HADAR project based on Fresnel lenses, Part I: Optical simulation study of the telescope unit*

Abstract The high altitude detection of astronomical radiation (HADAR) project proposes the use of a refracting telescope composed of four 5.0 m diameter water lenses arranged in a square configuration (100 m × 100 m). This configuration features a wide field of view (FoV, up to 0.84 sr) and low-energy threshold characteristics for observing Cherenkov light generated by high-energy cosmic rays in atmospheric air showers. The Fresnel lens exhibits excellent imaging performance, lightweight characteristics, mature manufacturing processes, strong adaptability in high-altitude low-temperature environments, and facilitates array deployment. The lens has been validated through a series of pilot missions in the Joint Exploratory Missions for an Extreme Universe Space Observatory program, leading to the proposal of a telescope unit design that utilizes the Fresnel lens as an alternative to the water lens. This study simulates and examines the effects of parameters such as the radius of curvature, tooth width, and Fresnel lens thickness on the focal length and image spot ( ). To this end, five Fresnel lenses with the same focal length as the 5.0 m diameter water lens were designed, the best focusing positions under different incident angles were extracted, and the curved image surface was constructed through fitting. The results indicate that the imaging quality of the Fresnel lens depends on the radius of curvature. With increasing focal length, decreases gradually until it remains unchanged. The tooth width and thickness of the lens affect the structural complexity of the lens and have little impact on imaging quality. The curved image surface design can effectively suppress the aberrations and changes in the solid angle caused by increased incidence angles, maintaining an acceptance that is approximately consistent across different incidence angles. To meet the scientific objectives (wide FoV and low-energy threshold) consistent with HADAR and consider the engineering constraints (focal length 10 m), we select a Fresnel lens with a diameter of 2.0 m and a focal length of 5.3 m (FoV angle 29°, total acceptance 9.81 m 2 ·sr) as the basic lens unit for subsequent array performance simulation. This is based on the premise that the total acceptance is not lower than that of the water lens unit (7.43 m 2 ·sr), the on-axis imaging is less than 7.5 cm, and the FoV is as wide as possible.