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.

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研究笔记：用于确定标量照度的平均球面半立方照度方法的准确性

在之前的一项比较从立方照度数据确定标量照度的替代方法的研究中，发现使用平均球面半立方照度（代表正负 x、y、z 轴）的方法具有最高的准确度。但是，这种方法（称为方法 2）随着更多点源引入场景而变得不那么准确。本研究报告报告了对多达 20 个点源的附加场景的计算结果，以评估所述方法的精度限制，与 Cuttle 提出的使用矢量和对称分量的原始方法（方法 1）进行比较。得出的结论是，对于大量的点源，使用方法 2 计算的和真实的标量照度之间的比率的平均值和标准偏差将分别收敛到 0.86 和 0.015。一般而言，方法 2 仅在光源数量较少时才能更准确地预测标量照度。总体而言，首选方法 1，因为它具有一致性。