Propagation of positioning uncertainties in near-field goniophotometers using the Monte Carlo method

Abstract

The method of near-field goniophotometry is used ever-increasingly to acquire detailed luminance information about various luminaires. It overcomes certain limitations of its predecessor, the widely used and thoroughly standardized far-field goniophotometry, and provides further opportunities to expand the scope of the measurement, but also introduces a new set of limiting factors. The aim of this paper is to examine the effect of positioning uncertainties on near-field goniophotometric measurements' results. For this, a simplified ray tracing model is constructed computable in closed form as stacked matrix equations, in order to reduce the computation time as much as possible. The model is then fed to a simulated goniophotometric measurement, loaded with various uncertainties according to the Monte Carlo method. Finally, the resulting uncertainties are derived from statistical analysis of the output in both the near and far fields. Various metrics are tested as potential criteria for acceptance, including correlation and repeated measures ANOVA tests, both faring well until the angle of incidence of the rays is below 55°, the ANOVA test being more sensitive to sampling and rejecting systems with 0.1° angular error and above, while the same results still pass the correlation test until 0.5°. Converted far-field results are compared to the standardized requirements, indicating the necessity of similar mechanical precision.