Measuring Vision

Every eye examination begins with a number: the smallest letter the patient can read. Behind it is one idea, the angle that the finest detail of a letter subtends at the eye, and a handful of conventions for writing it down. This chapter is about that number, what limits it, and what it leaves out.

#How small can you see?

Two points can be seen as two only if their images on the retina are far enough apart. What matters is not their size or their distance but the angle between them at the eye, which sets the separation of their images. The smallest angle a patient can resolve is the minimum angle of resolution, or MAR, usually given in minutes of arc (one minute, 1′, is a sixtieth of a degree). A normal young eye resolves about 1′; good eyes manage 0.5′ to 0.75′.

Visual acuity is the reciprocal of the MAR: an eye that resolves 1′ has an acuity of 1.0, and one that needs 2′ has an acuity of 0.5. Everything else is a way of writing this down.

#The Snellen letter

In 1862 Herman Snellen drew letters on a five-by-five grid, so that the whole letter subtends 5′ at a stated distance and each stroke, and each gap between strokes, subtends 1′. Reading such a letter requires resolving 1′ of detail. Move this 6/6 letter nearer and farther:

A letter that subtends 5′ at distance $d$ is $d\tan 5^{\prime }=1.454d$ mm tall (d in metres). The 6/6 letter, designed to be read at 6 m, is 8.73 mm tall (the 20/20 letter, for 20 ft, is 8.87 mm); the 6/60 letter is ten times taller.

The Snellen fraction records the test distance over the distance at which the smallest letter read subtends 5′. A patient at 6 m whose smallest line read is the one designed for 12 m has an acuity of 6/12, or 20/40 in feet. Those letters subtend 10′ at 6 m, with 2′ strokes, so the MAR is 2′. In general

The numerator is always the distance at which the test was actually done. A patient who can read nothing at 6 m but reads the 6/60 letter when brought to 3 m has 3/60 vision, the same as 6/120.

#Ways of writing acuity

Traditional Snellen charts have one letter at the top and more letters on each line down, with uneven steps between lines. Charts designed on logMAR principles (Bailey and Lovie in 1976, then the ETDRS chart used in clinical trials) fix all of that: every row has five letters, each row is 0.1 log units smaller than the one above, and the spacing between letters and rows is proportional to the letter size, so that the task is the same at every level. Acuity is recorded as the logarithm of the MAR:

So 6/6 (20/20) is logMAR 0.0, 6/12 (20/40) is 0.3 and 6/60 (20/200) is 1.0; better than 6/6 is negative. Each letter on a logMAR chart is worth 0.02, so acuity can be scored letter by letter. Drag the slider:

Clinical trials often report the ETDRS letter score, 85 − 50 × logMAR (the letters read at 4 m, plus 30 credited for the large letters): 85 is logMAR 0.0, and each line of five letters is 0.1. A change of 15 letters, three lines, is a change of 0.3 log units: a doubling (or halving) of the visual angle needed.

#Reading acuity

Near vision has its own notations. The most useful is the M unit: an M-sized letter subtends 5′ at that many metres, so a 1M letter is 1.45 mm tall, about the size of newspaper print. Near acuity converts to a Snellen fraction by dividing the reading distance in metres by the M size: reading 1M print at 40 cm is 0.40/1.0 = 0.4, the same as 20/50. The N notation gives the point size of standard print (N8 is close to 1M), and Jaeger numbers (J1, J2…) are a traditional scale that differs between manufacturers.

Being able to read a size at threshold is not the same as reading it comfortably. Fluent reading needs print two to three times larger than the smallest size that can just be made out, a reserve that matters a great deal in low vision (Chapter 18).

#What limits acuity

In a well-corrected eye three things set the limit. The first is the retina: at the centre of the fovea the cones are about 0.5′ apart, and a pattern can be resolved only if each light and dark bar falls on a separate row of cones. That allows about 60 cycles per degree, an acuity of roughly 20/10, which the best eyes approach.

