The vibration test is one of many tests that space telescopes endure to ensure that functionality is not impaired by severe launch. Telescopes undergo detailed measurements, including mirror surface accuracy measurements. Due to the design shortcomings, degradation of lightweight mirror surface accuracy may exceed the design error budget at times. In this paper, we demonstrate a method to determine the cause of the degradation. By using inertia relief, the influence functions were obtained, and structural deformation was derived from finite element analysis. Based on the structural deformation, we found that the back frame of the telescope had insufficient torsional and bending stiffness. With the indicated need for higher stiffness, the rigidity of the back frame was improved. In addition, high- and low-temperature cycling was used to reduce residual stresses that cause high-frequency distortion. The new vibration test verified the mechanical safety and optical stability of the improved structure. The surface accuracy measured by an optical interferometer was maintained at 0.015 wave within the design error budget.