Design and exploration of freeform three-mirror imaging systems with integrated primary and tertiary mirrors using same expression

A typical and widely used configuration of freeform imaging system is freeform off-axis three-mirror systems. However, as the system configuration and surface shape have no rotational symmetry, the assembly process will be very difficult. In this paper, we designed off-axis three-mirror systems in which the primary and tertiary mirrors are integrated into one single element. The two mirrors use different portions of a single mirror, which is represented by one mathematical expression. The design process of the system is demonstrated in detail, and three different kinds of light folding geometry are explored. The system design using different types of freeform surface is also explored and the imaging performance is compared. Finally, tolerance analysis which considers the local and random nature of surface error and actual manufacturing difficulty of the freeform surface is conducted.