In order to realize the long focal length wide-field off-axis three-mirror system in space telescope

the mathematical model of optical freeform mirror was disscussed

the design of new-style freeform off-axis three-mirror system based on freeform mirror was studied. The system required a focal length of 4500 mm

field of view of 11°

the ratio of the tatal length of system and the focal length is 1/3. The design and performance comparison between traditional off-axis three-mirror system and new-style freeform off-axis three-mirror system whose secondary mirror is freeform mirror were complished. In the new-style optical system

the freeform mirror was introduced to the secondary mirror

the variable of optimization was increased

and the balance capacity of optical aberration was enhanced. After the comparison and optimization

the relative aperture of 1/9.5 was chosen

the average of wavefront error of all field of view was better than 0.030λ(λ=632.8nm)

and the average of the MTF of all field of view was greater than 0.434(71.4lp/mm) which reached the diffraction limitation. The MTF was improved more than 5% compared to the traditional TMA system. During the design and optimization

the realizability of the manufacture technology was disscussed

the departure of the secondary freeform mirror and theoretical spherical surface was only 1.1λ

the highly precision testing was complished only by standard sphere and non-null testing method based on digital mask

the problem of large-aperture convex freeform mirror testing was solved

it is helpful for the manufacturing of freeform secondary mirror. The results indicates that the new-style off-axis three-mirror system based on freeform secondary mirror has a series of advantages of smaller cubage

better realizability in engineering

better wavefront error and higher MTF

and it can meet the requirement of space remote sensing optical system.