通过仪器获得的凹面光栅的衍射效率是相对值, 其测量值的精度受测量过程和补偿方法的影响。 为使效率测量值的测量精度得到进一步提高, 有必要对测量值产生影响的主要因素进行深入研究。 该文进一步考察了影响衍射效率测量精度的主要因素, 针对待测凹面光栅根据待测波长的测试要求进行旋转造成光束截面变化而产生的问题, 适当补充原理性方案, 并在此基础上推导出了适用于凹面光栅的光束截面变化因子k(θ)的解析表达式。 基于影响测量精度因素与理论值之间的非线性关系, 提出采用二次非线性回归分析的方法对测量结果进行补偿, 给出了提高衍射效率测量精度的补偿公式。 实验结果表明, 对光栅衍射效率的测量值进行进一步补偿后, 使得补偿值与理论值之间的整体误差范围由±2.5%缩小为±0.3%以内, 与线性回归分析方法相比, 显著缩小了补偿值与理论值之间的差距, 进一步保证了衍射效率的准确测量。 将补偿过程嵌入测量程序, 该方法能够实时补偿测量结果, 满足仪器准确测量的要求。

The present paper aimed at the question that the beam cross-section changes according to the rotation of concave grating during the measuring process, and the appropriate supplement to the principle of the program was done. The appropriate supplement to the principle lay the foundation for the derivation of the beam cross-section k(θ), and the whole analytical expression of changes factor of the beam cross-section k(θ) for concave grating was derived. Because of the relationship between the theoretical values and the factors which affect the diffraction efficiency measuring accuracy was nonlinear, the quadratic nonlinear regression analysis was introduced and the compensating formula was established. The results show further correction to diffraction efficiency measurements for concave grating, the range of differences between the compensated values and the theoretical values was reduced from ±2.5% to less than ±0.3% , compared with the linear regression analysis, and the quadratic nonlinear regression analysis significantly reduces the variation between the compensated values and the theoretical values, which further ensures the accurate measurement of the diffraction efficiency for concave gratings. The compensating process is embedded in the measurement program; this method is strongly real-time, which can satisfy the requirements of simple operation, testing speediness and preciseness.