Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation

Recently, freeform optics has been widely used due to its unprecedented compactness
and high performance, especially in the reflective designs for broad-wavelength imaging
applications. Here, we present a generalized differentiable ray tracing approach suitable for
most optical surfaces. The established automated freeform design framework simultaneously
calculates multi-surface coefficients with merely the system geometry known, very fast for
generating abundant feasible starting points. In addition, we provide a “double-pass surface”
strategy with desired overlap (not mutually centered) that enables a component reduction for very
compact yet high-performing designs. The effectiveness of the method is firstly demonstrated
by designing a wide field-of-view, fast f-number, four-mirror freeform telescope. Another
example shows a two-freeform, three-mirror, four-reflection design with high compactness and
cost-friendly considerations with a double-pass spherical mirror. The present 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.