Optimization of a merit function for the visual perception of color uniformity in spot lights

The objective of the present study is the development of an optimized evaluation method which describes color uniformity in the far field of light-emitting diode (LED) spot lights related to visual perception of color and pattern. The merit function is requested to evaluate measurements and optical simulations of spot light systems. A human factor experiment was performed as a two-alternative forced choice (2AFC) test. During the experiment, a pairs of spot lights with various spatial color distributions were shown successively to the subject. The subjects had to select the more even spot light of the pair shown. The perceived rank order of spot lights was calculated afterwards. It was compared with five different mathematical functions describing several aspects of spatial color uniformity based on the CIELAB color space. These are the widely used color difference  ΔE, gradient, difference of color average, circular symmetry description, and linear smoothness. No single basic function fits the perception in a sufficient way because none of the function considers all visual aspects. For a better correlation between the visual perception and the merit function, a linear combination of four basic functions is proposed. The designed merit function for the color uniformity of spot lights USL is more effective for the prediction of the visual perception. A correlation value of 0.91 is reached. It enables a quantitative evaluation of those LED lighting systems and protects against individual subjective judgments.