A comparison of three approaches for determining scalar illuminance from cubic illuminance data

Abstract

A method for calculating scalar illuminance using cubic illuminance values in a light field has been proposed in the literature. This enables exact measurement of the illuminance vector direction and magnitude by a fixed device, as well as providing a useful basis for calculation. However, the method yields an inexact estimate of the scalar illuminance which in some cases may lead to errors. Two alternative approaches using the concept of mean spherical semi-cubic and cubic illuminances are proposed in this paper, to determine which of these approaches yields the highest accuracy, and to observe the effect of source orientation in various multiple point source configurations. Three types of test are introduced: the first involves two, three, and four identical point sources, separated by a varying angle θ; the second involves four identical point sources arranged symmetrically at varying azimuth angle ψ and incident angle α; the third involves 10,000 combinations of up to six point sources with random luminous intensities and in random positions. Comparisons between the three approaches show that the approach using mean spherical semi-cubic illuminances yields the least amount of error and thus the highest accuracy for scalar illuminance and vector/scalar illuminance ratio in the first and second test. In the third test, this approach also yields the highest accuracy, even though it tends to underestimate the scalar illuminance in scenes with more sources.