Effectiveness of an alternative model for establishing mesopic luminance

Abstract

To determine mesopic luminance for a given photopic luminance and scotopic/photopic (S/P) ratio, the Commission Internationale de l’Eclairage (CIE) recommended system utilizes an equation. Whilst being accurate, it requires several iterations to achieve a stable result and requires the use of an adaptation coefficient. This article proposes an alternative approach, a model developed using a Rational Taylor function which does not require either iteration or an adaptation coefficient. Road lighting tends to use average photopic luminances in the range of 0.1 to 3 cd/m²; within this range, the model has an average error of 0.28% against the iteration approach, which is sufficient for most practical purposes.