Mitigation of even harmonics in the Fourier components of vertical illuminance around a reference point

Abstract

The use of Fourier components analysis has been recently proposed by Lynes to describe harmonics in vertical illuminance at various azimuth angles around a reference point. In cases with multiple light sources, it has been argued that the removal of even harmonics in the resulting Fourier components may correspond with good lighting practice. This paper therefore aims to demonstrate optimisation methods to mitigate even harmonics in Fourier components of vertical illuminance around a reference point due to two and three point light sources, by adjusting maximum vertical illuminance and subtended angles between the sources using sensitivity analysis and genetic algorithms. The results suggest that the genetic algorithm method yields more precise optimum solutions compared with the sensitivity analysis method, particularly for scenes with three point sources. For two point sources, the smallest root mean square value of even harmonics is achieved when the vertical illuminance due to the second source is 0.92 (relative to the vertical illuminance due to the first source) and the subtended angle is 90°. For three point sources, the optimum vertical illuminance due to the second and third sources is respectively 0.81 and 0.78, whereas the optimum subtended angles for the second and third sources with respect to the first are 64.4° and 116.8°, respectively.