In order to obtain the correlated color temperature (CCT) and Duv of light source, the color coordinate (u0, v0) of a point which is on the Plank blackbody radiation locus and nearest from the light source (uc, vc), and the curve slopes of some points, which are nearest from (u0, v0), are used to be obtained by classical methods. These methods are all time consuming because of large computing in the process of searching and comparison step by step. However, the existing curve-fitting methods, which are possess fast calculation speed, also have many problems, such as large calculation error, limited color temperature range, not able to obtain CCT and Duv at the same time etc. Hence, the relationship between the temperature, color coordinate in the CIE 1960 UCS, and the slope of each point on the Plank blackbody radiation locus is first derived in this paper, and a piece-wise cubic Hermite interpolating polynomial v (u) is built. Then, the color coordinate (u0, v0) and the shortest distance, which is known as D (uv), between (u0, v0) and (uc, vc) are obtained. Because this is an absolutely analytic method instead of traditional methods which are based on searching and comparison step by step, so our purpose of rapid calculation can be achieved. Finally, the color temperature T of (u0, v0) is obtained based on the trigonometry approximate method, so the correlated color temperature (CCT) of light source can be obtained. In the color temperature range of 1 000～20 000 K, we calculated the CCT of the "standard chromatic coordinate table for the isothermal lines of blackbody locus" and the "standard color temperature lamp" respectively by the method introduced in this paper, both results were satisfied, at the same time of obtaining the result of CCT and Duv rapidly, the relative error was effectively controlled under 10-4.%为了确定光源的相关色温 (correlated color temperature, CCT) 和色偏差Duv, 传统算法需要通过逐步搜索比较以确定普朗克黑体辐射轨迹上与光源色坐标 (uc, vc) 距离最近点的色坐标 (u0, v0), 以及与点 (u0, v0) 相邻较近的若干点的曲线斜率, 计算量大、耗时长, 而现有的曲线拟合计算方法虽然计算速度较快, 但普遍存在计算误差大、适用色温范围有限、不能同时获得CCT和Duv等问题.本文首先在CIE 1960 UCS色度空间内推导普朗克黑体辐射轨迹上温度、色坐标、曲线斜率三者之间的对应关系, 并在此基础上建立分段三次Hermite插值函数v (u) 来精确描述普朗克黑体辐射轨迹;然后根据点到曲线距离的函数关系快速计算光源 (uc, vc) 到黑体轨迹v (u) 的最近点色坐标 (u0, v0) 以及最短距离Duv, 由于此计算过程完全采用数学公式进行解析推导, 避免了逐步搜索比较, 因此可达到快速计算的目的;最后利用三角形几何近似的方法确定 (u0, v0) 的色温T, 进而得到光源的相关色温.在1 000～20 000 K的色温范围内, 使用本文算法分别计算了"标准黑体轨迹等温线色度坐标表"和标准色温灯的相关色温以及Duv, 均获得了较为理想的计算结果.在实现快速计算相关色温和Duv目的的同时, 相对误差被有效地控制在10-4的范围内.
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