Large numerical aperture off-axis reflective telescope design with a freeform mirror based on aperture expansion strategy

Currently, the emission of greenhouse gases is one of humanity’s leading threats. To accurately and efficiently measure greenhouse gas levels in the atmosphere, we must develop imaging spectrometer systems with larger numerical apertures (NAs). However, designing a telescope with a large NA is difficult in this system. This paper presents a design strategy for aperture expansion to create a freeform telescope with a large NA. We compared different off-axis reflective telescopes and chose the Korsch structure, which has obvious advantages because of its wide field of view (FoV), large NA, and low stray light. Moreover, based on the influence of the position of the freeform surface in the aberration correction, we propose to use a single freeform surface to reduce the cost and increase manufacturability. A freeform telescope with an effective focal length of 84 mm, a large NA of 0.25, and a wide FoV of 20° is successfully designed. The modulation transfer function of the system is better than 0.62, the maximum distortion is controlled to be less than 0.486%, and the incident angle of the beam on the image plane is less than 10°. The design result shows that the instrument has wide FoV, large NA, low stray light, and high performance. At the same time, the design strategy in this paper provides an effective method for the telescope design of the imaging spectrometer with a large NA.