RR.2 Reference Tables For Equivalent Visual Acuity Notations

RR.2.1 Background

Visual acuity is defined as the reciprocal of the ratio between the letter size that can just be recognized by a patient, relative to the size just recognized by a standard eye. If the patient requires letters that are twice as large (or twice as close), the visual acuity is said to be 1/2; if the letters need to be 5x larger, visual acuity is 1/5, and so on.

Note that the scales in the tables extend well above the reference standard (1.0, 20/20, the ability to recognize a letter subtending a visual angle 5 min. of arc), since normal acuity is often 1.25 (20/16), 1.6 (20/12.5) or even 2.0 (20/10).

Today, the ETDRS chart and ETDRS protocol, established by the National Eye Institute in the US, are considered to represent the de facto gold standard for visual acuity measurements The International Council Of Ophthalmology, Visual Standard, Aspects and Ranges of Vision Loss (April, 2002) is a good reference document.

The full ETDRS protocol requires a wide chart, in the shape of an inverted triangle, on a light box, and cannot be implemented on the limited screen of a projector (or similar) chart.

For most routine clinical measurements projector charts or traditional charts with a rectangular shape are used; these non-standardized tools are less accurate than ETDRS measurements.

This appendix contains two lookup tables, one for traditional charts and one for ETDRS measurements.

RR.2.2 Notations

Various notations may be used to express visual acuity. Snellen (in 1862) used a fractional notation in which the numerator indicated the actual viewing distance; this notation has long been abandoned for the use of equivalent notations, where the numerator is standardized to a fixed value, regardless of the true viewing distance. In Europe the use of decimal fractions is common (1/2 = 0.5, 1/5 = 0.2); in the US the numerator is standardized at 20 (1/2 = 20/40, 1/5 = 20/100), while in Britain the numerator 6 is common (1/2 = 6/12, 1/5 = 6/30).

The linear scales on the right side of the tables are not meant for clinical records. They are required for statistical manipulations, such as calculation of differences, trends and averages and preferred for graphical presentations. They convert the logarithmic progression of visual acuity values to a linear one, based on Weber-Fechner's law, which states that proportional stimulus increases lead to linear increases in perception.

The logMAR scale is calculated as log (MAR) = log (1/V) = - log (V). LogMAR notation is widely used in scientific publications. Note that it is a scale of vision loss, since higher values indicate poorer vision. The value "0" indicates "no loss", that is visual acuity equal to the reference standard (1.0, 20/20). Normal visual acuity (which is better than 1.0 (20/20) ) is represented by negative logMAR values.

The VAS scale (VAS = Visual Acuity Score) serves the same purpose. Its formula is: 100 - 50 x logMAR or 100 + 50 x log (V). It is more user friendly, since it avoids decimal values and is more intuitive, since higher values indicate better vision. The score is easily calculated on ETDRS charts, where 1 point is credited for each letter read correctly. The VAS scale also forms the basis for the calculation of visual impairment ratings in the AMA Guides to the Evaluation of Permanent Impairment.

RR.2.3 Use of The Lookup Table

Data input: Determine the notation used in the device and the values of the lines presented. No device will display all the values listed in each of the traditional columns. Convert these values to the decimal DICOM storage values shown on the left of the same row. DICOM values are not meant for data display. In the table, they are listed in scientific notation to avoid confusion with display notations.

In the unlikely event that a value must be stored that does not appear in the lookup table, calculate the decimal equivalent and round to the nearest listed storage value.

Data display: If the display notation is the same as the input notation, convert the DICOM storage values back to the original values. If the notation chosen for the display is different from the input notation, choose the value on the same row from a different column. In certain cases this may result in an unfamiliar notation; unfortunately, this is unavoidable, given the differences in size progressions between different charts. If a suffix (see attribute "Visual Acuity Modifiers" (0046,0135) ) is present, that suffix will be displayed as it was recorded.

Suffixes: Suffixes may be used to indicate steps that are smaller than a 1 line difference. On traditional charts, such suffixes have no defined numerical value. Suffixes +1, +2, +3 and -1, -2, -3 may be encountered. These suffixes do not correspond to a defined number of rows in the table.

The Traditional charts used in clinical practice are not standardized; they have an irregular progression of letter sizes and a variable number of characters per line. Measurement accuracy may further suffer from hidden errors that cannot be captured by any recording device, such as an inconsistent, non-standardized protocol, inaccurate viewing distance, inaccurate projector adjustment and contrast loss from room illumination. Therefore, the difference between two routine clinical measurements should not be considered significant, unless it exceeds 5 rows in the table (1 line on an ETDRS chart).

