基于非对称三角形仪器函数的最优加权表方法

Optimum Weighting Table Method Based on Asymmetric Triangular Instrumental Function

研究了仪器函数形状稍微偏离对称三角形情形下的三刺激值计算问题,探索了其对应的最优加权表。结果发现,最优权重可以通过求解三个系数矩阵的线性方程组来得到,且系数矩阵是对称正定三对角矩阵。将本课题组前期研究获得的最优加权表方法推广到仪器函数形状为非对称三角形的情形。仿真结果表明,对于10 nm和20 nm测量间隔,最优加权表方法的精度优于三点和五点校正方法;对于5 nm测量间隔,最好的计算方法是先对测量数据进行三点校正,再使用直接选取方法计算三刺激值。

The problem of the calculation of the tristimulus value when the shape of the instrument function is slightly deviated from the symmetrical triangle is studied, and the corresponding optimal weighting table is explored. The results show that the optimal weight can be obtained by solving the linear equations of three coefficient matrices, and the coefficient matrices are symmetric positive definite tridiagonal matrices. The optimal weighting table method obtained in the previous study is extended to the case where the instrument function shape is asymmetric triangle. The simulation results show that the accuracy of the optimal weighting table method is better than that of the three-point and five-point calibration methods for the 10-nm and 20-nm measurement intervals. For the measurement interval of 5 nm, the best calculation method is to conduct three-point correction of the measurement data first, and then use the direct selection method to calculate the tri-stimulus value.