Legibility Index for Examining Common Viewing Situations: A New Definition Using Solid Angle

Abstract

The legibility levels of text and graphics can be assessed using the Legibility Index, conventionally defined as the distance at which material can be read with perfect accuracy (the legibility distance) divided by the character height. The ratio equals the inverse tangent of the visual angle subtended by the character. The definition assumes that the viewing material is perpendicular to the observer, which is not always true. Although text and graphics are, in reality, often viewed not perpendicular to the display, they are rarely studied. To examine the legibility of characters viewed not perpendicular to the display, this paper has redefined the Legibility Index as the inverse square root of the solid angle subtended by the target, based on a hypothesis that the three-dimensional solid angle, rather than the twodimensional visual angle, both subtended by the character, captures how people recognize text and graphics that usually have two significant dimensions (width and height). This hypothesis proves consistent with how retinal images of text and graphics activate cones in the fovea of a viewer's eyes, and has also been verified in a laboratory using legibility data collected from 20 human subjects. Using these data, the calculated steady redefined Legibility Index closely matches the fact that the 20 subjects have similar recognition performance (critical legibility level with 100 percent accuracy) of text (same target) under the same lighting conditions (L b ϭ120 cd/m 2 , C % ϭ97.9, zero ambient light) at different viewing angles (perpendicular or not perpendicular to the displays), while the calculated ratio of legibility distance to character height rapidly decreases with increased viewing angles.

Effects of curved computer displays on visual performance, visual fatigue, and emotional image quality

“…A new legibility equation, given by Equation 3, that quantifies the impact of display angles in the range of 0.0°to 90.0°on the legibility of Sans-Serif 5 × 5 (ie, framed tangentially by a square, 5 units high and 5 units wide) capitalized letters C, D, E, F, H, K, N, P, R, U, V, and Z is commonly used for acuity tests. This equation addresses three issues that are not tackled in previous studies, [31][32][33] including extremely large viewing angles in the range of 82.8°to 90.0°, multiple letters (a single letter E was previously used), and the interference of people's normal reading habit with legibility evaluation. 26 The variables in Equation 3 are as follows: D = viewing distance to the display viewed at any angle, H = normal text height, S w = stroke width, S d = denominator of an observer's Snellen acuity, L b = background luminance, C % = luminance contrast percent, and ξ = incident angle between the display normal and an observer's sightline.…”

“…A new legibility equation, given by Equation , that quantifies the impact of display angles in the range of 0.0° to 90.0° on the legibility of Sans‐Serif 5 × 5 (ie, framed tangentially by a square, 5 units high and 5 units wide) capitalized letters C, D, E, F, H, K, N, P, R, U, V, and Z is commonly used for acuity tests. This equation addresses three issues that are not tackled in previous studies, including extremely large viewing angles in the range of 82.8° to 90.0°, multiple letters (a single letter E was previously used), and the interference of people's normal reading habit with legibility evaluation …”

A practical Legibility Index: From Definition to Measurement Technology

“…One is the conventional D/H ratio commonly used in sign industry, defined as (1), the legibility distance D divided by the character normal height H. This definition does not take width into account and assumes characters are viewed perpendicularly to the observer, which is not always true (Cai & Green, 2009). Otherwise, this definition examines only linear targets without width, such as a vertical line, which is also not practical (Cai & green, 2009). On the other hand, the D/H ratio is independent of viewing angle, which is convenient for field measurement.…”

“…Yet for convenience in practice, it often has a unit expressed as feet/inch (abbr. ft/in) as of viewing distance over character height, which is commonly used in the signage industry (Cai & Green, 2009). In light of all possible Snellen acuity levels of human eyes, range from 5.7 ft/in (for the worst Snellen acuity 20/200 listed in Table 1) to 114.9 ft/in (the best acuity 20/10), with 57.4 ft/in (20/20, the normal acuity of population), 71.8 ft/in (20/16), and 91.2 ft/in (20/12.5) in between.…”

“…Based on an extensive review of almost 100 equations carried out by Cai (2008), nearly all of those equations examine only perpendicular viewing in that the displays are perpendicular to the sightline of a viewer. Oblique viewing, which is common in daily life, such as pedestrians read off-angle signs for wayfinding, has rarely been examined until recently (Cai, 2008;Cai & Green, 2009;Cai, Kim & Green, 2011). In these studies, viewing angle was examined together with all other critical factors, such as background luminance, contrast, size, distance, and Snellen acuity ratio.…”