Table RR-1 contains many blank lines to make the vertical scale consistent with that used in Table RR-2. Notations within the same gray band are interchangeable for routine clinical use, since their differences are small compared to the clinical variability, which is typically in the order of 5 rows (1 ETDRS line).

Table RR-1. Reference Table for Use with Traditional Charts

DICOM

Notations for Clinical Use with Traditional Charts

Scales for statistics and graphical displays

Decimal Visual Acuity

Linear Scales

Decimal

US

6 m

LogMAR

VAS

2.00 E+00

2.0

20/10

6/3

-0.30

115

1.91 E+00

-0.28

114

1.82 E+00

-0.26

113

1.74 E+00

-0.24

112

1.66 E+00

-0.22

111

1.60 E+00

1.6

20/12.5

6/3.8

-0.20

110

1.50 E+00

1.5

20/13

6/4

-0.18

109

1.45 E+00

-0.16

108

1.38 E+00

-0.14

107

1.30 E+00

1.3

20/15

6/4.5

-0.12

106

1.25 E+00

1.25

20/16

6/4.8

-0.10

105

1.20 E+00

1.2

20/17

6/5

-0.08

104

1.15 E+00

-0.06

103

1.10 E+00

1.1

20/18

6/5.5

-0.04

102

1.05 E+00

-0.02

101

1.00 E+00

1.0

20/20

6/6

0

100

9.55 E-01

0.02

99

9.00 E-01

0.9

20/22

6/66

0.04

98

8.70 E-01

0.06

97

8.30 E-01

0.08

96

8.00 E-01

0.8

20/25

6/7.5

0.10

95

7.50 E-01

0.75

20/26

6/8

0.12

94

7.20 E-01

0.14

93

7.00 E-01

0.7

20/28

6/8.7

0.16

92

6.60 E-01

0.66

20/30

6/9

0.18

91

6.30 E-01

0.63

20/32

6/9.5

0.20

90

6.00 E-01

0.6

20/33

6/10

0.22

89

5.75 E-01

0.24

88

5.50 E-01

0.26

87

5.25 E-01

0.28

86

5.00 E-01

0.5

20/40

6/12

0.30

85

4.80 E-01

0.32

84

4.57 E-01

0.34

83

4.37 E-01

0.36

82

4.17 E-01

0.38

81

4.00 E-01

0.4

20/50

6/15

0.40

80

3.80 E-01

0.42

79

3.60 E-01

0.44

78

3.50 E-01

0.46

77

3.33 E-01

0.33

20/60

6/18

0.48

76

3.20 E-01

0.32

20/63

6/19

0.50

75

3.00 E-01

0.3

20/66

6/20

0.52

74

2.90 E-01

0.28

20/70

6/21

0.54

73

2.75 E-01

0.56

72

2.63 E-01

0.58

71

2.50 E-01

0.25

20/80

6/24

0.60

70

2.40 E-01

0.62

69

2.30 E-01

0.64

68

2.20 E-01

0.66

67

2.10 E-01

0.68

66

2.00 E-01

0.2

20/100

6/30

0.70

65

1.90 E-01

0.72

64

1.82 E-01

0.74

63

1.74 E-01

0.76

62

1.66 E-01

0.17

20/120

6/36

0.78

61

1.60 E-01

0.16

20/125

6/38

0.80

60

1.50 E-01

0.15

20/130

6/40

0.82

59

1.45 E-01

0.84

58

1.38 E-01

0.86

57

1.30 E-01

0.13

20/150

6/45

0.88

56

1.25 E-01

0.125

20/160

6/48

0.90

55

1.20 E-01

0.12

20/170

6/50

0.92

54

1.15 E-01

0.94

53

1.10 E-01

0.96

52

1.05 E-01

0.98

51

1.00 E-01

0.1

20/200

6/60

1.00

50

9.55 E-02

1.02

49

9.00 E-02

1.04

48

8.70 E-02

1.06

47

8.30 E-02

0.083

20/240

6/72

1.08

46

8.00 E-02

0.08

20/250

6/75

1.10

45

7.50 E-02

1.12

44

7.20 E-02

1.14

43

7.00 E-02

1.16

42

6.60 E-02

0.065

20/300

6/90

1.18

41

6.30 E-02

0.063

20/320

6/95

1.20

40

6.00 E-02

0.06

20/330

6/100

1.22

