在高功率固体激光装置中，大口径光学元件的波前引入的低频相位畸变对激光的焦斑尺寸有很大的影响。光学元件的波前梯度均方根(GRMS)是衡量波前低频相位畸变的重要指标。过去的研究主要通过数值模拟的手段，获得GRMS值与焦斑尺寸的对应关系。通过理论分析，对GRMS值的求法提出了修正，并推导了修正后GRMS值与焦斑尺寸的解析式。

In the high-power solid-state laser facilities, the low-frequency phase distortion introduced by the large-aperture optics has major influence on the size of the laser focal spot. The root-mean-squared gradient (GRMS) is an important specification for measuring the low-frequency phase distortion. In the past, the relationship between the GRMS and the size of focal spot was acquired by numerical simulation. A modification of the definition of the GRMS by theoretical analysis is introduced, and an analytical expression of the relationship between the GRMS and the spot size is deduced.