Fully-nonsymmetric freeform reflective systems generation based on confocal property and nodal aberration theory

Reflective systems directly generated based on confocal theory suffer from significant field-dependent aberrations. Moreover, existing system generation methods and aberration correction methods are limited to plane-symmetric systems. This paper proposes a method for designing fully-nonsymmetric freeform reflective systems based on confocal theory and nodal aberration theory (NAT). This approach allows the quick calculation of the system's surface and structural parameters based on design requirements. The aberrations induced by freeform surface terms overlay in fully-nonsymmetric systems are derived. Additionally, an aberration balancing approach for fully-nonsymmetric reflective systems is proposed, including a correction method for field-linear field-asymmetric (FLFA) astigmatism, a correction method for field-constant aberrations, and a method for adjusting the tilt of image planes. These methods do not impose restrictions on the system's symmetry and focal power distributions. The resulting systems can be considered as starting points for further optimization. The effectiveness and feasibility of the proposed approach were verified through the design of multiple systems with different numbers of surfaces and varying fully-nonsymmetric optical path folding configurations. The methods and theories developed by this study provide an important foundation and reference for the design and aberration theory of generalized freeform optical systems.