39

5.75 E-02

1.24

38

5.50 E-02

1.26

37

5.25 E-02

1.28

36

5.00 E-02

0.05

20/400

6/120

1.30

35

4.80 E-02

1.32

34

4.60 E-02

1.34

33

4.40 E-02

1.36

32

4.20 E-02

1.38

31

4.00 E-02

0.04

20/500

6/150

1.40

30

3.80 E-02

1.42

29

3.60 E-02

1.44

28

3.50 E-02

1.46

27

3.33 E-02

1.48

26

3.20 E-02

0.032

20/630

6/190

1.50

25

3.02 E-02

0.03

20/650

6/200

1.52

24

2.90 E-02

1.54

23

2.75 E-02

1.56

22

2.63 E-02

1.58

21

2.50 E-02

0.025

20/800

6/240

1.60

20

2.40 E-02

1.62

19

2.30 E-02

1.64

18

2.20 E-02

1.66

17

2.10 E-02

1.68

16

2.00 E-02

0.02

20/1000

6/300

1.70

15

1.90 E-02

1.72

14

1.82 E-02

1.74

13

1.74 E-02

1.76

12

1.66 E-02

1.78

11

1.60 E-02

0.016

20/1250

6/380

1.80

10

1.50 E-02

0.015

20/1300

6/400

1.82

9

1.45 E-02

1.84

8

1.38 E-02

1.86

7

1.30 E-02

1.88

6

1.25 E-02

0.0125

20/1600

6/480

1.90

5

1.20 E-02

1.92

4

1.15 E-02

1.94

3

1.10 E-02

1.96

2

1.05 E-02

1.98

1

1.00 E-02

0.01

20/2000

6/600

2.00

0

RR.2.5 ETDRS Charts

ETDRS charts feature Sloan letters with proportional spacing, 5 letters on each line, and a logarithmic progression of letter sizes with consistent increments of approximately 25% per line (10 lines equal a factor 10x). The ETDRS protocol specifies letter-by-letter scoring, viewing distance, illumination, use of different charts for right and left eye and other presentation parameters.

The full ETDRS protocol requires a wide chart on a light box, and cannot be implemented on the limited screen of a projector (or similar) chart. The logarithmic progression, however, can be implemented on any device. This progression was first proposed by John Green in 1868 and follows the standard "Preferred Numbers, ISO standard 3 (1973) " series and the rounding preferences.

Use of ETDRS charts allows use of letter-by-letter scoring, which is more accurate than the line-by-line scoring used on traditional charts. Each row in the table is equivalent to 1 letter on an ETDRS chart (50 letters for a factor 10x). These steps are smaller than the just discernible difference; steps this small only become significant in statistical studies where a large number of measurements is averaged.

The smaller steps for letter by letter scoring may be expressed in two ways; either by using suffixes to a familiar (sometimes slightly rounded) set of values or by using calculated values. For clinical use suffixes have the advantage of using only familiar acuity notations and reverting to the nearest clinical notation when the suffix is omitted. Calculated values look less familiar; but are sometimes used in statistical studies. Note that suffixes used in the context of an ETDRS chart have a defined value and affect the DICOM storage value, whereas suffixes used in the context of traditional charts do not.

