相关色温是表征光源光谱特性的重要参量,而国际上并无相关色温测量不确定度的解析公式。本文分别采用不确定度传播律法和蒙特卡罗两种方法分析相关色温的测量不确定度。对于不确定度传播律方法,从相关色温的基本定义推导给出相关色温灵敏度系数公式,进而评价相关色温测量不确定度。数值计算的相关色温随光谱功率的变化验证了相关色温灵敏度系数公式的正确性。对于蒙特卡罗方法,采用蒙特卡罗模拟生成一组光谱数据,然后计算相应的相关色温及其分布,从而得到相关色温的测量不确定度。结果表明两种方法得到的相关色温测量不确定度吻合,在不考虑光源光谱的关联时,相关色温不确定度与波长间隔的平方根近似成正比。

The correlated color temperature (CCT) is an important parameter to characterize light sources. However, no analytical expression has been provided by international organizations for evaluating the uncertainty of CCT. The uncertainty propagation law and Monte Carlo method are used to analyze the uncertainty of CCT. When using the uncertainty propagation law method, a CCT sensitivity coefficient formula can be derived based on the definition of CCT to evaluate its uncertainty. The variation in CCT due to the change in spectral power evaluated via numerical calculations is used to validate the formula. When using the Monte Carlo method, a group of spectral data can be generalized using numerical simulations. The corresponding CCT and its distribution are calculated to obtain the uncertainty of CCT. The results obtained using the uncertainty propagation law and Monte Carlo method exhibit a good agreement. When the spectral correlation is neglected, the uncertainty of CCT is observed to be proportional to the square root of the wavelength interval.