Li Changjun, Cui Guihua, Melgosa Manuel, Ruan Xiukai, Zhang Yaoju, Ma Long, Xiao Kaida, Luo M Ronnier
Opt Express. 2016 Jun 27;24(13):14066-78. doi: 10.1364/OE.24.014066.
For the correlated color temperature (CCT) of a light source to be estimated, a nonlinear optimization problem must be solved. In all previous methods available to compute CCT, the objective function has only been approximated, and their predictions have achieved limited accuracy. For example, different unacceptable CCT values have been predicted for light sources located on the same isotemperature line. In this paper, we propose to compute CCT using the Newton method, which requires the first and second derivatives of the objective function. Following the current recommendation by the International Commission on Illumination (CIE) for the computation of tristimulus values (summations at 1 nm steps from 360 nm to 830 nm), the objective function and its first and second derivatives are explicitly given and used in our computations. Comprehensive tests demonstrate that the proposed method, together with an initial estimation of CCT using Robertson's method [J. Opt. Soc. Am. 58, 1528-1535 (1968)], gives highly accurate predictions below 0.0012 K for light sources with CCTs ranging from 500 K to 10 K.
为了估计光源的相关色温（CCT），必须解决一个非线性优化问题。在所有先前可用于计算CCT的方法中，目标函数仅得到了近似处理，其预测的准确性有限。例如，对于位于同一条等温线上的光源，已预测出不同的不可接受的CCT值。在本文中，我们建议使用牛顿法来计算CCT，这需要目标函数的一阶和二阶导数。按照国际照明委员会（CIE）目前关于计算三刺激值（从360nm到830nm以1nm步长求和）的建议，目标函数及其一阶和二阶导数在我们的计算中被明确给出并使用。综合测试表明，所提出的方法与使用罗伯逊方法[《美国光学学会杂志》58, 1528 - 1535 (1968)]对CCT进行的初始估计相结合，对于CCT范围从500K到10K的光源，能给出低于0.0012K的高度准确预测。
