The cubic illuminance concept has long been proposed to indicate light modelling in three-dimensional space. An issue relatively less discussed with regard to its measurement is the potential error due to the finite size of the cube centred at the reference point, yielding a parallax effect. In short, the measured cubic illuminance around a finite-sized object will differ from the designed values that are based on the assumption that the object is a point in space. This paper therefore aims to determine the frequency distribution of errors in estimating scalar (Esr) and cylindrical (Ecl) illuminances, vector to scalar illuminance ratio, and cylindrical to horizontal illuminance ratio, due to finite cube size. General uncertainty principle in measurement is employed by introducing random values of cube length and its spatial position. A linear trend is observed between cubic illuminance on the finite cube and the corresponding true values. The Esr and Ecl are approximated more accurately in the case of a point source with a small beam angle. The cube length also influences the accuracy of the results; larger cube length tends to yield less accurate estimations. To achieve maximum error of 20% in estimating Esr and Ecl for a given source–reference point distance, the cube length should not exceed 15% of such a distance.

中文翻译：

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立方照度测量中的视差误差

立方照度概念早已被提出来表示三维空间中的光建模。关于其测量的一个相对较少讨论的问题是由于以参考点为中心的立方体的有限尺寸导致的潜在误差，从而产生视差效应。简而言之，有限尺寸物体周围测得的立方照度将不同于基于物体是空间中一个点的假设的设计值。因此，由于立方体尺寸有限，本文旨在确定估计标量 (Esr) 和柱面 (Ecl) 照度、矢量与标量照度比以及柱面与水平照度比时误差的频率分布。测量中的一般不确定性原理是通过引入立方体长度及其空间位置的随机值来应用的。在有限立方体上的立方照度和相应的真实值之间观察到线性趋势。在具有小光束角的点源的情况下，Esr 和 Ecl 更准确地近似。立方体长度也会影响结果的准确性；较大的立方体长度往往会产生不太准确的估计。为了在给定源-参考点距离的估计 Esr 和 Ecl 中实现 20% 的最大误差，立方体长度不应超过该距离的 15%。