Generating selected color using RGB, auxiliary lights, and simplex search

ABSTRACT A mixed light source generates various colors with the potential to adjust the intensities of multiple LEDs, which makes it possible to generate arbitrary colors. Currently, PCs and OSs provide color selection windows that can obtain the red, green, and blue (RGB) or hue, saturation, and lightness (HSL) color coordinates of a user’s selection. Mixed light sources are usually composed of primary-colored LEDs with LEDs in auxiliary colors such as white and yellow used in a few cases. The number of LED inputs and the dimming levels are greater than the number of elements in the color coordinate when using auxiliary-colored LEDs, which causes an under-determined problem. This study proposes a method to determine the dimming levels of LEDs based on a simplex search method (SSM). Commercial LEDs have different optical power values and impure color elements, even if they are RGB. Hence, the characteristics of the LEDs were described using a linear model derived from the tri-stimulus values (an XYZ color coordinate model) and dimming levels. Color mixing models were derived for an arbitrary number of auxiliary-colored LEDs. The under-determined problem was solved using an SSM without an inverse matrix operation. The proposed method can be applied to a machine vision system and an RGBW light mixer for semiconductor inspection. The dimming levels, obtained using the proposed method showed better optical responses than those derived using other methods.