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The concept of illumination vector quantities at a given point in three-dimensional space has been proposed since long time ago, but it is mostly described for scenes with point light sources. In real scenes with area light sources, numerical approximations are required to estimate the illumination vector quantities, which can be done by discretising the area into an array of point sources. Two different approaches are proposed in this study; Approach 1 is applicable in the design phase, where the positions of the source and receiver point are exactly known. Approach 2 is applicable during field measurement, based on the obtained cubic illuminances. This study aims to determine the required number of point source elements in the computation and to investigate the difference between both calculation approaches. The proposed concept is demonstrated using a scenario with horizontal, square source and a scenario with vertical, rectangular source, with various luminous intensity distribution patterns, by observing various illumination vector quantities. Grid sensitivity analyses suggest that the largest grid size satisfying the five-to-one approximation rule shall yield quantities that converge within no more than 5% to the final value. For a given size of area source, at a given distance, the differences of illumination vector quantities obtained from both calculation approaches are expected to be approximately the same, regardless the luminous intensity distribution. The estimation of cylindrical illuminance is generally more accurate than that of scalar illuminance.

On Illumination Vector Quantities Due to Area Light Sources: Comparison of Two Calculation Approaches