Generating Selected Color using RGB, Auxiliary Lights, and Simplex Search

A mixed light source generates various colors, with the potential to adjust intensities of multiple LEDs, which makes it possible to generate arbitrary colors. Currently, PCs and OSs provide color selection windows that can obtain the RGB or HSL color coordinates of a user’s selection. Mixed light sources are usually composed of LEDs in the primary colors, with LEDs in auxiliary colors such as white and yellow used in a few cases. When using auxiliary color LEDs, the number of LED inputs, the dimming levels, is larger than the number of elements in the color coordinate, which causes an under-determined problem. This study proposed how to determine the dimming levels of LEDs based on the selected color. Commercial LEDs have di_erent optical power values and impure color coordinates, 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 the arbitrary number of auxiliary color LEDs. The under-determined problem was solved using a simplex search method 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 were better than derived using other methods