The second is diffraction (Chapter 19). Even a perfect eye images a point as a small blurred disc, the Airy disc, whose angular diameter is $2.44\lambda /D$ for a pupil of diameter D. It grows as the pupil shrinks: about 1.6′ at 3 mm, but 4.7′ at 1 mm. The third is the eye’s aberrations, its spherical aberration and the rest, which grow rapidly as the pupil widens. The best pupil is the compromise that gives the least total blur, about 2.5 to 3 mm:

With some defocus left uncorrected, the best pupil moves smaller: that is the pinhole effect of Chapter 6. A pinhole much smaller than 1 mm makes vision worse again, because diffraction takes over. Acuity also falls steeply away from the fovea; a few degrees out it is already several lines worse.

#Contrast sensitivity

A letter chart tests black letters on a white background, at nearly 100% contrast. The world is mostly low contrast: faces, steps, a car at dusk. Contrast sensitivity is the reciprocal of the faintest contrast that can be seen, measured with gratings of light and dark bars at different spatial frequencies (cycles per degree). Plotted against frequency it forms the contrast sensitivity function, which peaks at about 3 to 6 cycles per degree and falls to 1 (log 0: even a full-contrast grating is only just visible) at the finest grating the eye can resolve. Acuity measures only that high-frequency end: a grating of 30 cycles per degree has 1′ bars, the detail of a 20/20 letter.

In the chart below, the bars get finer to the right and fainter upward. The edge where they fade into grey traces your own contrast sensitivity function (roughly: the frequencies depend on how far you sit from the screen, and a screen cannot draw the very faintest stripes). Underneath are typical curves:

Cataract, glaucoma, optic neuritis and macular disease can all reduce contrast sensitivity while Snellen acuity is still good, which is why patients with early cataract may read 20/25 yet struggle to drive at dusk. Clinically it is measured with letter charts of fixed size and falling contrast, such as the Pelli–Robson chart, on which letters are grouped in triplets, each 0.15 log units fainter (0.05 per letter); healthy adults typically score around log 1.6 to 1.9. Glare testing, for example with a brightness acuity tester that surrounds the eye with bright light, reveals the scatter of an early cataract.

#When letters won’t do

The Landolt C, a ring with a gap of 1′ at the threshold size, is the international reference optotype: the patient reports which way the gap faces. Tumbling E charts work the same way. Children who cannot yet name letters match them, or simple shapes, on a hand-held card (HOTV letters, Lea symbols). Infants are tested by preferential looking: shown a card with a grating on one side and plain grey of the same mean luminance on the other, a baby looks toward the grating if it can see it (Teller acuity cards, scored in cycles per degree). In a patient with cataract, the potential acuity of the retina can be estimated by projecting a chart or interference fringes through a clear part of the lens (Chapter 19).

#Recap

• Acuity is the reciprocal of the minimum angle of resolution. A Snellen letter subtends 5′ at its design distance, each stroke 1′.
• Snellen fraction = test distance / design distance. 6/12 = 20/40: MAR 2′, decimal 0.5, logMAR 0.3. The 6/6 letter is 8.7 mm tall.
• logMAR charts have five letters per row in 0.1 log steps; each letter is worth 0.02. Fifteen letters is a doubling of the visual angle.
• M units: a 1M letter subtends 5′ at 1 m (1.45 mm, newsprint). Acuity = distance (m) / M size: 1M at 40 cm is 20/50.
• Acuity is limited by cone spacing (about 20/10 at best), diffraction (Airy disc 2.44λ/D) and aberrations; the best pupil is about 2.5–3 mm.
• Contrast sensitivity peaks at 3–6 cycles per degree; it can fall in cataract, glaucoma and optic neuritis while acuity is still good.

#Test yourself

#Further reading

• American Academy of Ophthalmology, Basic and Clinical Science Course, Section 3: Clinical Optics and Vision Rehabilitation, chapters on the optics of the eye and vision rehabilitation.
• I. L. Bailey and J. E. Lovie, New design principles for visual acuity letter charts. American Journal of Optometry and Physiological Optics 53 (1976) 740–745.
• F. L. Ferris, A. Kassoff, G. H. Bresnick and I. Bailey, New visual acuity charts for clinical research. American Journal of Ophthalmology 94 (1982) 91–96.
• D. G. Pelli, J. G. Robson and A. J. Wilkins, The design of a new letter chart for measuring contrast sensitivity. Clinical Vision Sciences 2 (1988) 187–199.
• F. W. Campbell and R. W. Gubisch, Optical quality of the human eye. Journal of Physiology 186 (1966) 558–578.