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.