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.