With the development of space optics, optical freeform surfaces have gradually been utilized in reflective optical imaging systems in recent years. Freeform surfaces not only bring many benefits to the optical imaging system, but also present many challenges to their manufacture. Regardless of the machining method used, machining errors during the fabrication of freeform surfaces will exist, which limits the accuracy of freeform surface machining. In this paper, the deviation root mean square (RMS) of a freeform surface from the reference aspheric surface is proposed to evaluate the manufacturability of the freeform surface by using single-point diamond turning. Then the deviation RMS of freeform surfaces is added to the design process of the optical system as a manufacturing constraint. Subsequently, an off-axis three-mirror system and an off-axis two-mirror system with and without manufacturing constraints are designed, respectively. Then the imaging quality of these optical systems and the linear interpolation error RMS of freeform mirror are analyzed. It can be concluded that, on the basis of reaching the imaging quality requirements, the machining difficulty of a freeform mirror can be reduced when adding manufacturing constraints to the design process.& COPY; 2023 Optica Publishing Group