Uncertainty Analysis of Cylindrical Illuminance Approximation

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.

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