Multi-channel LED light sources (MCLLSs) offer numerous advantages over traditional light sources in terms of spectral tunability and dimming control. These advantages have gained wide attention from the lighting community over the past decades. However, controlling the color produced by MCLLSs has always been a challenging problem in the lighting community. Traditionally, it is assumed that the photometric quantities produced by MCLLSs are proportional to the control signal, such as the driving current for analog dimming and the duty cycle for the pulse width modulation (PWM) dimming. However, each single LED channel of practical MCLLSs tends to show nonlinear response and chromaticity variability due to chip material, junction temperature, driving circuit, and control signal modulation. Existing color mixing algorithms based on the linear hypothesis lead to poor mixing accuracy. A high-accuracy color mixing algorithm depends on accurately characterizing the luminous properties of MCLLSs. A three-stage color prediction model is therefore proposed to predict the CIE 1931 tristimulus values of MCLLSs in our study.

The proposed color prediction model is composed of three stages. The first stage characterizes the nonlinear response of individual channels, i.e., the characterization model for channel response property, which can transform the control signal value of an LED channel into one of the CIE 1931 tristimulus values of the channel based on a polynomial fitting method. The polynomial of each channel can be obtained by fitting a training sample dataset. The training sample dataset is constructed by measuring the CIE 1931 tristimulus values and chromaticity coordinates of a ramp control signal sample for each single channel. The second stage predicts the remaining two CIE 1931 tristimulus values of each channel by accounting for chromaticity variability. Chromaticity variability is overcome by searching for the chromaticity coordinates at the nearest control signal sample in the training sample dataset. The last stage is the channel additive model, which predicts the CIE 1931 tristimulus values produced by MCLLSs for a group of input control signal values from the CIE 1931 tristimulus values of each single channel based on Grassmann’s law. The CIE 1931 tristimulus values of each individual channel are calculated in the second stage.

Two multi-channel LED light sources, including a four-channel source and a seven-channel source, are adopted to test the prediction performance of the proposed model. The four-channel source consists of a cool-white LED chip and three narrow-band LED chips, whereas the seven-channel source is composed of a neutral-white channel and six narrow-band channels. The four-channel and seven-channel sources are dimmed by 10-bit PWM and amplitude modulation, respectively. Accordingly, ramp samples including control signal values are obtained in the range of 0 to 1023 with the interval of 64 for balancing measurement workload and model prediction accuracy. A total of 16 control signals for each channel are measured through a Konica Minolta spectroradiometer CS-2000. One hundred control signal points are randomly generated and measured as test samples in the control signal space for the two test sources. Each point contains a group of control signal values corresponding to each single channel. The two test sources show nonlinear channel response and chromaticity nonconstancy. The nonlinear channel response of the two test sources can be well characterized by a three-order polynomial. The relative luminance error (ΔL_v) and CIE 1976 UCS chromaticity difference (Δ_{u′, v′}) between measured and predicted CIE 1931 tristimulus values are employed to evaluate the prediction accuracy of the proposed model. The results show that the proposed model is significantly higher than the widely used linear model in terms of both luminance and chromaticity prediction accuracy for the two test sources. Specifically, the average ΔL_v values for the four-channel and seven-channel test sources are 1.13% and 1.18%, and the average Δ_{u′, v′} values are 0.99×10^-3 and 0.81×10^-3, respectively. In contrast, the average ΔL_v values for the linear model for the four-channel and seven-channel test sources are 107.08% and 9.01%, and the average Δ_{u′, v′} values are 50.07×10^-3 and 8.44×10^-3, respectively. Interestingly, the seven-channel test source has a lower prediction error for the linear model than that of the four-channel source. This can be explained by the fact that the four-channel source shows more obvious nonlinear response properties. The color prediction error of the four-channel source is mainly caused by the third-stage channel additive model. All three stages can contribute to the color prediction accuracy of the seven-channel source. Overall, given the repeatability and stability of the two test sources, the proposed model achieves excellent color prediction accuracy.

Accurately characterizing the luminous properties of MCLLSs is an essential prerequisite for the design of the color mixing algorithm. Factors such as chip material, junction temperature, driving circuit, and control signal modulation can lead to nonlinear channel response and chromaticity nonconstancy of MCLLSs. Based on the evaluation of the luminous properties of MCLLSs, a color prediction model for MCLLSs is proposed. The proposed model can realize channel response characterization, color prediction of a single channel, and channel additive characterization. The prediction performance of the proposed and traditional linear models is examined by two practical MCLLSs with 10-bit PWM and amplitude modulation dimming, respectively. The prediction accuracy of the proposed model is vastly superior to that of the linear model for the two MCLLSs in terms of luminance and chromaticity. The proposed model, applicable to different dimming technologies, effectively characterizes the nonlinear channel response and chromaticity nonconstancy of MCLLSs. In conclusion, the proposed model has outstanding prediction performance and is a strong candidate for designing color-mixing algorithms for MCLLSs.