add) power is introduced, the patient's range of vision is shifted. The near segment acts as a helper, adding a baseline amount of positive power. When the patient looks through the near segment, their range of vision is bounded by a new near limit and far limit.

Calculating the Far Limit through the Add Segment

The far limit of the range of vision through a bifocal segment represents the furthest distance the patient can see clearly when looking through the reading area. This occurs when their accommodation is completely relaxed (0.00 D of accommodation). The formula is:

Far Limit (meters) = 1 / Add

For a +2.00 D Add, the far limit is:

Far Limit = 1 / 2.00 D = 0.50 meters = 50 cm

The patient cannot see anything beyond 50 cm through this segment.

Calculating the Near Limit through the Add Segment

The near limit of the range of vision through the segment represents the closest distance they can see clearly. This occurs when they exert their maximum available amplitude of accommodation (Acc). The formula is:

Near Limit (meters) = 1 / (Add + Acc)

For a patient with a +2.00 D Add and 1.00 D of remaining accommodation:

Near Limit = 1 / (2.00 D + 1.00 D) = 1 / 3.00 D = 0.33 meters = 33 cm

Through the segment, this patient has a clear range of vision from 33 cm to 50 cm.

The Intermediate Visual Gap

In advanced presbyopes, a problem arises: the visual gap. If a patient has a high Add power (e.g., +2.50 D) and very little accommodation (e.g., 0.50 D):

• Through Distance Lens: The patient can see from infinity to 1 / 0.50 = 2.0 meters.
• Through Near Segment: The patient can see from 1 / 2.50 = 0.40 meters (40 cm) to 1 / (2.50 + 0.50) = 1 / 3.00 = 0.33 meters (33 cm).
• The Gap: There is an intermediate zone between 2.0 meters and 0.40 meters where the patient cannot focus clearly. This is a common complaint of patients who struggle to see computer monitors (usually positioned at 50 cm to 70 cm). To resolve this, opticians prescribe trifocals (which have an intermediate segment set at 50% of the Add power) or progressive addition lenses (which provide a continuous gradient of power).

Range of Vision Reference Table

The table below illustrates the range of vision (near limit to far limit) through a near segment for various combinations of Add power and Amplitude of Accommodation (Acc), assuming an emmetropic distance correction.