为了进一步提高平面光栅衍射效率测试仪的测量精度, 分析了影响平面光栅衍射效率测量值的主要因素。根据平面光栅相对衍射效率测量原理, 提出光束截面因子的概念并推导出了平面光栅光束截面因子k(θ)的解析表达式。进一步分析了影响衍射效率测量值的因素(光谱宽度与光束截面因子), 并结合衍射效率测量值定义了两个用于回归分析的自变量。针对作为因变量的理论值与所定义自变量之间存在的非线性关系, 提出了采用二次完全式回归分析的数学方法, 进而建立了提高衍射效率测量精度的修正公式。结果表明: 对平面光栅衍射效率测量值进行修正后, 修正值与理论值之间的误差可控制在±0.5%以内, 提高了衍射效率的测量精度, 改进了衍射效率测试仪的整机性能。

To improve the measurement accuracy of a plane grating diffraction efficiency measuring instrument, the affect factors on the diffraction efficiency measurement of a plane gating were researched. According to the measuring principle of relative diffraction efficiency of the plane grating, the concept of beam cross-section factor k(θ) of plane grating was proposed and the correspondent expression was developed. Then, the factors affecting the measurement accuracy of diffraction efficiency, the spectral width and the beam cross-section factor were analyzed, and two independent variables for the regression were defined by combination with the measurement value of diffraction efficiency. Regarding the nonlinear relation between the theoretical value of dependent variable and the independent variable defined, the complete quadratic regression analysis was applied as the methodology to establish a revised equation to improve the measurement accuracy of the diffraction efficiency. The results show that the variation between the revised and the theoretical values is less than 0.5%, which means the measurement accuracy of diffraction efficiency has been improved and the performance of the instrument is enhanced significantly.