Phasor Method to Estimate Illuminances Due to Parallel Arrays of Light Sources

Direct horizontal illuminance along a calculation row due to two parallel arrays of large numbers of identical light sources behaves like a periodic signal with a sinusoidal pattern, which contains useful information for design purpose. This study aims to describe, verify, and discuss the theoretical concept on the superposition of direct horizontal illuminance from both arrays in such configurations, and how to extract the information using the phasor method. Four different approaches are proposed to estimate the total direct horizontal illuminance ET(x) and to verify the concept. Sensitivity analysis is also conducted to observe the influence of each input variable to the resulting ET(x) pattern. The differences between obtained values using the four approaches are found very small, so that the proposed concept is verified. Based on the sensitivity analysis, the luminous intensity distribution of the sources significantly affects the illuminance fluctuation; whereas the impact of lateral position of the calculation row and the spatial phase difference are inconsistent. Overall, the advantage of using phasor method has been demonstrated for this purpose, which is expected to help in understanding the superposition phenomenon of sinusoidal pattern of illuminance, and in achieving the desired spatial contrast.