# Freeform Wide Field-of-View Spaceborne Imaging Telescope: From Design to Demonstrator
## 1 Introduction  
Earth observation from space provides an endless source of vital information for weather forecasting, sea monitoring, monitoring of forest fires and deforestation, and agriculture production cycles, to name but a few [1, 2, 3]. In view of climate change, Earth observation is indispensable for monitoring the effects of increasing temperatures [4, 5, 6]. To obtain accurate information with a high spatial resolution and temporal coverage, ongoing research and evaluation tend towards miniaturization and thus the use of cost-effective small satellites that are suitable for use in satellite constellations. Imaging telescopes can be considered one of the key instruments for Earth observation. Reflective imaging telescopes are widely used for space applications, and often favored above refractive designs as the latter often suffer from chromatic aberrations when considering broadband imaging designs. A wide diversity of reflective telescope designs has already been proposed, of which the Three Mirror Long and WALRUS designs have been shown to present the largest field-of-view (FOV), able to reach 90\({}^{\circ}\) full angle, but at the cost of a large lens diameter [7]. Over the last decade, freeform optics has been shown to offer a large potential for space telescopes, enabling a decrease in the mass and volume of the optical systems, while improving the optical performance and image quality [8, 9]. Freeform optical components are generally defined as optical elements whose surfaceslack translational and rotational symmetry. In contrast to spherical and aspheric optical surfaces, which are described by the radius of curvature and a limited number of aspheric coefficients, freeform surfaces are generally described as point clouds or via the use of a combination of polynomial functions, adding a high number of degrees of freedom to the design. Recent advancements in freeform technology, including design methodologies, manufacturing, and metrology capabilities, have enabled this approach to surpass classic reflective designs in terms of FOV and f-number while enabling the minimizing of the number of optical elements. A freeform mirror telescope system was integrated into the tropospheric Monitoring Instrument (TROPOMI), developed in the framework of the ESA Copernicus space mission and launched in 2017 on the Sentinel-5 precursor satellite. The freeform components enabled the telescope to cover a high spectral range (UV to short wave infrared (SWIR) wavelengths), to reach a high resolution of 7 \(\times\) 7 km\({}^{2}\) and a large FOV of 108\({}^{\circ}\) while correcting for geometrical aberrations [10; 11]. In addition, [PERSON] et al. proposed a freeform three-mirror space telescope to attain high-resolution imaging for Earth or planetary science [12], while [PERSON] et al. outlined the use of freeform mirrors in astronomical instruments [13]. We propose an innovative two-mirror pushbroom telescope imaging the Earth with 120\({}^{\circ}\) FOV, featuring a spatial resolution of 2.6 km while fitting in 1 CubeSat Unit and showing a diffraction-limited performance. The telescope can be used as a stand-alone component, but also serve as input for a spectroscopy unit [14]. Pushbroom non-scanning wide FOV instruments, such as the Ozone Monitoring Instrument (OMI), TROPOMI, and the future UVN and UVNS instruments, have inspired the design of our instrument. As in the TROPOMI telescope, we use two freeform mirrors to achieve the extremely wide FOV. However, in comparison with TROPOMI, our goal is to improve the spatial resolution from 7 km to 2.6 km at the nadir, while extending the FOV from 108\({}^{\circ}\) to 120\({}^{\circ}\), almost reaching an Earth observation from limb to limb from an altitude of about 700 km. We envision the use of our instrument in the near-infrared wavelength range (1100-1700 nm). This wavelength range is complementary to TROPOMI [11] and would enable greenhouse gas monitoring when supplementing the telescope with a spectrometer.