Visual Function Scales Related to Visual Acuity
The measurement of visual acuity starts with defining the stimulus parameters: symbol size and viewing distance. The reference standard for size was defined by Snellen; the term “M-unit” was coined by Sloan. The reference standard for distance is the meter and its inverse, the diopter.
Based on these parameters, we can describe how the eye functions by calculating the Magnification Requirement (MAR) needed to bring a person up to performance standard. MAR provides a scale for vision loss that can extend to very high numbers; its counterpart, the visual acuity value, provides a scale for visual function, limited to the range from 0 to 1.0 (the reference standard) and slightly above. MAR and visual acuity scales are useful for calculating viewing distance, print size, and magnification requirements.
From these linear measurements of visual function (how the eye functions), we can derive a statistical estimate of a person’s visual ability (functional vision, how the person can function). This is done by taking the logarithm of the measurements in accordance with Weber-Fechner’s law, which states that a proportional increase in stimulus intensity gives a linear increase in sensation. Like MAR, logMAR is a scale for vision loss; higher values indicate poorer performance; like visual acuity, the visual acuity score (VAS) is a scale for visual function; higher values indicate better performance. 0 logMAR = standard vision; 0 VA = blindness.
MEASUREMENT OF VISUAL ACUITY – BASIC CONCEPTS
Because letter chart visual acuity is so often measured, it is a common misconception that visual acuity defines vision quality in general or even the ability to function visually. This is not the case. Visual acuity is only one of many parameters that describe aspects of vision. Letter chart tests compare the smallest line the subject can see with a reference standard (i.e., the line that a person with “normal” vision can just see). Letter chart testing thus determines the Magnification Requirement (MAR) for detail recognition; the reciprocal of this value is known as visual acuity (VA = 1/MAR). A person who needs characters or symbols twice as large is said to have a visual acuity of 1/2 (20/40, 0.5). Conversely, a person with a visual acuity of 1/5 (20/100, 0.2) needs letters five times larger. The ability to recognize letters or other symbols depends on the size of their retinal image. This size depends on the relationship between the object’s size and its viewing distance. Visual acuity therefore defines the angle of view under which an object is seen, not its absolute size. When the size of a test object is made 10 times larger, and the viewing distance is also made 10 times longer, the angle of view remains the same. When a constant object is brought twice as close, its angle of view doubles. Herman Snellen expressed optotype sizes indirectly as “the distance at which they subtend 5 arc minutes.”
Good Screening Test, But Not a Good Diagnostic Test
Letter recognition is a fairly complex function; a normal test result requires all three stages of vision to function properly: a healthy optical system to produce a sharp retinal image, healthy retinal receptors to convert this image into neural impulses, and a healthy nervous system to analyze and recognize the image. Testing also requires the motor ability to respond. Many different disorders can therefore result in poor test results. Because of this, visual acuity is a good screening test, but it is not a good diagnostic test. Other tests (e.g., ophthalmoscopy) are needed for differential diagnosis. Furthermore, the letter chart only tells us something about the small area of the retina where the letter or symbol is projected; it does not tell us anything about the surrounding or peripheral retina.
HISTORICAL DEVELOPMENT
Reading tests have been used since before the Middle Ages to test eye function. Significant changes began to occur in the mid-19th century. In 1843, Kuechler, a German ophthalmologist in Darmstadt, wrote a dissertation on the need for standardized vision tests. He developed a set of three charts to avoid memorization. However, he was a decade too early, and his work was almost completely forgotten. Around 1850, what would later be called the golden age of ophthalmology began. In 1850, Donders from Utrecht in the Netherlands visited William Bowman, famous for his anatomical and histological work, at an international conference in London. Here he met Albrecht von Graefe, who would become the father of German clinical ophthalmology. Donders and von Graefe became lifelong friends. Together with Bowman and Hermann von Helmholtz, who invented the ophthalmoscope in 1851, they formed the quartet that would make ophthalmology the first organ-oriented specialty.
