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

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 908. 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 64.48 and 116.88, respectively.