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Reflective imaging systems form an important part of photonic devices such asspectrometers, telescopes, augmented and virtual reality headsets orlithography platforms. Reflective optics provide unparalleled spectralperformance and can be used to reduce overall volume and weight. So far, mostreflective designs have focused on two or three reflections, whilefour-reflection freeform designs can deliver a higher light throughput (fasterF-number) as well as a larger field-of-view (FOV). However, advanced opticaldesign strategies for four-reflection freeform systems have been rarelyreported in literature. This is due to the increased complexity in solutionspace but also the fact that additional mirrors hinder a cost-effectiverealization (manufacture, alignment, etc.).  Recently, we have proposed a novel design method to directly calculate thefreeform surface coefficients while merely knowing the mirror positions andtilts. Consequently, this method allows laymen with basic optical designknowledge to calculate 'first time right' freeform imaging systems in a matterof minutes. This contrasts with most common freeform design processes, whichrequires considerable experience, intuition or guesswork. Firstly, wedemonstrate the effectiveness of the proposed method for a four-mirrorhigh-throughput telescope with 250mm-focal-length, F/2.5 and a wide rectangularFOV of 8.5{\deg} x 25.5{\deg}. In a subsequent step, we propose an effectivethree-mirror but four-reflection imaging system, which consists of two freeformmirrors and one double-reflection spherical mirror. Compared with commonthree-mirror and three-reflection imagers, our novel multi-reflection systemshows unprecedented possibilities for an economic implementation whiledrastically reducing the overall volume.

Freeform imaging system design with multiple reflection surfaces