EUSO (Extreme Universe Space Observatory) is a next-generation space-based UHECR observation concept to detect extensive air shower events by the fluorescence technique. The determination of the exposure for UHECR observations is essential to reach the scientific objectives. It involves trigger efficiency, observational duty cycle, impacts of clouds etc. UV light from the terrestrial and extraterrestrial sources is a major background for UHECR observations. It includes man-made light, airglow emission starlight, moonlight, zodiacal light etc. In the EUSO pathfinder missions, we carried out the measurements of the UV light by operating a prototype 1~m square refractive Fresnel telescope with a photo-detector module on balloons and on the ground. So far, flights of EUSO-Balloon and EUSO-SPB~(Supper Pressure Balloon) achieved 1- and 12-night flights in Canada and south Pacific, respectively. Using different optics, two satellite-borne pathfinders, TUS~(Tracking Ultraviolet Set-up) has been operational and Mini-EUSO are currently scheduled. On the ground EUSO-TA has been operational at the Telescope Array experiment site. All the pathfinders are designed to measure UV light to provide a larger amount of data in various conditions. In the present contribution, the basic concept to establish a scheme to determine the exposure for space-based UHECRs is discussed. A part of results from EUSO-Balloon about the background light measurements relevant to the exposure determination are presented. We also intrdouce an outlook for further studies by EUSO-SPB, TUS and Mini-EUSO.