Franciscus Cornelis Donders (1818-1889) was not only an outstanding scientist, but he also had a strong social conscience. In 1852, after returning from London, he privately founded an “Eye Infirmary for the Indigent,” which became an independent foundation in 1858. Donders’ most famous work was his book “The Anomalies of Accommodation and Refraction,” where he clarified the difference between asthenopia and hyperopia and provided the scientific basis for the correction of refractive errors. Donders was an excellent teacher and explained his subjects in a way that was understandable to practicing physicians.
In 1850, he visited London, where he met Bowman and von Graefe. He later wrote: “I had just seen Jaeger perform cataract surgeries alternately with his left and right hand when a young man came rushing into the room and embraced his mentor. It was Albrecht von Graefe. Jaeger thought we would get along well, and we quickly agreed. Those were memorable days. Von Graefe was my guide in all practical matters, and in scientific matters, he eagerly listened to the smallest detail. We lived together for a month, parting as brothers. Having William Bowman and Albrecht von Graefe as friends became an incredible treasure on my life’s journey.” The scene had thus changed significantly by 1854 when Eduard von Jaeger in Vienna published a set of reading samples, originally as an appendix to his book on cataracts and cataract surgery. He labeled his reading samples with catalog numbers from the Vienna State Printing Office. They immediately became an international success as a means of documenting functional vision.
Eduard Jaeger, Ritter von Jaxtthal (1818-1884), was born into a prominent family of Viennese ophthalmologists. His father, Friedrich, was one of the most prominent ophthalmologists of his time; Donders met him in London in 1850. In addition to his reading samples, Eduard is known for an early Atlas of the Ocular Fundus. He was a strong advocate for the use of Helmholtz’s direct ophthalmoscope and spent many hours making very detailed drawings. Since his reading samples had no external standard, other than the Vienna State Printing Office catalog, others could only imitate them with locally available typefaces. This explains the enormous variation among later imitations. While Snellen focused on measuring visual acuity, Jaeger focused on reading ability; this may be one of the reasons why he stubbornly refused to add Snellen’s letter size notation to his reading samples. Meanwhile, Donders was working on his groundbreaking studies of refraction and accommodation, where he clarified the nature of hyperopia as a refractive error rather than as a form of “asthenopia” (“eye weakness”), bringing the practice of eyeglass fitting from trial and error to a scientific routine. For this work, Donders not only needed reading samples for presbyopes but also distance measurements to determine the refractive error in myopes and hyperopes. He had used some of the larger print samples from Jaeger’s publication as distance measurements, but he felt the need for a more scientific method and a unit of measurement for visual function. He used the term “visual acuity” to describe “the sharpness of vision” and defined it as the ratio of a subject’s performance to a reference standard. In 1861, he proposed his formula and asked his colleague and later successor, Herman Snellen, to develop a measuring tool.
Donders’ Formula – and the Emergence of a Standard
Donders compared the letter size the patient had just recognized with a reference standard, the size that a standard person recognized. Visual acuity is the reciprocal value of this value.
(Angular) size seen by the subject/size of the reference standard = Magnification Requirement Visual Acuity = 1/Magnification Requirement Magnification Requirement: 2× Visual Acuity: 1/2 0.5 20/40 4× 1/4 0.25 20/80 10× 1/10 0.1 20/200
Note that his reference standard is based on a physical measurement (letter height 5 arc minutes). This choice was partly inspired by the work of the English astronomer Robert Hooke, who two centuries earlier had discovered that the human eye could distinguish double stars when they were 1 arc minute apart. Because Snellen chose an external, physical standard, others could reproduce his charts accurately.
The use of an arc minute to determine visual acuity goes back to how the Snellen chart was designed.
An arc degree is divided into 60 arc minutes, and each arc minute can be further divided into 60 arc seconds. When we talk about “5 minutes of an arc” in relation to the construction of an eye chart, it refers to the size of the letters or symbols on the chart. Each letter or symbol occupies an angle in the visual field when viewed from a certain distance. “5 minutes of an arc” indicates the size of this angle, where each letter or symbol occupies an angle of 5 arc minutes when viewed from a specific distance. The scientific explanation for the use of “5 minutes of an arc” in constructing an eye chart is based on the principles of vision’s structure and function. Visual acuity is tested by measuring the ability to distinguish between two separate points in the visual field, and this ability is related to the angle between these two points. By standardizing the size of the letters or symbols on the eye chart expressed in “5 minutes of an arc,” visual acuity can be accurately and uniformly evaluated across different tests and clinics.
