Initial design with conic mirrors for four-mirror freeform imaging systems

Freeform surfaces have been widely used in various imaging applications. The selection of the initial structure is particularly critical in the optical design of freeform imaging systems due to the significantly expanded solution space. Here, we introduce a method to identify an initial point for the optical design of four-mirror freeform reflective imaging systems. The initial design method for four-mirror freeform imaging systems leverages the optical property of conical surfaces and the linear-astigmatism-free condition, which is computationally simple, easily accessible and theoretically supported. The initial configurations prioritize the elimination of field-constant aberration and linear astigmatism, providing a robust foundation for subsequent optimization of freeform imaging systems. We generalize the design method for linear-astigmatism-free confocal systems to four-mirror confocal off-axis systems with “double-pass surface”. We present a design example in which the field-constant aberration and the linear astigmatism are eliminated, showcasing the effectiveness of the proposed method. The proposed approach proves capable of delivering a promising starting point for the development of four-mirror freeform off-axis reflective imaging systems.