Approach for optimization of the color rendering index of light mixtures

The general CIE color rendering index (CRI) of light is an important index to evaluate the quality of illumination. However, because of the complexity in measurement of the rendering ability under designated constraints, an approach for general mathematical formulation and global optimization of the rendering ability of light emitting diode (LED) light mixtures is difficult to develop. This study is mainly devoted to developing mathematical formulation and a numerical method for the CRI optimization. The method is developed based on the so-called complex method [Computer J.8, 42 (1965); G. V. Reklaitis et al., Engineering Optimization-Methods and Applications (Wiley, 1983)] with modifications. It is first applicable to 3-color light mixtures and then extended to a hierarchical and iterative structure for higher-order light mixtures. The optimization is studied under the constraints of bounded relative intensities of the light mixture, designated correlated color temperature (CCT), and the required approximate white of the light mixture. The problems of inconsistent constraints and solutions are addressed. The CRI is a complicated function of the relative intensities of the compound illuminators of the mixture. The proposed method requires taking no derivatives of the function and is very adequate for the optimization. This is demonstrated by simulation for RGBW LED light mixtures. The results show that global and unique convergence to the optimal within required tolerances for CRI and spatial dispersivity is always achieved.