The Snellen Chart
measures visual acuity based on the angle at which the smallest details on the chart can be resolved by the eye. In the Snellen chart, each letter is designed to occupy a specific angle in the visual field when viewed from a certain distance. The letter “E” at the top of the chart is designed to occupy an angle of 5 arc minutes when viewed from a distance of 3 meters. This means that the thickness of the lines forming the letter “E” occupies an angle of 5 arc minutes at the observer’s eye when standing 3 meters away from the chart.
In 1862, Snellen published his letter chart.
His most important decision was not to use existing typefaces but to design special measures for assessing visual acuity, which he called optotypes. He experimented with various designs based on a 5 × 5 grid. Eventually, he chose letters. Some others also published charts based on Donders’ formula but used existing typefaces instead of optotypes. Snellen’s chart prevailed and quickly spread worldwide. One of the first major orders came from the British army, which wanted to standardize testing of recruits.
Herman Snellen and His Charts
Donders had chosen Herman Snellen Sr. (1834-1908) as co-director of his eye clinic. Snellen would later become his successor. Donders was a scientist and teacher, Snellen was practically oriented and an excellent surgeon. Snellen advocated a fractional notation for visual acuity V = d/D, where d = the actual viewing distance in any unit of measurement, and D = the distance at which the optotype subtends 5 arc minutes. Louise Sloan introduced the term M-unit and modified the formula to V = m/M to make the use of the metric system explicit and to avoid confusion with D = diopters. Today, the actual Snellen fractions are rarely used and are most often replaced by Snellen equivalents (and these are gradually being replaced by logarithmic measurements).
To implement Donders’ formula, Snellen defined as the reference standard the ability to recognize one of his optotypes when it subtends an arc of 5 minutes with a line thickness of 1 minute. Because Snellen chose an external, physical standard, others could accurately reproduce his charts. On his charts, Snellen marked the letter size for each line (the distance at which the optotypes subtend 5 arc minutes); this is the denominator in the Snellen fraction for the corresponding line. He left it to the user to specify the viewing distance as the numerator.
20/20 or 6/6 Is Not the Normal
It is therefore incorrect to refer to the reference standard “20/20” (1.0) as “normal” vision, let alone as “perfect” vision. In fact, the connection between normal vision and the reference standard is no closer than the connection between the American standard foot and the average length of “normal” American feet. From his studies on refraction and accommodation and related topics, Donders knew that normal acuity decreases with age. While Snellen was working on his chart, Donders commissioned a study from one of his doctoral students to document the changes with age using prototypes of Snellen’s symbols. The study was published in 1862, the same year Snellen published his chart.
Since it is difficult to compare visual acuity values for different distances when using Snellen’s fractional notation, Felix Monoyer from Lyon, France, proposed replacing fractional notation with its decimal equivalent (e.g., 20/40 = 0.5, 6/12 = 0.5, 5/10 = 0.5). His decimal notation made it easy to compare visual acuity values regardless of the original measurement distance and has been commonly used in Europe—up until now, as logarithmic measurement takes over.
Landolt’s Broken Ring
Landolt’s “C” or broken ring is designed on Snellen’s 5 × 5 grid and has only one detail element, the gap, which is 1 unit wide. It can be presented in four or eight positions. Relatively little happened in the following period. There were attempts at standardization, such as a standard proclaimed by the International Council of Ophthalmology in 1909, but such documents were archived and never gained widespread acceptance. The fact that clinicians did not feel an urgent need for standardization can be explained by the fact that the most common uses of letter charts do not require it. For refractive correction, any set of measures is sufficient, as the only question is “better or worse?” For screening, the distinction between “within normal limits” and “not within normal limits” is the most important. Snellen’s reference standard at the lower limit of normal vision is well-placed for screening purposes. For screening, the difference between 20/100 (0.2), 20/200 (0.1), and 20/400 (0.05) is insignificant; they all indicate significant vision loss.
