基于应变梯度理论,提出了一种玻璃基底光栅铝膜本构关系的表征方法。建立了包含基底参数和铝膜参数的本构关系数学模型，并逐一表征了相关参数。进行了79 g/mm中阶梯光栅铝膜的纳米压痕实验，验证了上述本构关系表征过程的正确性。提出了光栅薄膜材料和基底材料都具有尺度效应的假设，并应用纳米压痕实验对铝膜的尺度效应和基底效应进行了实验表征。对光栅铝膜压痕实验与含基底压深实验的结果进行了比较，结果显示，在有无基底条件下，压痕结果在应力方向上相差0.8倍，在应变方向上相差3倍。进行了光栅刻划实验，结果显示压痕实验对刻划实验具有重要的指导作用。研究过程及研究结果表明: 理论分析和两种实验可有效地分析光栅刻划过程，有助于在实际光栅刻划过程中减小误差，对光栅刻划的工艺过程具有较好的理论指导意义。

Based on strain gradient theory, a characterization method to describe the constitutive relationship of an aluminum grating with the glass substrate is proposed. A mathematical model is established including the constitutive relationship of the glass substrate and the aluminum film parameters and the corresponding parameters are characterized. In order to verify the accuracy of the proposed constitutive relationship, the nano-indentation experiment of the 79 g/mm echelle aluminum grating is carried out. It proposes an assumption that the grating film and substrate materials have the size effect, then performs a nano-indentation experiment to verify the size effect and the substrate effect for the aluminum film. As compared with grating aluminium film experiments, the results on the nano-indentation under the conditions with and without substrates show the differences for 0.8 times in the direction of stress and 3 times in the direction of strain. A grating ruling experiment is also carried out, and the results indicate that the indentation experiment has an important guiding role for the ruling experiment. The research process and results show that theoretical analysis and two kinds of experiments can effectively help to analyze the grating ruling process and reduce the errors of grating ruling. The method provides a good theoretical guidance for the process of the grating ruling.