ABSTRACT Cylindrical illuminance has long been known as a metric of light modeling in three-dimensional space. Though it is possible to employ a dedicated meter to measure this metric, it is considered more practical to measure cubic illuminance data on the field. However, the cubic illuminance method is an approximation, which may yield errors relative to the true value. This article therefore presents uncertainty analysis of the calculation of cylindrical illuminance at a point due to multiple random point sources, using three different approaches. It is found that the original approach with the sum of individual cylindrical illuminance yields results highly similar to the true values. A similar approach only considering the total cubic illuminance yields uncertainty and is comparable to the alternative approach using averaged vertical illuminance. Applying the last approach with a larger number of axes leads to higher accuracy. To ensure very low uncertainty, in-field cylindrical illuminance measurement should be performed on at least 16 axes on the x–y plane.

中文翻译：

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圆柱照度近似的不确定度分析

摘要 圆柱照度长期以来一直被认为是三维空间中光建模的度量标准。虽然可以使用专用仪表来测量该指标，但在现场测量立方照度数据被认为更实用。但是，三次照度方法是一种近似值，可能会产生相对于真实值的误差。因此，本文使用三种不同的方法，对由于多个随机点源而导致的点柱面照度计算的不确定性进行了分析。发现使用单个柱面照度总和的原始方法产生与真实值高度相似的结果。仅考虑总立方照度的类似方法会产生不确定性，并且与使用平均垂直照度的替代方法相当。使用具有更多轴的最后一种方法会导致更高的精度。为确保非常低的不确定性，应在 x-y 平面上的至少 16 个轴上进行场内柱面照度测量。