Table RR-2. Reference Table for Use with ETDRS Charts or Equivalent

DICOM

Notations for Research Use with ETDRS Charts or Equivalent

Scales for statistics and graphical displays

Decimal Visual Acuity

Use with suffixes

Calculated values

Linear Scales

Decimal

US

6 m

Decimal

US

6 m

LogMAR

VAS

2.00 E+00

2.0

20/10

6/3

2.00

20/10

6/3.0

-0.30

115

1.91 E+00

-

-

-

1.91

20/10.5

6/3.2

-0.28

114

1.82 E+00

- -

- -

- -

1.82

20/11

6/3.3

-0.26

113

1.74 E+00

+ +

+ +

+ +

1.74

20/11.5

6/3.5

-0.24

112

1.66 E+00

+

+

+

1.66

20/12

6/3.6

-0.22

111

1.60 E+00

1.6

20/12.5

6/3.8

1.58

20/12.5

6/3.8

-0.20

110

1.50 E+00

-

-

-

1.51

20/13

6/4.0

-0.18

109

1.45 E+00

- -

- -

- -

1.45

20/14

6/4.2

-0.16

108

1.38 E+00

+ +

+ +

+ +

1.38

20/14.5

6/4.4

-0.14

107

1.30 E+00

+

+

+

1.32

20/15

6/4.6

-0.12

106

1.25 E+00

1.25

20/16

6/4.8

1.26

20/16

6/4.8

-0.10

105

1.20 E+00

-

-

-

1.20

20/17

6/5.0

-0.08

104

1.15 E+00

- -

- -

- -

1.15

20/17.5

6/5.2

-0.06

103

1.10 E+00

+ +

+ +

+ +

1.10

20/18

6/5.5

-0.04

102

1.05 E+00

+

+

+

1.05

20/19

6/5.8

-0.02

101

1.00 E+00

1.0

20/20

6/6

1.00

20/20

6/6.0

0

100

9.55 E-01

-

-

-

0.95

20/21

6/6.3

0.02

99

9.00 E-01

- -

- -

- -

0.91

20/22

6/6.6

0.04

98

8.70 E-01

+ +

+ +

+ +

0.87

20/23

6/6.9

0.06

97

8.30 E-01

+

+

+

0.83

20/24

6/7.2

0.08

96

8.00 E-01

0.8

20/25

6/7.5

0.79

20/25

6/7.5

0.10

95

7.50 E-01

-

-

-

0.76

20/26

6/7.9

0.12

94

7.20 E-01

- -

- -

- -

0.72

20/28

6/8.3

0.14

93

7.00 E-01

+ +

+ +

+ +

0.69

20/29

6/8.7

0.16

92

6.60 E-01

+

+

+

0.66

20/30

6/9.1

0.18

91

6.30 E-01

0.63

20/32

6/9.5

0.63

20/32

6/9.5

0.20

90

6.00 E-01

-

-

-

0.60

20/33

6/10.0

0.22

89

5.75 E-01

- -

- -

- -

0.58

20/35

6/10.5

0.24

88

5.50 E-01

+ +

+ +

+ +

0.55

20/36

6/11.0

0.26

87

5.25 E-01

+

+

+

0.52

20/38

6/11.5

0.28

86

5.00 E-01

0.5

20/40

6/12

0.50

20/40

6/12.0

0.30

85

4.80 E-01

-

-

-

0.48

20/42

6/12.5

0.32

84

4.57 E-01

- -

- -

- -

0.46

20/44

6/13.2

0.34

83

4.37 E-01

+ +

+ +

+ +

0.24

20/46

6/13.8

0.36

82

4.17 E-01

+

+

+

0.42

20/48

6/14.5

0.38

81

4.00 E-01

0.4

20/50

6/15

0.40

20/50

6/15.1

0.40

80

3.80 E-01

-

-

-

0.38

20/52

6/15.8

0.42

79

3.60 E-01

- -

- -

- -

0.36

20/55

6/16.6

0.44

78

3.50 E-01

+ +

+ +

+ +

0.35

20/58

6/17.4

0.46

77

3.33 E-01

+

+

+

0.33

20/60

6/18.2

0.48

76

3.20 E-01

0.32

20/63

6/19

0.32

20/63

6/19.1

0.50

75

3.00 E-01

-

-

-

0.30

20/66

6/20.