After World War II, interest in the rehabilitation of the visually impaired increased. It was recognized that most of those considered “industrially blind” actually had some degree of usable vision. In 1953, the first low vision services opened in New York at the Industrial Home for the Blind and at the New York Lighthouse. In the context of rehabilitation, the difference between 20/100, 20/200, and 20/400, which was not important for screening, became very important because a patient with 20/200 needs twice as much magnification as a patient with 20/100, and a patient with 20/400 needs twice as much again. It is therefore not surprising that significant improvements in clinical measurement of visual acuity came from clinicians involved in low vision rehabilitation. In 1959, Louise Sloan, the founder of the Low Vision Service at the Wilmer Eye Institute at Johns Hopkins University, designed a new optotype set with ten letters. She chose sans-serif letters while maintaining Snellen’s 5 × 5 grid. She recognized that not all letters were equally recognizable and therefore suggested using all ten letters on each line. This results in long lines where many letter sizes require more than one physical line.
Sloan’s Optotypes
Sloan designed a series of sans-serif letters that are widely used in the United States. They were designed based on Snellen’s 5 × 5 grid. Although the difficulty of individual letters varies, the average difficulty is approximately the same as for Landolt C’s. Sloan also introduced the term “M-unit.”
Snellen had defined visual acuity as: V = d/D, where d = test distance and D = “distance where the letter subtends 5 minutes of an arc.” To make this definition less wordy and to avoid confusion with D = diopters, Sloan proposed: V = m/M, where m = test distance in meters and M = letter size in M-units. 1 M-unit subtends 5′ at 1 m (1.454 mm, approx. 1/16 in).
Thus, Sloan’s M corresponds to Snellen’s D, provided the measurements are made in meters.
In the 1960s, the World Health Organization (WHO) investigated national definitions of “legal blindness” and found that 65 countries used as many different definitions. In 1974, the World Health Assembly approved the 9th revision of the International Classification of Diseases (ICD-9). Here, the old dichotomy between “legally sighted” and “legally blind” was abandoned in favor of a range of vision loss areas. The same year, the International Council of Ophthalmology (ICO) adopted the same ranges, extended them to include normal vision, and used the named ranges used in this chapter and in the International Classification of Diseases, 9th Revision: Clinical Modification (ICD-9-CM) (the US extension of WHO’s ICD-9).
Bailey and Jan Lovie
In 1976, Ian Bailey and Jan Lovie (then at the Kooyong Low Vision Service in Melbourne) published a new chart layout with five letters on each line and spacing between letters and lines corresponding to the letter size.
This layout standardized the crowding effect and the number of errors that could be made on each line. Thus, letter size became the only variable between acuity levels, making it easier to adjust the calculation of viewing distance, object size, and magnification requirements. Their new layout increased interest in logarithmic measurements, which had been known for more than a century. The logarithm of the minimum angle of resolution (logMAR) is the logarithm (to the base 10) of the reciprocal value of visual acuity. In 1984, the International Council of Ophthalmology approved the use of logMAR. It was recommended that all visual acuity measurements be made in logarithmic units.
The same year, Hugh Taylor, also in Melbourne, applied these design principles to an E-chart for illiterates used to test the visual acuity of Australian Aboriginals. He discovered that, as a group, Australian Aboriginals had significantly better visual acuity than Europeans. This is another reason not to consider 20/20 visual acuity as normal or perfect vision.
The Emergence of ETDRS and Logarithmic Measurement.
Based on the above work, the National Eye Institute chose the Bailey-Lovie layout, implemented with Sloan letters, to establish a standardized method for measuring visual acuity for the Early Treatment of Diabetic Retinopathy Study (ETDRS). These charts were used in all subsequent clinical studies and did much to familiarize the profession with the new layout and logarithmic progression.
Data from ETDRS were later used for a revised set of charts where all lines have the same average difficulty. Because the Sloan letters (designed on Snellen’s 5×5 grid) are wider than the British letters (designed on a 4×5 grid) used by Bailey and Lovie, the ETDRS chart was designed for a distance of 4 meters, not the 6 meters used by Bailey and Lovie.
Bailey-Lovie and ETDRS Charts (Early Treatment of Diabetic Retinopathy Study).
