Design of off-axis reflective system with four mirrors based on freeform surface

Reflective system of four mirrors has a small volume and good image quality, which is used popularly in space detection and airborne filed. Here the formula of reflective system with four mirrors is deducted based on the third-order aberration,secondly the initial configuration of reflective system is calculated with formula, then the data of initial configuration is optimized by optical software ZEMAX. The off-axis reflective system is obtained based on the coaxial reflective system, the freeform surface is also added to extend the view field, finally an off-axis reflective system with large view field is designed and obtained.