在光学加工中，反射镜可以很好地补偿待检镜，解决加工中的一些难题。通过三级像差理论求解反射镜补偿检验二次曲面的初始结构参量，令球差系数∑S1=0，补偿镜e21可选择球面或椭球面，推导出补偿镜和待检镜之间关系的表示式。e21=0、0.1、0.2、0.3、0.4，按公式画出e22/α～β，αr02/r01～β的曲线图，从中确定β∝α，e21，e22，r01，r02，d12的对应关系，解出补偿检验的初始结构参量，分析补偿镜放置待检镜曲率中心前α>0，α>1和后α<0、β≥0，β≤0对应待检镜的e22各种求解。分析看出：这包括了补偿检验的全部功能，对凸和凹的二次曲面都可以进行补偿检验，其中有以前提出的解，也有以前没有发现的解，对补偿检验的全面分析是非常有益的。

从三级像差理论出发，分析伽里略（Galilean）和开卜勒（Keplerian）两种类型扩束器的轴外像差没有得到很好校正的原因。通过合理的光路分析，设计出一种轴上和轴外像差都得到很好校正、大口径大相对孔径、视场可增大的、光学性能优于伽里略和开卜勒扩束器的新型扩束器的并给出了物镜通光口径为300mm、物镜焦距为800mm、视场为4mrad、放大倍率为30倍、主工作波长为0.6328μm的非球面扩束器光学系统结构参量，且进行了像质评价。调整此扩束器目镜组中各镜片的间隔以及物镜和目镜的间隔可以使该扩束器在三个波长使用。

Based on the third-order aberration theory, the equation expressing the relationship between the conic constant and unaberration conjugate points is obtained. The corresponding graphs illuminating the relationship between e2 and β are given. According to the equation and graphs, the analyses of convex and concave surfaces are given in detail. We not only consider the unification of all kinds of reflective testing methods, such as Hindle test, concave elliptical mirror test and Ritchey-Common test etc, but also apply the unaberrational conjugate points test to refractive surface. The auto-collimating and interferometer diagnostic methods are powerful for the manufacture of lens. Kinds of convex and concave aspheric lenses have been manufactured with the detecting methods as mentioned above.

In the field of space flight, aviation and astronomy, R-C (Ritchey-Chrétien) camera composed by two hyperboloid mirrors is one of the main instruments for detection and photography. A R-C system has been designed, which is composed of a primary mirror with clear aperture of Φ0=600mm, radius of curvature of 1440mm, conic constant k1 of-1.00486, relative aperture A1 of 1/1.2, lightweight ratio of 53%; and a secondary mirror with clear aperture of 12-92mm, curvature radius of 236.2mm, conic constant k2 of-1.66923. Therefore, the focal length of the R-C optical system is 6000mm, and the relative aperture A is 1/10. Based on classical methods, the new testing methods have been developed. The R-C optical system has been tested by both classical and new test methods, the measurement results have been compared with a perfect agreement. The manufacture precision of the secondary mirror includes the spot diaphragm with a diameter of 0.02mm in size and PV 0.12λ (λ=0.6328µm) of wavelength.. The spot diaphragm's size of the primary mirror is 0.02mm. The spot diaphragm's size of the system is 0.02mm, RMS is 0.18λ and PV is 1.2λ measured by WYKO laser interferometer. Because it is used in infrared wave band, this optical system has already met the designed technical data perfectly. The R-C optical system has been checked and accepted by the user.

Schmidt system is a famous optical system. The corrector equation based on the third-order aberration theory has been acknowledged all along. When the previous equation is confirmed in characteristic of the aspheric surface equation and optical design program ZEMAX, it is found that the equation of the corrector has some errors. Analyses of this problem are given. A new corrector equation is established. The new equation is confirmed seriously by the optical design program ZEMAX again, it can be deduced that the coefficient a=1/2ra2, and the spherical aberration coefficient ∑S1=0. This improvement is very useful for the optical design of Schmidt system, which quickens the optimization and easily reaches the optimal design data.