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<p>The color fidelity index CIE <i>R</i><sub>f</sub> is an important metric for evaluating light quality and has attracted considerable attention in both the lighting industry and the academic community. However, studies have shown that in the calculation process, the reference illuminant correlated color temperature (CCT) derived from the CIE D-series empirical formula does not equal to the CCT of the test light source within the CCT range of 4000–25,000&#xa0;K, the maximum discrepancy reaches 81.62&#xa0;K. To improve the theoretical framework of CIE and related industry standards and to strictly ensure equality between CCTs of the reference illuminant and test light source, this study proposes a nonlinear least-squares optimization method to modify the combination coefficients of CIE D-Series. Furthermore, to investigate the influence of the improved algorithm on the CIE <i>R</i><sub>f</sub> index, 417 illuminants were selected for the evaluation. Among them, 255 were measured using a spectrally tunable LED lighting box, 22 were generated using Planckian radiation formula, and 140 were selected from the dataset of illuminants accumulated by Houser et al. The evaluation results demonstrate that the proposed method ensures the consistency of CCT between the test and reference illuminants while having no impact on the calculation of the color fidelity index. The proposed method not only improves the theoretical framework for computing the CIE <i>R</i><sub>f</sub> but also provides a theoretical reference for the lighting industry and related fields.</p>

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Revisiting the CIE D-series daylight empirical formula for CIE Rf

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Chenxi Yang,
  • Cheng Gao,
  • Changjun Li,
  • Xiaohui Zhang

摘要

The color fidelity index CIE Rf is an important metric for evaluating light quality and has attracted considerable attention in both the lighting industry and the academic community. However, studies have shown that in the calculation process, the reference illuminant correlated color temperature (CCT) derived from the CIE D-series empirical formula does not equal to the CCT of the test light source within the CCT range of 4000–25,000 K, the maximum discrepancy reaches 81.62 K. To improve the theoretical framework of CIE and related industry standards and to strictly ensure equality between CCTs of the reference illuminant and test light source, this study proposes a nonlinear least-squares optimization method to modify the combination coefficients of CIE D-Series. Furthermore, to investigate the influence of the improved algorithm on the CIE Rf index, 417 illuminants were selected for the evaluation. Among them, 255 were measured using a spectrally tunable LED lighting box, 22 were generated using Planckian radiation formula, and 140 were selected from the dataset of illuminants accumulated by Houser et al. The evaluation results demonstrate that the proposed method ensures the consistency of CCT between the test and reference illuminants while having no impact on the calculation of the color fidelity index. The proposed method not only improves the theoretical framework for computing the CIE Rf but also provides a theoretical reference for the lighting industry and related fields.