Research note: The accuracy of the mean spherical semi-cubic illuminance approach for determining scalar illuminance

In a previous study comparing alternative approaches for determining scalar illuminance from cubic illuminance data, the approach using mean spherical semi-cubic illuminances (representing the positive and the negative x-, y-, z-axes) was found to have the highest accuracy. However, this approach, referred to as Approach 2, becomes less accurate as more point sources are introduced into the scene. This research note reports the results of calculations of additional scenes with up to 20 point sources so as to evaluate the accuracy limit of the said approach, in comparison with the original approach using vector and symmetric components as proposed by Cuttle (Approach 1). It is concluded that for a very large number of point sources, the mean and standard deviation of the ratio between the calculated and the true scalar illuminance using Approach 2 will converge respectively to 0.86 and 0.015. Approach 2 in general yields more accurate predictions of scalar illuminance only when the number of sources is small. Overall, Approach 1 is to be preferred for its consistency.