Freeform imaging system design with multiple reflection surfaces

We present a generalized differentiable ray-tracing approach suitable for most optical surfaces, including freeform surfaces. The established freeform design method simultaneously calculates multi-surface coefficients with merely the system geometry known. In addition, we provide a ‘double-pass surface’ strategy with the desired overlap (not mutually centered) that enables a component reduction for very compact yet high-performing designs. Two different examples are used to demonstrate the effectiveness of the proposed method. This work provides a robust design scheme for reflective freeform imaging systems in general, and it unlocks a series of new ‘double-pass surface’ designs for very compact, high-performing freeform imaging systems.