New definition of legibility index to examine off-axis viewing of text and graphics

Abstract

Reading text and graphics is a common issue in lighting design and practice. Legibility of text and graphics is often measured 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 to the inverse tangent of the visual angle V. This definition assumes the material to be read is perpendicular to the viewer, which is always not true. Off-axis viewing of text and graphics is common in reality, yet rarely researched. To examine off-axis legibility, this paper has developed a new definition of the Legibility Index, defined as the inverse square root of solid angle ω subtended by the target, based on a hypothesis that the three-dimensional solid angle, rather than the two-dimensional visual angle, captures how people recognize text and graphics. This hypothesis has been verified in light of how retinal images activate cones. When viewed, text or graphics form a retinal image that activates the underlying cones in the center fovea of viewer’s eyes. Legibility is then determined by the spatial distribution of these activated cones. For linear targets, their retinal images have only one dimension. Their activated cones are linearly distributed. Thus, visual angle is sufficient to examine the legibility of linear targets. For common nonlinear targets, their retinal images usually have two significant dimensions (width and height) and activate a two-dimensional collection of cones. Solid angle should be used to examine the legibility of these real viewing targets.