针对胶粘固定的透镜会由于透镜、镜框和粘结层的材料热膨胀系数不匹配而在透镜内部产生径向应力，影响系统光学性能的问题，对无热粘结厚度进行研究以最小化甚至消除这种径向应力。首先，对现有的几种基于胡克定律推导的无热粘结厚度方程进行了分析对比，对粘结层提出了一种新的约束，并由此推导了一个无热粘结厚度的简化近似方程，通过修正粘结层轴向约束得到改进的近似方程。然后，采用有限元方法，对几个粘结层高宽比不同的胶粘透镜装配体进行了热应力分析，得出它们的无热粘结厚度仿真解。最后，将仿真解与解析方程计算的数值结果进行对比，指出解析方程的适用范围。对比分析表明：改进的近似方程适用于粘结层高宽比小于1/10的情况；高宽比在1/10~1/3之间时使用高宽比近似方程较好；简化近似方程适用于高宽比大于1/3的情况。结果显示，无热粘结厚度的解析方程在各自的使用范围内具有足够的准确性，能够满足各种工程应用的需要。

As the mismatch of thermal expansion coefficients among the optics, frames and the bond layer can bring a radial stress on the optics and can affect the properties of optical systems, this paper researches how to select the athermal bond thickness to minimize or cancel the radial stress. First, the existing derivations for the athermal bond thickness based on Hooke's Law are compared, then a novel way for constraining the bond is proposed and a simplified approximation formula for the athermal bond thickness is derived. By modifying the axial constrain of the bond layer, a modified approximation formula is also derived. Furthermore, a series of bonded lenes with different bond aspect ratios are built, the simulation value of athermal bond thickness of each assembly is solved by the finite element analysis. Finally, the simulation and analytic solutions of athermal bond thickness are compared, and the application scopes of the analytic equations are pointed out . According to the comparison and analysis, it indicates that the modified approximation formula is applicable to the bond layer with a aspect less than 1/10, the approximation formula is suitable for that with a aspect in 1/10~1/3; and when respect ratio is more than 1/3, the simplified approximation formula is more appropriate. In their application scopes, athermal bond thickness equations have adequate accuracy, and can satisfy the requirement of engineering applications.