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

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 (Lb!120 cd/m , C%!97.9, 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. Keywords—Legibility Index, viewing angle, text and graphics, nonperpendicular viewing, solid angle, visual angle, equation. 1. (Corresponding author) Research Associate, Department of Building Services Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong, [email protected] 2. Research Professor, University of Michigan Transportation Research Institute, 2901 Baxter Rd., Ann Arbor, MI 48109, [email protected] L E U K O S V O L 5 N O 4 A P R I L 2 0 0 9 P A G E S 2 7 9 – 2 9 5 ©2009 The Illuminating Engineering Society of North America doi: 10.1582/LEUKOS.2008.05.04.002