The ETDRS chart implemented the layout of the Bailey-Lovie chart with Sloan letters. The Bailey-Lovie chart has 4×5 letters and extends to 60 M for use at 6 meters; the ETDRS chart has 5×5 Sloan letters and extends to 40 M for use at 4 meters. Both follow the same logarithmic progression. The International Council of Ophthalmology approved in 1984 a “Visual Acuity Measurement Standard,” which also includes the above features. The International Council of Ophthalmology explicitly recommended the ETDRS protocol as an international standard in 2002 in a report on “Aspects and Ranges of Vision Loss,” which also drew attention to other aspects of vision loss beyond visual acuity.
Different Progressions in Letter Size
On a logarithmic scale, each step represents the same ratio (e.g., 2-4-8-16-32); on a linear scale, each step represents the same increment (e.g., 2-4-6-8-10). Only a geometric progression can span a wide range of values with equal steps throughout. The logarithms of a geometric scale provide a linear scale with equal steps throughout. Examples are the log(MAR) scale and the VAR scale. Snellen recommended reducing the viewing distance to improve the measurement of lower visual acuities. Using a logarithmic scale, which maintains the same accuracy at all levels, was first proposed by Green (1868). It was recommended by many subsequent researchers, including Sloan and Bailey-Lovie, but did not gain widespread recognition until it was adopted in the ETDRS protocol, which has become the de facto standard worldwide.
The use of a logarithmic (geometric) progression of stimuli aligns with Weber-Fechner’s law, which states that geometric (proportional) increases in stimulus give rise to linear increases in perception. Westheimer has shown that this also applies to visual acuity. Massof and Fletcher showed that it also applies to the relationship between visual acuity and visual (dis)ability.
Choice of Test Symbols Most visual acuity charts use letters. For the patient, this choice gives a sense of immediate validity, as the primary goal for most patients is to read. For the practitioner, it is easy to spot errors because most practitioners know their chart by heart. However, the use of letters is only justified if one can assume that letter recognition is trivially easy. The ETDRS charts use the Sloan letter set, which has made it the preferred set in many studies. There are many other letter sets, including sets for non-Roman alphabets. For less literate adults, it may be more appropriate to use a number chart. Number charts can also be used for deaf patients who use sign language, as they can respond by holding up the appropriate number of fingers.
An alternative is to use various symbol sets.
Internationally Used Symbol Sets
The Landolt C has become the preferred symbol for many scientific measurements. However, they are much less commonly used in clinical settings. When used in a chart format, it is harder to detect errors unless the observer points to the symbol. However, pointing, as with a single presentation, can affect the difficulty of the test.
The International Council of Ophthalmology’s standard for measuring visual acuity from 1984 recommended that letter charts in non-Roman alphabets (e.g., Cyrillic, Arabic, Hindi, Kanji, Hebrew) be calibrated against Landolt Cs to achieve the same recognizability. Since the ETDRS chart has become a de facto standard, calibration against an ETDRS chart is another option.
Tumbling Es are likely the most commonly used symbols for testing children. They are also widely used in developing countries and in countries where the Roman alphabet is not used. Tumbling Es and Landolt Cs require a sense of laterality, which can be a barrier for young and developmentally delayed children. They can be presented in a chart format or as single symbols. When comparing results, it is important to remember that presentation as single symbols is an easier test than presentation in a chart format.
Symbol Sets Commonly Used in the USA The HOTV test uses the four letters H, O, T, and V as symbols with distinctive shapes that can be recognized even by children who are not yet literate; these letters were chosen because they do not require a sense of laterality. For children who are shy or have difficulty naming symbols, matching cards can be used, where the child only needs to point to the matching symbol.
Use of Pictures
For illiterate individuals and preschool children, pictures can be used. It can be challenging to determine whether letters and various pictures are equivalent, and the child’s performance may depend on whether they are familiar with the objects. Most pictures are not designed on Snellen’s 5×5 grid. Others are not properly calibrated. ISOeyes’s Eyekey and Similar are designed on Snellen’s 5×5 grid. They have been calibrated to be recognizable on par with Sloan letters. Therefore, there is no shift in visual acuity when a child transitions from these drawings to letters. They can also be used by adults who are not familiar with the Roman alphabet.
