在非球面的检测中，工艺球面补偿检测是最普遍的方法。针对该方法适用范围的局限性，本文提出了应用工艺球面补偿检测时非球面所必须满足的条件。根据波像差理论和瑞利判据，推导出凸二次曲面能够应用工艺球面补偿检测所必须满足的条件，并采用有限距离正面补偿检测的方法，对工艺球面补偿检测的局限性提出了改进。最终结果表明本文所提出的理论能够判定，所需要研制的凸双曲面镜不能直接应用工艺球面补偿检测，而组合补偿检测方法能够保证凸双曲面的面形精度δPV=0.159 8λ 优于λ/6(λ=632.8 nm)，满足技术指标。

In the testing of aspheric surface, the method of spherical compensation testing is always applied widely. Referring to the limitation of this method, the conditions are put forward which the aspheric surface has to meet. According to aberration theory and Rayleigh criterion, we could get the principles of applying the spherical compensation testing method to test convex quadric surface. And according to the compensation tests with the beam incidence at a distance, we can improve the method of spherical compensation testing. After accomplishing the manufacture of convex quadric surface mirror, the finial consequence shows that the theory and practices in this article can determine that spherical compensation testing can not be used to the test of this convex hyperboloidal surface mirror and δPV of the surface is 0.158 9λ which is better than λ/6 (λ=632.8 nm) under the use of combined compensation testing.