0.52

74

2.90 E-01

- -

- -

- -

0.29

20/69

6/21

0.54

73

2.75 E-01

+ +

+ +

+ +

0.28

20/72

6/22

0.56

72

2.63 E-01

+

+

+

0.26

20/76

6/23

0.58

71

2.50 E-01

0.25

20/80

6/24

0.25

20/79

6/24

0.60

70

2.40 E-01

-

-

-

0.24

20/83

6/25

0.62

69

2.30 E-01

- -

- -

- -

0.23

20/87

6/26

0.64

68

2.20 E-01

+ +

+ +

+ +

0.22

20/91

6/28

0.66

67

2.10 E-01

+

+

+

0.21

20/95

6/29

0.68

66

2.00 E-01

0.2

20/100

6/30

0.20

20/100

6/30

0.70

65

1.90 E-01

-

-

-

0.191

20/105

6/32

0.72

64

1.82 E-01

- -

- -

- -

0.182

20/110

6/33

0.74

63

1.74 E-01

+ +

+ +

+ +

0.174

20/115

6/35

0.76

62

1.66 E-01

+

+

+

0.166

20/120

6/36

0.78

61

1.60 E-01

0.16

20/125

6/38

0.158

20/126

6/38

0.80

60

1.50 E-01

-

-

-

0.151

20/132

6/40

0.82

59

1.45 E-01

- -

- -

- -

0.145

20/138

6/42

0.84

58

1.38 E-01

+ +

+ +

+ +

0.138

20/145

6/44

0.86

57

1.30 E-01

+

+

+

0.132

20/151

6/46

0.88

56

1.25 E-01

0.125

20/160

6/48

0.126

20/158

6/48

0.90

55

1.20 E-01

-

-

-

0.120

20/166

6/50

0.92

54

1.15 E-01

- -

- -

- -

0.115

20/174

6/52

0.94

53

1.10 E-01

+ +

+ +

+ +

0.110

20/182

6/55

0.96

52

1.05 E-01

+

+

+

0.105

20/191

6/58

0.98

51

1.00 E-01

0.1

20/200

6/60

0.100

20/200

6/60

1.00

50

9.55 E-02

-

-

-

0.095

20/210

6/63

1.02

49

9.00 E-02

- -

- -

- -

0.091

20/220

6/66

1.04

48

8.70 E-02

+ +

+ +

+ +

0.087

20/230

6/69

1.06

47

8.30 E-02

+

+

+

0.083

20/240

6/72

1.08

46

8.00 E-02

0.08

20/250

6/75

0.079

20/250

6/76

1.10

45

7.50 E-02

-

-

-

0.076

20/260

6/79

1.12

44

7.20 E-02

- -

- -

- -

0.072

20/280

6/83

1.14

43

7.00 E-02

+ +

+ +

+ +

0.069

20/290

6/87

1.16

42

6.60 E-02

+

+

+

0.066

20/300

6/91

1.18

41

6.30 E-02

0.063

20/320

6/95

0.063

20/315

6/95

1.20

40

6.00 E-02

-

-

-

0.060

20/330

6/100

1.22

39

5.75 E-02

- -

- -

- -

0.058

20/350

6/105

1.24

38

5.50 E-02

+ +

+ +

+ +

0.055

20/360

6/110

1.26

37

5.25 E-02

+

+

+

0.052

20/380

6/115

1.28

36

5.00 E-02

0.05

20/400

6/120

0.050

20/400

6/120

1.30

35

4.80 E-02

-

-

-

0.048

20/420

6/126

1.32

34

4.60 E-02

- -

- -

- -

0.046

20/440

6/132

1.34

33

4.40 E-02

+ +

+ +

+ +

0.044

20/460

6/138

1.36

32

4.20 E-02

+

+

+

0.042

20/480

6/145

1.38

31

4.00 E-02

0.04

20/500

6/150

0.040

20/500

6/151

1.40

30

3.80 E-02

-

-

-

0.038

20/520

6/158

1.42

29

3.60 E-02

- -

- -

- -

0.036

20/550

6/166

1.44

28

3.50 E-02

+ +

+ +

+ +

0.035

20/575

6/174

1.46

27

3.33 E-02

+

+

+

0.033

20/600

6/182

1.48

26

3.20 E-02

0.032

20/630

6/190

0.032

20/630

6/191

1.50

25

3.02 E-02

-

-

-

0.030

20/660

6/200

1.52

24

2.90 E-02

- -

- -

- -

0.029

20/690

6/210

1.54

23

2.75 E-02

+ +

+ +

+ +

0.028

20/720

6/220

1.56

22

2.63 E-02

+

+

+

0.026

20/760

6/230

1.58

21

2.50 E-02

0.025

20/800

6/240

0.025

20/800

6/240

1.60

20

2.40 E-02

-

-

-

0.024

20/830

6/250

1.62

19

2.30 E-02

- -

- -

- -

0.023

20/870

6/260

1.64

18

2.20 E-02

+ +

+ +

+ +

0.022

20/910

6/280

1.66

17

2.10 E-02

+

+

+

0.021

20/950

6/290

1.68

16

2.00 E-02

0.020

20/1000

6/300

0.0200

20/1000

6/300

1.70

15

1.90 E-02

-

-

-

0.0191

20/1050

6/315

1.72

14

1.82 E-02

- -

- -

- -

0.0182

20/1100

6/330

1.74

13

1.74 E-02

+ +

+ +

+ +

0.0174

20/1150

6/350

1.76

12

1.66 E-02

+

+

+

0.0166

20/1200

6/363

1.78

11

1.60 E-02

0.016

20/1250

6/380

0.0158

20/1250

6/380

1.80

10

1.50 E-02

-

-

-

0.0151

20/1300

6/400

1.82

9

1.45 E-02

- -

- -

- -

0.0145

20/1380

6/420

1.84

8

1.38 E-02

+ +

+ +

+ +

0.0138

20/1450

6/440

1.86

7

1.30 E-02

+

+

+

0.0132

20/1500

6/460

1.88

6

1.25 E-02

0.0125

20/1600

6/480

0.0126

20/1600

6/480

1.90

5

1.20 E-02

-

-

-

0.0120

20/1660

6/500

1.92

4

1.15 E-02

- -

- -

- -

0.0115

20/1740

6/520

1.94

3

1.10 E-02

+ +

+ +

+ +

0.0110

20/1820

6/550

1.96

2

1.05 E-02

+

+

+

0.0105

20/1910

6/575

1.98

1

1.00 E-02

0.010

20/2000

6/600

0.0100

20/2000

6/600

2.00

0